Chapter 3 of the first-year chemistry course, titled “Gases,” is a fundamental and intriguing exploration of one of the three primary states of matter. This chapter delves into the fascinating world of gases, offering a comprehensive understanding of their properties, behavior, and the underlying principles that govern their interactions. Students in their first year of chemistry study this chapter to grasp the concept of the kinetic molecular theory, which explains how gas particles move and collide, leading to the macroscopic properties we observe.
Additionally, students learn about the gas laws, such as Boyle’s law, Charles’s law, and Avogadro’s law, which provide valuable tools for predicting gas behavior under different conditions. The chapter also introduces the ideal gas law, a critical equation that relates pressure, volume, temperature, and the number of moles in a gas sample. By studying Chapter 3, students gain a solid foundation in the fundamental concepts of gases, setting the stage for a deeper understanding of chemistry’s intricate world.
Short Questions of Chemistry 1st Year Chapter 3 Gases
What are the four states of matter, and which one is considered the simplest form?
The four states of matter are solid, liquid, gas, and plasma. The simplest form of matter is the gaseous state.
Why is the liquid state less common than solids, gases, and plasmas?
The liquid state of a substance can exist only within a relatively narrow range of temperature and pressure.
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What are the general properties of gases according to the kinetic molecular theory?
- Gases don’t have a definite volume and occupy all available space.
- They don’t have a definite shape and take the shape of the container.
- Gases can diffuse and effuse.
- Gases can be compressed.
- Gases can expand on heating or by increasing the available volume.
- Gases exhibit random molecular motion.
- The intermolecular forces in gases are very weak.
What are the properties of liquids?
- Liquids don’t have a definite shape but have a definite volume.
- Molecules of liquids are in constant motion, leading to evaporation and diffusion.
- The densities of liquids are much greater than those of gases but close to those of solids.
- The spaces among the molecules of liquids are negligible.
- The intermolecular attractive forces in liquids are intermediate between gases and solids.
- Liquids possess kinetic energy due to molecular motion.
Describe the properties of solids.
- Particles in solid substances are closely packed and non-compressible.
- Solids have definite shape and volume.
- Solid particles possess only vibrational motion.
- There are strong attractive forces holding solid particles together.
What is the pressure of air that can support a 760 mmHg column at sea level, and what is this pressure called?
The pressure of air that can support a 760 mmHg column at sea level is called one atmosphere.
How is one atmosphere defined in terms of the force exerted by a column of mercury?
One atmosphere is defined as the force exerted by a 760 mm or 76 cm long column of mercury on an area of 1 cm² at 0°C.
What is the SI unit of pressure, and how is it expressed?
The SI unit of pressure is expressed in Nm⁻² (Newtons per square meter).
How many pascals are equivalent to 760 torr, and what is another unit of pressure that is equivalent to it?
760 torr is equivalent to 101325 pascals (Pa), and another unit of pressure equivalent to it is 101.325 kilopascals (kPa).
What is the common unit used in engineering for pressure, and how does it relate to one atmosphere?
The common unit used in engineering for pressure is pounds per square inch (psi), and 1 atm is equal to 14.7 pounds per square inch.
Which unit of pressure is commonly used by meteorologists?
The unit commonly used by meteorologists for pressure is millibar.
What do the gas laws describe, and what are they based on?
The gas laws describe the uniform behavior of gases when external conditions of temperature and pressure are changed. They are based on the relationships between the volume of a given amount of gas and the prevailing conditions of temperature and pressure.
What is Boyle’s law, and under what conditions does it apply?
Boyle’s law states that the volume of a given mass of a gas at constant temperature is inversely proportional to the pressure applied to the gas. It applies when the temperature and the number of moles of gas are constant.
How is Boyle’s law mathematically expressed, and what does ‘k’ represent in the equation?
Boyle’s law is mathematically expressed as PV = k when temperature (T) and the number of moles (n) are constant. ‘k’ represents a constant quantity that depends on the specific gas and its amount.
How is Boyle’s law experimentally verified, and what happens to the volume of a gas as pressure increases at constant temperature?
Boyle’s law is experimentally verified by observing that at constant temperature, the volume of a given quantity of gas is reduced in proportion to the increase in pressure. As pressure increases, the volume of the gas decreases.
What is the initial volume of the gas in the vessel?
The initial volume of the gas is 10 dm3.
What is the initial temperature of the gas in degrees Celsius and Kelvin?
The initial temperature of the gas is 0°C, which is equivalent to 273 K.
What is the formula used to calculate the final volume of the gas after expansion?
The formula used is Boyle’s law: P1V1 = P2V2 (when T and n are constant).
What type of graph is obtained when pressure is plotted against volume at constant temperature?
A curve called an isotherm is obtained.
How does the isotherm change when the temperature of the gas is increased?
When the temperature is increased, the isotherm moves away from both the axes.
What type of graph is obtained when 1/V is plotted against pressure at constant temperature?
A straight line is obtained.
What does a straight line on the graph of pressure against the product PV indicate?
It indicates that ‘k’ is a constant quantity.
Is Boyle’s law applicable to non-ideal gases?
Boyle’s law is applicable only to ideal gases.
Who formulated Charles’s law, and what does it describe?
Charles’s law was formulated by French scientist J. Charles in 1787, and it describes the quantitative relationship between the temperature and volume of a gas when the pressure is kept constant.
What is the mathematical expression for Charles’s law?
The mathematical expression for Charles’s law is V ∝ T (when pressure and number of moles are constant), which can be written as V = kT.
What does the ratio of volume to temperature represent in Charles’s law?
The ratio of volume to temperature remains constant for the same amount of gas at the same pressure.
How is Charles’s law experimentally verified?
Charles’s law is experimentally verified by heating a gas in a cylinder with a movable piston, observing an increase in both volume and temperature, and confirming that V1/T1 = V2/T2.
What is Charles’s law?
Charles’s law states that at constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its original volume at 0°C for every 1°C rise or fall in temperature, respectively.
How is Charles’s law mathematically represented?
Charles’s law can be represented by the equation Vt = Vo(1 + 273t), where Vt is the volume of the gas at temperature T, Vo is the volume of the gas at 0°C, and t is the temperature on the Celsius scale.
What happens to the volume of a gas when it is warmed by 1°C according to Charles’s law?
According to Charles’s law, if a gas is warmed by 1°C, it expands by 1/273 of its original volume at 0°C. For example, if the original volume is 546 cm³, a 1°C rise in temperature results in a 2 cm³ increase in volume.
Does Charles’s law hold true when temperature is measured on the Celsius scale?
No, Charles’s law does not hold true when temperature is measured on the Celsius scale. The volume does not increase in proportion to the increase in temperature on the Celsius scale.
What is the new temperature scale developed to overcome the limitations of Charles’s law on the Celsius scale?
A new temperature scale known as the Kelvin scale was developed, starting from 273°C (precisely -273.16°C), which is referred to as zero Kelvin or absolute zero.
How is Charles’s law obeyed when temperature is measured on the Kelvin scale?
Charles’s law is obeyed when temperature is measured on the Kelvin scale. For instance, at 283 K (10°C), the volume is 566 cm³, and at 373 K (100°C), the volume is 746 cm³, as per Table (3.1).
What is the significance of the temperature -273.16°C in the context of absolute zero?
The temperature of -273.16°C (0 Kelvin) represents the coldest possible temperature. It is the point at which the volume of a gas would theoretically become zero. However, this temperature cannot be achieved for a real gas because a zero volume is impossible for real gases.
What is the zero mark on the Centigrade scale, and what does 100°C represent?
The zero mark is the temperature of ice at one atmospheric pressure. 100°C represents the temperature of boiling water at 1 atmospheric pressure.
How is the Fahrenheit scale defined in terms of the melting point of ice and boiling water?
The Fahrenheit scale has a mark of 32°F for the melting point of ice and 212°F for the boiling point of water at 1 atmospheric pressure.
What is the Kelvin scale, and how is it related to the Celsius scale?
The Kelvin scale starts with the melting point of ice at 1 atmospheric pressure, which is 273K. It’s related to the Celsius scale through the equation K = °C + 273.16.
What is the general gas equation, and what does it represent?
The general gas equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. It represents the relationship between these variables for an ideal gas.
What is the ideal gas constant (R) and how is it calculated?
The value of the ideal gas constant (R) depends on the units used for pressure, volume, and temperature. It can be calculated using various units, such as 0.0821 dm3 atm K-1 mol-1 or 8.3143 Nm K-1 mol-1, depending on the unit system being used.
How is the value of R related to the energy demand of ideal gases?
The value of R indicates the energy demand of one mole of an ideal gas at specific conditions. For example, at 273.16K and 1 atm, if the temperature is increased by 1 K, it will absorb 0.0821 dm3-atm of energy.
What does the value of R tell us about all ideal gases?
The value of R is a universal parameter for all ideal gases, indicating that Avogadro’s number of molecules of any ideal gas has the same energy demand.
How is the value of R different when pressure is expressed in mm of mercury or torr and the volume in cm3?
When pressure is in mm of mercury or torr and volume is in cm3, the value of R is 62.4 dm3 torr K-1 mol-1.
What is the value of R when pressure is given in Nm-2 and volume in m3 using SI units?
When pressure is given in Nm-2 and volume in m3 using SI units, the value of R is 8.3143 Nm K-1 mol-1 or 8.3143 J K-1 mol-1.
How is the density of an ideal gas calculated?
The density of an ideal gas is calculated by using the equation d = PM / RT, where d is the density, P is the pressure, M is the molar mass, R is the gas constant, and T is the temperature in Kelvin.
What does the density of an ideal gas depend on?
The density of an ideal gas is directly proportional to its molar mass. It also depends on pressure and temperature. Higher pressure increases density, while higher temperature decreases density.
How can you calculate the relative molar mass (M) of an ideal gas?
You can calculate the relative molar mass (M) of an ideal gas using the equation d = PM / RT if you know the temperature, pressure, and density of the gas.
How is the density of a gas affected by an increase in temperature?
An increase in temperature leads to a decrease in the density of a gas. This is because higher temperatures cause gas molecules to expand and move farther apart.
How does an increase in pressure affect the density of a gas?
An increase in pressure increases the density of a gas. Higher pressure brings gas molecules closer together, resulting in greater density.
What happens to the density of CH4 gas when the temperature is increased from 0°C to 27°C?
The density of CH4 gas decreases when the temperature is increased from 0°C to 27°C. It goes from 0.7138 g/dm³ to 0.649 g/dm³.
How does doubling the pressure affect the density of CH4 gas at 0°C?
Doubling the pressure of CH4 gas at 0°C increases its density. The density almost doubles when the pressure is doubled.
How do you calculate the mass of 1 dm³ of NH3 gas at 30°C and 1000 mm Hg pressure?
The mass of 1 dm³ of NH3 gas at those conditions is calculated using the equation m = (PVM) / RT, where P is pressure, V is volume, M is molar mass, and T is temperature. In this case, the mass is 0.907 g.
What is Avogadro’s Law?
Avogadro’s Law states that equal volumes of all ideal gases at the same temperature and pressure contain an equal number of molecules.
How can we calculate the volume of one mole of an ideal gas at 273.16K and one atm pressure?
One mole of an ideal gas at 273.16K and one atm pressure has a volume of 22.414 dm3.
What is Avogadro’s number, and how does it relate to the volume of gases at STP?
Avogadro’s number is 6.02 x 10^23, and 22.414 dm3 of various ideal gases at STP contains Avogadro’s number of molecules, which is 6.02 x 10^23.
If we have one dm3 of each of H2, He, N2, O2, and CO in separate vessels at STP, what is the number of molecules in each vessel?
The number of molecules in each vessel will be 2.68 x 10^22.
What does Dalton’s Law of Partial Pressures state?
Dalton’s Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of their individual partial pressures.
How is the partial pressure of a gas defined in a mixture?
The partial pressure of a gas in a mixture is the pressure that it would exert on the walls of the container if it were present alone in the same volume under the same temperature.
If you have three gases, H2, CH4, and O2, in separate containers with partial pressures of 400 torr, 500 torr, and 100 torr, what is the total pressure when they are combined in a single container?
The total pressure when they are combined in a single container is 1000 torr.
Why do non-reacting gases in a mixture behave independently under normal conditions?
Non-reacting gases in a mixture behave independently because the rapidly moving molecules of each gas have equal opportunities to collide with the walls of the container, and each gas exerts a pressure independent of the pressure of other gases.
How does the total pressure of a mixture of gases depend on the number of moles of the gases?
The total pressure of a mixture of gases depends on the total number of moles of the gases, as described by the general gas equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
How can you calculate the partial pressure of a gas in a mixture?
The partial pressure of a gas in a mixture can be calculated using the mole fraction of that gas multiplied by the total pressure of the mixture.
What is the relationship between partial pressure, volume, number of moles, and temperature for a gas?
The relationship is described by the ideal gas equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
How is the mole fraction of a gas in a mixture calculated?
The mole fraction of a gas is calculated by dividing the number of moles of that gas by the total number of moles in the mixture.
What is Dalton’s Law of Partial Pressures?
Dalton’s Law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas in the mixture.
What is aqueous tension, and how is it related to Dalton’s Law?
Aqueous tension is the partial pressure exerted by water vapor in a moist gas. It is subtracted from the total pressure to find the partial pressure of dry gases.
How does Dalton’s Law apply to the process of respiration?
In respiration, the difference in partial pressures of gases, such as oxygen and carbon dioxide, is crucial. Oxygen moves from the air into the lungs due to differences in partial pressure.
Why do pilots feel uncomfortable breathing at higher altitudes?
Pilots feel uncomfortable at higher altitudes because the partial pressure of oxygen in unpressurized cabins is lower than what is required for comfortable breathing.
How do deep-sea divers adjust the partial pressure of oxygen during their dives?
Deep-sea divers adjust the partial pressure of oxygen by mixing it with an inert gas like helium to ensure safe and comfortable breathing at different depths.
What is diffusion, and how is it explained by the kinetic molecular theory of gases?
Diffusion is the spontaneous intermingling of molecules of one gas with another at a given temperature and pressure. It occurs as gas molecules move haphazardly, colliding among themselves and changing directions, leading to their scattering.
Give an example of diffusion in everyday life.
The spreading of the fragrance of a rose or a scent is an example of diffusion.
What is effusion, and how does it differ from diffusion?
Effusion is the movement of gas molecules through an extremely small opening into a region of low pressure. Unlike diffusion, effusion is not due to collisions but rather the tendency of gas molecules to escape one by one through an opening.
Who formulated Graham’s Law of Diffusion, and what does it state?
Thomas Graham formulated Graham’s Law of Diffusion. It states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its density at constant temperature and pressure.
How can Graham’s Law of Diffusion be expressed in terms of molar masses?
Graham’s Law of Diffusion can be expressed as: (Rate of diffusion of Gas 1 x √Molar mass of Gas 2) = (Rate of diffusion of Gas 2 x √Molar mass of Gas 1).
What are the fundamental postulates of the Kinetic Molecular Theory of Gases?
The fundamental postulates of the Kinetic Molecular Theory of Gases are:
- Gases consist of small particles called molecules.
- Gas molecules move randomly, collide, and change directions.
- Pressure results from the collisions of gas molecules with the container walls.
- Gas molecules are widely separated and have no attraction for each other.
- Molecules have negligible volume compared to the gas.
- The effect of gravity on molecular motion is negligible.
- Average kinetic energy of molecules is proportional to temperature.
What is the root mean square velocity (Crms) in the context of the kinetic theory of gases?
The root mean square velocity (Crms) is the square root of the average of the squares of all possible velocities of gas molecules. It is a measure of the average speed of gas molecules in a sample.
What is the relationship between root mean square velocity (Crms), temperature, and molar mass of a gas?
The relationship is given by the equation: Crms = √(3RT / M), where Crms is the root mean square velocity, T is the temperature in Kelvin, R is the gas constant, and M is the molar mass of the gas.
How can the kinetic equation be used to explain gas laws?
The kinetic equation, which relates pressure, volume, number of molecules, and root mean square velocity, can be used to explain various gas laws by showing how changes in these variables affect each other. For example, Boyle’s law, Charles’s law, and Avogadro’s law can all be derived from the kinetic theory of gases.
How does kinetic theory of gases explain Boyle’s Law?
Kinetic theory of gases explains Boyle’s Law by showing that at constant temperature and number of moles, the product PV is a constant quantity.
What law does the equation PV = kT represent?
The equation PV = kT represents Charles’s Law.
How does Avogadro’s Law relate to the number of molecules in a gas?
Avogadro’s Law states that equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.
What is Graham’s Law of Diffusion based on in the kinetic theory of gases?
Graham’s Law of Diffusion is based on the root mean square velocity of gas molecules being proportional to the rate of diffusion of the gas.
What does the kinetic molecular theory of gases state?
The kinetic molecular theory of gases states that gas molecules move randomly, collide among themselves and with the walls of the container, and change their directions. These collisions are elastic, and the pressure of the gas is a result of these collisions with the container walls.
How is pressure related to the kinetic interpretation of gases?
Pressure in gases is the result of molecules colliding with the walls of the container. These collisions are elastic, contributing to the overall pressure of the gas.
What does the kinetic equation of gases PV = mNc represent?
The kinetic equation of gases PV = mNc relates the pressure (P), volume (V), and properties of gas molecules, including their mass (m), number (N), and mean square velocity (2c).
What is the average kinetic energy associated with one molecule of a gas due to its translational motion?
The average kinetic energy (Ek) associated with one molecule of a gas due to its translational motion is given by the equation Ek = (1/2)mv^2, where m is the mass of the molecule, and v is its velocity.
How is temperature defined according to the kinetic interpretation of temperature?
According to the kinetic interpretation of temperature, the Kelvin temperature of a gas is directly proportional to the average translational kinetic energy of its molecules. In other words, a change in temperature represents a change in the intensity of molecular motion.
What is the critical temperature of a substance?
The critical temperature (Tc) of a substance is the highest temperature at which it can exist as a liquid, no matter how much pressure is applied.
How does the critical pressure relate to liquefaction of gases?
The critical pressure (Pc) is the pressure required to bring about liquefaction of a gas at its critical temperature. Liquefaction of gases requires high pressure and low temperature.
What is the significance of critical temperature and pressure in dealing with gases?
Critical temperature and pressure provide information about the conditions under which gases liquefy. Different gases have different critical temperatures and pressures, which determine their liquefaction behavior.
What is meant by critical volume in gases?
Critical volume (Vc) is the volume occupied by 1 mole of a gas at its critical temperature and critical pressure. It is a characteristic volume for each gas at these conditions.
How does the critical temperature of a gas depend on its properties?
The critical temperature of a gas depends on factors such as its size, shape, and the intermolecular forces present in it. Different gases have different critical temperatures.
What is Linde’s method of liquefaction of gases based on?
Linde’s method of liquefaction of gases is based on the Joule-Thomson effect.
How does the Joule-Thomson effect work in liquefying gases?
The Joule-Thomson effect involves allowing a compressed gas to expand into a region of low pressure, which cools the gas. This cooling occurs as the gas molecules move apart, requiring energy to overcome intermolecular attractions, and this energy is taken from the gas itself.
What gases can be liquefied using Linde’s method?
All gases except hydrogen (H2) and helium (He) can be liquefied using Linde’s method.
What is the compressibility factor, and why is it important in the behavior of real gases?
The compressibility factor, denoted as PV/nRT, is important in understanding the behavior of real gases. It indicates the deviation of a gas from ideal behavior. In ideal gases, the compressibility factor is always equal to 1, but real gases deviate from this ideal behavior, and the value of the compressibility factor varies with pressure and temperature.
How do attractive forces among gas molecules affect their behavior?
Attractive forces among gas molecules become significant at high pressure and low temperature, causing deviations from ideal gas behavior. These forces result in the gas molecules not behaving as ideal gases and can lead to the liquefaction of gases.
What is the van der Waals equation for real gases, and what do ‘a’ and ‘b’ represent in this equation?
The van der Waals equation for real gases is (P + a/V^2)(V – b) = RT, where ‘a’ represents the co-efficient of attraction or attraction per unit volume among gas molecules, and ‘b’ represents the excluded volume or incompressible volume per mole of gas.
How are the values of ‘a’ and ‘b’ determined for a specific gas?
The values of ‘a’ and ‘b’ can be determined experimentally by measuring the values of pressure (P), volume (V), and temperature (T) of a gaseous system under two different conditions. By using these values in the van der Waals equation, ‘a’ and ‘b’ for that gas can be calculated.
Why does hydrogen (H2) have a small ‘a’ value in the van der Waals equation?
Hydrogen (H2) has a small ‘a’ value in the van der Waals equation because it is a small-sized and non-polar molecule with weak intermolecular forces.
What is plasma, and why is it often referred to as the “fourth state of matter”?
Plasma is often called the “fourth state of matter” because it is distinct from solids, liquids, and gases. It was identified by William Crookes in 1879 and makes up more than 99 percent of the visible universe.
How is plasma formed?
Plasma is formed when atoms or molecules gain enough heat to become ionized. This means that they lose or gain electrons, creating a mixture of ions, electrons, and neutral atoms.
What are the characteristics of plasma?
A plasma must have a sufficient number of charged particles to collectively respond to electric and magnetic fields. It is macroscopically neutral, meaning that the number of electrons and ions are equal.
Where is plasma found in the universe?
Plasma is found throughout the universe, from the sun to quarks, and it is the most abundant form of matter. On Earth, it occurs in limited places like lightning bolts, flames, auroras, and fluorescent lights.
What are some applications of plasma?
Plasma has numerous technological applications, including fluorescent light bulbs, neon signs, semiconductor processing, sterilization of medical products, lasers, and more. It plays a crucial role in various industries and scientific research.
What are the future horizons for plasma applications?
Scientists are exploring ways to use low-energy plasma that can survive without reacting immediately. Magnetic fields are used to create low-temperature plasma, which can be selective in its reactivity and potentially solve problems like radioactive contamination. Experiments with plasma mixtures for specific applications are ongoing.
Long Questions of Chemistry 1st Year Chapter 3 Gases
Question: What is Boyle’s law of gases? Give its experimental veriication.
Answer: Boyle’s Law, also known as Boyle-Mariotte Law, is a fundamental principle in the field of gas physics that describes the relationship between the pressure and volume of a gas while keeping the temperature and the amount of gas constant. It is usually expressed as:
PV=k
Where P is the pressure of the gas and V is the volume of the gas. k is a constant.
Boyle’s Law states that the product of the pressure and volume of a given amount of gas is constant as long as the temperature and the amount of gas remain unchanged. In other words, if you decrease the volume of a gas, its pressure will increase proportionally, and vice versa, as long as the other factors are constant.
Experimental Verification of Boyle’s Law
Boyle’s Law can be experimentally verified through various setups, and one common method is using a closed-end manometer or a piston-cylinder apparatus. Here’s a basic description of an experiment that verifies Boyle’s Law:
Materials Needed
A gas sample (usually air).
A piston-cylinder apparatus or a closed-end manometer.
Pressure gauge.
Ruler or measuring device.
Stopwatch or timer.
Procedure
Start with a known volume of gas in the piston-cylinder apparatus or manometer. Make sure the gas temperature remains constant throughout the experiment.
Measure the initial volume V1 and the initial pressure P1 of the gas. Slowly decrease the volume of the gas while keeping track of the pressure changes. You can do this by moving the piston or adjusting the volume of the manometer.
Record the final volume V2 and the final pressure P2 of the gas.
Observations
You should observe that as you decrease the volume of the gas, the pressure of the gas increases, and vice versa. These observations confirm the inverse relationship between pressure and volume, as described by Boyle’s Law.
This experimental verification demonstrates that as long as temperature and the amount of gas remain constant, the product of the pressure and volume of a gas is indeed constant, supporting Boyle’s Law.
Question: What are isotherms? What happens to the positions of isotherms when they are plotted at high temperature for a particular gas.
Answer: Isotherms are graphical representations of the relationship between the pressure and volume (or other thermodynamic variables) of a gas at a constant temperature. In other words, isotherms show how the pressure and volume of a gas change while keeping its temperature constant.
When isotherms are plotted at high temperatures for a particular gas, several things happen:
Shift to the Right: Isotherms for a gas at higher temperatures shift to the right. This means that as the temperature increases, the gas occupies a larger volume for the same pressure compared to when it was at a lower temperature. In other words, the gas expands more as it gets hotter while keeping the pressure constant.
Greater Volume Range: The range of volumes covered by the isotherms increases at higher temperatures. This indicates that the gas has a broader range of volumes it can occupy without changing its temperature significantly.
Less Pressure Sensitivity: At higher temperatures, gases become less sensitive to changes in pressure. This is evident from the fact that as you increase the pressure along an isotherm, the change in volume becomes less significant compared to what it would be at lower temperatures.
Ideal Gas Behavior: At very high temperatures, real gases tend to behave more like ideal gases. Ideal gases follow the ideal gas law (PV = nRT) perfectly, and their isotherms are perfectly straight lines. In reality, real gases deviate from ideal behavior at low temperatures and high pressures, but these deviations become less pronounced at higher temperatures.
In summary, when isotherms are plotted at high temperatures for a particular gas, they show that the gas occupies a larger volume for the same pressure, has a broader range of volumes, becomes less sensitive to pressure changes, and tends to behave more like an ideal gas.
Question: Why do we get a straight line when pressures exerted on a gas are plotted against inverse
of volumes? This straight line changes its position in the graph by varying the temperature. Justify it.
Answer: When pressures exerted on a gas are plotted against the inverse of volumes (1/V), we obtain a straight line, which is known as an isothermal or Boyle’s line on a pressure-volume graph. This behavior can be explained by Boyle’s Law, which states that at constant temperature and quantity of gas, the product of pressure (P) and volume (V) is constant (PV=k).
Now, let’s justify why this straight line changes its position on the graph as the temperature varies:
Boyle’s Law: Boyle’s Law, which is expressed as PV=k, holds true at a constant temperature. This means that for a given amount of gas, the product of pressure and volume remains constant as long as the temperature is constant.
Inverse Relationship: When we rearrange Boyle’s Law to isolate one of the variables, we get
P=k/V. This equation shows that pressure is inversely proportional to volume when temperature and the quantity of gas are held constant. In other words, as volume increases, pressure decreases, and vice versa.
Effect of Temperature: When the temperature of a gas changes, it can cause the position of the Boyle’s line to shift on the graph. This is because temperature affects the kinetic energy of gas molecules, which, in turn, influences their behavior.
Increase in Temperature: When the temperature of the gas increases, the gas molecules gain kinetic energy and move more rapidly. This results in more frequent and forceful collisions with the container walls. As a consequence, the gas occupies a larger volume for the same pressure, and the Boyle’s line shifts to the right on the graph.
Decrease in Temperature: Conversely, when the temperature decreases, the gas molecules have lower kinetic energy, move more slowly, and collide with less force. As a result, the gas occupies a smaller volume for the same pressure, and the Boyle’s line shifts to the left on the graph.
In summary, the straight line obtained when plotting pressures against the inverse of volumes is a manifestation of Boyle’s Law, which describes the inverse relationship between pressure and volume at constant temperature and quantity of gas. The position of this line on the graph changes with temperature because temperature affects the kinetic energy of gas molecules and, consequently, their behavior in terms of pressure and volume.
Question: How will you explain that the value of the constant k in the equation PV = k depends upon
(i) the temperature of a gas (ii) the quantity of a gas
Answer: The constant k in the equation PV=k depends on both the temperature of a gas and the quantity of a gas, and here’s an explanation for each:
(i) Dependence on Temperature
The ideal gas law, PV=nRT, relates the pressure (P), volume (V), quantity of gas (n), temperature (T), and the universal gas constant (R). When we consider a fixed quantity of gas (n remains constant), the equation becomes PV=k, where k=nRT is the constant.
Temperature Effect: As temperature increases, the kinetic energy of gas molecules also increases. This means that the gas molecules move faster and collide with each other and the container walls more frequently and with greater force. Consequently, at a higher temperature, a given quantity of gas will occupy a larger volume for the same pressure. This results in a higher value of k because k=nRT.
Lower Temperature: Conversely, at lower temperatures, the gas molecules have less kinetic energy, move more slowly, and collide less frequently and with less force. Therefore, a given quantity of gas will occupy a smaller volume for the same pressure at lower temperatures, leading to a lower value of k.
(ii) Dependence on Quantity of Gas
When considering the effect of the quantity of gas on k, we are essentially changing the number of gas molecules (moles) while keeping temperature and other variables constant. The equation
PV=k becomes PV=nRT when considering the effect of the quantity of gas.
Quantity Effect: If we increase the quantity of gas (n), while keeping temperature and pressure constant, the value of k will increase because k=nRT. This is because there are more gas molecules in the system, leading to a higher value for k.
Lower Quantity: Conversely, if we decrease the quantity of gas, the value of k will decrease because there are fewer gas molecules in the system.
In summary, the value of the constant k in the equation PV=k depends on both the temperature of the gas and the quantity of the gas. Increasing temperature or quantity leads to a higher value of k, while decreasing them leads to a lower value of k. This relationship is consistent with the ideal gas law (PV=nRT), where k is directly proportional to the quantity of gas and temperature.
Question: What is the Charles’s law? Which scale of temperature is used to verify that V/T = k (pressure and number of moles are constant)?
Answer: Charles’s Law, also known as the law of volumes, describes the relationship between the volume (V) and the absolute temperature (T) of a gas, while keeping pressure and the number of moles constant. Charles’s Law states that: V/T=k
Where V is the volume of the gas.T is the absolute temperature of the gas (usually measured in Kelvin). k is a constant.
In simple terms, Charles’s Law asserts that when the pressure and the number of moles of a gas are held constant, the volume of the gas is directly proportional to its absolute temperature.
To verify V/T=k, the absolute temperature scale, specifically the Kelvin (K) scale, is used. The Kelvin scale is directly related to the Celsius scale and is based on the absolute zero point of temperature. In the Kelvin scale, the lowest possible temperature is 0 K, which corresponds to -273.15°C.
Using the Kelvin scale is essential for Charles’s Law because it ensures that temperature is expressed in absolute terms. In other words, temperature values on the Kelvin scale are directly proportional to the kinetic energy of gas molecules. This allows Charles’s Law to hold true as a straight-line relationship, and it simplifies calculations involving temperature and volume.
So, to verify Charles’s Law (V/T=k) with pressure and the number of moles held constant, one should use the Kelvin scale for temperature measurements to ensure that temperature is expressed in absolute terms.
Question: What is the general gas equation? Derive it in various forms.
Answer: The general gas equation, also known as the ideal gas equation or the universal gas equation, relates the pressure (P, in pascals), volume (V, in cubic meters), temperature (T, in kelvin), and quantity of gas (n, in moles) for an ideal gas. The general gas equation is expressed as:
PV=nRT
Where P is the pressure of the gas.V is the volume of the gas. n is the quantity of gas (number of moles). R is the universal gas constant (8.314 J/(mol•K) or 0.0821 L•atm/(mol•K)). T is the absolute temperature in kelvin.
This equation is versatile and can be derived in various forms to solve for different variables. Here are some common forms of the general gas equation derived by rearranging it:
- Rearranged for Pressure (Boyle’s Law):
If you want to isolate pressure, you can rearrange the general gas equation as follows:
P= V/nRT
This form is useful when you know the quantity of gas (n), temperature (T), and volume (V) and want to calculate the pressure (P).
- Rearranged for Volume (Charles’s Law):
If you want to isolate volume, you can rearrange the equation as follows:
V= nRT/P
This form is useful when you know the quantity of gas (n), temperature (T), and pressure (P) and want to calculate the volume (V).
- Rearranged for Quantity of Gas:
If you want to isolate the quantity of gas (n), you can rearrange the equation as follows:
n= PV/RT
This form is useful when you know the pressure (P), volume (V), temperature (T), and want to calculate the quantity of gas (n).
- Rearranged for Temperature:
If you want to isolate temperature, you can rearrange the equation as follows:
T= PV/nR
This form is useful when you know the pressure (P), volume (V), quantity of gas (n), and want to calculate the absolute temperature (T) in kelvin.
These derived forms of the general gas equation are handy for various gas law applications, including Boyle’s Law, Charles’s Law, and calculations involving the ideal behavior of gases under different conditions.
Question: Can we determine the molecular mass of an unknown gas if we know the pressure, temperature and volume along with the mass of that gas.
Answer: Yes, you can determine the molecular mass of an unknown gas if you know the pressure, temperature, volume, and mass of that gas, provided that you assume the gas behaves ideally. To do this, you can use the ideal gas law:
PV=nRT
Where P is the pressure of the gas (in pascals or atmospheres). V is the volume of the gas (in cubic meters or liters). n is the number of moles of gas. R is the universal gas constant (8.314 J/(mol•K) or 0.0821 L•atm/(mol•K)). T is the absolute temperature in kelvin.
First, you need to determine the number of moles (n) of the unknown gas. You can calculate the number of moles using the given mass of the gas (m) and its molecular mass (M):
n= m/M
Now, substitute this expression for n into the ideal gas law:
PV=(m/M )RT
You have values for P, V, T, and m, and you want to solve for M, the molecular mass of the unknown gas. Rearrange the equation to isolate
M= mRT/PV
Now, plug in the known values for pressure (P), volume (V), temperature (T), and mass (m) to calculate the molecular mass (M) of the unknown gas.
It’s important to note that this method assumes that the gas behaves ideally, meaning it follows the ideal gas law under the given conditions. Additionally, this calculation is valid only if the gas is not chemically reacting or undergoing any phase changes (e.g., condensation or evaporation) under the specified conditions. If the gas deviates significantly from ideal behavior or if there are chemical reactions occurring, the calculated molecular mass may not be accurate.
Question: How do you justify from general gas equation that increase in temperature or decrease of pressure decreases the density of the gas?
Answer: To justify that an increase in temperature or a decrease in pressure decreases the density of a gas using the general gas equation PV=nRT, we can rearrange the equation to express density and then analyze the relationships between these variables. The density (ρ) of a gas is defined as the mass per unit volume:
ρ= m/V
Where ρ is the density of the gas (in kg/m³ or g/L). m is the mass of the gas (in kilograms or grams). V is the volume of the gas (in cubic meters or liters). Now, let’s manipulate the general gas equation to express the density:
PV=nRT
We know that the number of moles (n) is equal to the mass (m) of the gas divided by its molar mass
n= m/M
Substitute this into the general gas equation:
PV= (m/M) RT
Now, rearrange this equation to isolate ρ (density):
ρ= m/V = P/RT
From this equation, we can see the relationships between density (ρ), pressure (P), temperature (T), and the gas constant (R):
Temperature (T): As temperature increases while pressure is constant, the density (ρ) decreases. This is because the numerator (P) remains constant, but the denominator (RT) increases with higher temperature. This means that for the same mass of gas (m) in a given volume (V), the density decreases as the temperature rises.
Pressure (P): As pressure decreases while temperature is constant, the density (ρ) also decreases. This is because the numerator (P) decreases, while the denominator (RT) remains constant. As a result, for the same mass of gas (m) in a given volume (V), the density decreases as the pressure decreases.
Question: Why do we feel comfortable in expressing the densities of gases in the units of g dm-3 rather than g cm-3, a unit which is used to express the densities of liquids and solids.
Answer: Expressing the densities of gases in units of grams per decimeter cubed (g dm⁻³) rather than grams per centimeter cubed (g cm⁻³) is a matter of practicality and convenience based on the characteristics of gases and the typical scales of gas volumes encountered in everyday situations. Here’s why g dm⁻³ is a more convenient unit for gas densities:
Gas Volumes Are Often Larger: Gases occupy much larger volumes compared to solids and liquids under standard conditions. For example, one mole of a gas at standard temperature and pressure (STP) occupies approximately 22.4 liters (or 22,400 cm³). Using g cm⁻³ for gas densities would result in very small numbers, making calculations and comparisons cumbersome.
Conversion Simplicity: Using g dm⁻³ makes it easier to convert between units, as 1 dm³ is equivalent to 1,000 cm³. So, when you convert a density value from g dm⁻³ to g cm⁻³, you simply multiply by 1,000. This conversion factor simplifies calculations.
Consistency in Scientific Reporting: In scientific research and reporting, it’s common to use consistent units. Expressing gas densities in g dm⁻³ aligns with the SI (International System of Units) convention, which prefers the use of the decimeter as a standard unit for volume. This consistency simplifies data exchange and communication among scientists.
Avoidance of Small Decimal Fractions: Gases often have densities less than 1 g cm⁻³, resulting in decimal fractions when using g cm⁻³. These fractions can be cumbersome and less intuitive to work with compared to whole numbers or values close to 1 when using g dm⁻³.
Historical Convention: The use of g dm⁻³ for gases is a historical convention that has been established over time. It simplifies laboratory work and data analysis for gases.
In summary, while both g dm⁻³ and g cm⁻³ are valid units for expressing density, g dm⁻³ is more practical and convenient for gases due to the large volumes they occupy, the ease of conversion, consistency with SI units, avoidance of small decimal fractions, and historical convention. On the other hand, g cm⁻³ is more commonly used for solids and liquids because they typically have much higher densities than gases and occupy smaller volumes.
Question: Dalton’s law of partial pressures is only obeyed by those gases which don’t have attractiveforces among their molecules. Explain it.
Answer:
Dalton’s law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of each individual gas in the mixture. Mathematically, it can be expressed as:
P total =P1 +P2 +P3 +…
Where P total is the total pressure of the gas mixture.
P1,P2,P3 ,… are the partial pressures of each individual gas in the mixture.
This law is based on the assumption that gas molecules do not exert attractive forces on each other. In other words, it assumes that the gases behave ideally. An ideal gas is a hypothetical gas in which the molecules occupy negligible volume and do not interact with each other.
Now, let’s explain why Dalton’s law of partial pressures is primarily obeyed by gases that don’t have attractive forces among their molecules:
Ideal Gases Have Negligible Attractive Forces: In the ideal gas model, gas molecules are considered to have no attractive forces between them. They are assumed to move independently and do not attract or repel each other. This assumption simplifies the calculations and predictions of gas behavior.
Partial Pressures Reflect Non-Interaction: When gases with negligible attractive forces are mixed, the partial pressures they exert are additive. Each gas exerts its pressure as if it were the only gas present because there are no interactions or deviations from this behavior.
Real Gases Deviate from Ideality: Real gases, in contrast to ideal gases, do have attractive forces among their molecules. These attractive forces become significant at high pressures and low temperatures. As a result, real gases may deviate from the predictions of Dalton’s law at extreme conditions.
Low Pressure and High Temperature Favor Ideality: At low pressures and high temperatures, gas molecules are far apart, and their kinetic energy dominates any intermolecular forces. This conditions gases to behave more ideally.
In summary, Dalton’s law of partial pressures is primarily obeyed by gases that do not have attractive forces among their molecules because the law is based on the ideal gas model, which assumes non-interacting gas molecules. While real gases do exhibit deviations from this behavior under certain conditions, the ideal gas model remains a useful approximation for many practical applications, especially at moderate temperatures and pressures.
Question: Derive an equation to find out the partial pressure of a gas knowing the individual moles
of component gases and the total pressure of the mixture.
Answer: To derive an equation for finding the partial pressure of a gas within a mixture, you can use Dalton’s law of partial pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas in the mixture.
Let’s consider a mixture of gases containing n different components (gases) labeled as Gas 1, Gas 2, …, Gas n. The total pressure of the mixture is denoted as P total , and the partial pressures of each gas component are denoted as P1,P2,P3,Pn.
According to Dalton’s law: P total =P1 +P2 +P3 +…Pn
Now, to find the partial pressure (Pi) of a specific gas component i, you can rearrange this equation as follows:
Pi= P total – (P1+P2 +…+Pi−1 +Pi+1 +…+Pn)
This equation allows you to calculate the partial pressure of any specific gas component within the mixture. To use this equation, you need to know the total pressure of the mixture (P total) and the partial pressures of all the other gas components (P1,P2,…,Pi−1 ,Pi,1 ,…,Pn)
In summary, the equation to find the partial pressure (Pi) of a specific gas component within a gas mixture is:
Pi= P total – (P1+P2 +…+Pi−1 +Pi+1 +…+Pn)
This equation is derived from Dalton’s law of partial pressures and allows you to determine the partial pressure of a specific gas in a mixture when you know the total pressure and the partial pressures of all other gas components in the mixture.
Question: Explain that the process of respiration obeys the Dalton’s law of partial pressures.
Answer: The process of respiration in living organisms, including humans, indeed obeys Dalton’s law of partial pressures. This law states that in a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of each individual gas in the mixture. In the context of respiration, this law can be explained as follows:
Inhalation and Gas Mixture: During inhalation (the process of breathing in), a person inhales a mixture of gases from the surrounding environment. This mixture primarily consists of oxygen (O2), which is essential for respiration), nitrogen (N2), carbon dioxide (CO2), and traces of other gases.
Partial Pressures in the Air: According to Dalton’s law, each gas in the atmospheric mixture exerts its own partial pressure. The total atmospheric pressure (P total) is the sum of the partial pressures of all the gases present, primarily O2 and N2.
Gas Exchange in the Lungs: When a person inhales, the inhaled air (with its specific partial pressures of gases) is drawn into the lungs. Inside the lungs, gas exchange occurs. Oxygen (O2) from the inhaled air diffuses from the alveoli (tiny air sacs in the lungs) into the bloodstream, where it binds to hemoglobin and is transported to body tissues for cellular respiration.
Exchange of Gases in Body Tissues: In body tissues, oxygen is delivered to cells, and cellular respiration occurs. Meanwhile, carbon dioxide (CO2), which is produced as a metabolic waste product, diffuses from the cells into the bloodstream.
Exhalation: During exhalation (the process of breathing out), the air that is expelled from the lungs contains the accumulated CO2 and traces of other gases produced by cellular respiration. This exhaled air has a different composition and different partial pressures compared to the inhaled air.
Dalton’s Law in Action: Dalton’s law applies to this situation by considering the partial pressures of the gases involved. The partial pressure of O2 in the inhaled air is responsible for oxygen diffusion into the bloodstream, while the partial pressure of
CO2 in the exhaled air reflects the waste gas produced by cells.
In summary, the process of respiration, from inhalation to exhalation, is consistent with Dalton’s law of partial pressures. The law helps explain how the exchange of gases, primarily oxygen and carbon dioxide, occurs between the respiratory system and the bloodstream, and ultimately to and from body tissues. Each gas in the mixture exerts its own partial pressure, facilitating the movement of gases necessary for respiration to take place.
Question: How do you differentiate between diffusion and effusion? Explain Graham’s law of diffusion.
Answer: Diffusion and effusion are both processes related to the movement of gases, but they occur under slightly different conditions and involve distinct mechanisms. Here’s how they differ:
Diffusion
Definition: Diffusion is the process by which molecules or particles in a gas or liquid move from an area of higher concentration to an area of lower concentration. It is a result of random molecular motion and occurs in all directions.
Conditions: Diffusion occurs in gases, liquids, and even solids. It takes place when there is a concentration gradient, meaning that there is a difference in the concentration of particles between two regions.
Examples: The spreading of perfume scent in a room, the mixing of two gases when they come into contact, and the movement of ions in a solution are all examples of diffusion.
Effusion
Definition: Effusion is a specific type of diffusion that occurs when gas molecules escape through a tiny opening or small hole into a vacuum or a region of lower pressure. It involves the movement of gas molecules from a container with higher pressure to one with lower pressure.
Conditions: Effusion typically occurs in gases, and it requires a confined space from which the gas can escape into a less crowded or lower-pressure environment.
Examples: A common example of effusion is the escape of gas molecules through a small hole in a balloon or a small opening in a container. The rate at which a gas effuses depends on various factors, including the size of the opening and the molar mass of the gas.
Graham’s Law of Diffusion
Graham’s law relates the rates of effusion or diffusion of two different gases under the same conditions. The law is named after Thomas Graham, who formulated it in the 19th century. Graham’s law is mathematically expressed as follows:
(Rate of Effusion or Diffusion of Gas 1/Rate of Effusion or Diffusion of Gas 2)=(Molar Mass of Gas 2/Molar Mass of Gas 1)^1/2
Where the rate of effusion or diffusion is typically measured as the volume of gas passing through a small opening per unit of time. The molar mass of each gas is represented in the equation.
Key points about Graham’s law
Lighter gases effuse or diffuse more quickly than heavier gases, assuming all other conditions are equal.
The law helps us compare the rates of effusion or diffusion of two gases based on their molar masses.
It’s important to note that Graham’s law is applicable only when the gases are at the same temperature and pressure.
In summary, diffusion is the movement of molecules from areas of high concentration to low concentration in a gas, liquid, or solid, while effusion specifically refers to the escape of gas molecules through a small opening. Graham’s law provides a quantitative relationship between the rates of effusion or diffusion of two gases based on their molar masses.
Question: Derive van der Waal’s equation for real gases.
Answer: The van der Waals equation is an equation of state that describes the behavior of real gases, taking into account the finite size of gas molecules (volume exclusion) and the attractive forces between them. It was developed by Johannes Diderik van der Waals in the late 19th century.
The van der Waals equation is given by:
(P+a(n^2/V^2) V−nb)=nRT
Where
P is the pressure of the gas.
V is the volume of the gas.
n is the number of moles of the gas.
T is the absolute temperature.
R is the universal gas constant.
a and b are van der Waals constants specific to the gas.
Now, let’s derive the van der Waals equation step by step:
Volume Exclusion (Correction for Molecular Volume)
In a real gas, molecules occupy space, and this reduces the available volume for the gas particles to move around. We account for this by subtracting the volume occupied by the gas molecules from the total volume:
V real =V−nb
Where:
V real is the effective volume available to gas molecules.
n is the number of moles of gas.
b is a constant representing the volume excluded by one mole of gas molecules.
Correction for Intermolecular Attractive Forces:
Real gas molecules experience attractive forces due to Van der Waals forces. These forces tend to reduce the pressure exerted by the gas. We account for this by adding a correction term to the pressure:
P real = (nRT/V real) + a(n^2/V^2real)
Where:
P real is the corrected pressure.
a is a constant specific to the gas and represents the strength of the attractive forces between molecules.
Combining Corrections
Now, we can combine the corrections for both volume exclusion and intermolecular forces to obtain the van der Waals equation:
P real = (nRT/V – nb) + a(n^2/(V – nb)^2)
Rearranging the Equation
To get the standard form of the van der Waals equation, multiply both sides by
(P+a(n^2/V^2)(V – nb) = nRT
And there you have it, the van der Waals equation for real gases. This equation takes into account the finite volume of gas molecules (represented by nb) and the attractive forces between them (represented by a). The constants a and b are specific to each gas and can be experimentally determined.
Question: What is the physical significance of van der Waals ‘constants, ’a’ and ’b? Give their units.
Answer: The van der Waals constants, ‘a’ and ‘b,’ are empirical parameters introduced in the van der Waals equation of state to account for the deviations of real gases from ideal behavior. These constants have specific physical significance and units:
‘a’ (Van der Waals constant for attractive forces)
Physical Significance: ‘a’ represents the strength of the intermolecular attractive forces between gas molecules. It quantifies how much the gas molecules attract each other. When ‘a’ is larger, it indicates stronger attractive forces, and the gas is more likely to deviate from ideal behavior.
Units: The units of ‘a’ depend on the units used for pressure, volume, and temperature in the van der Waals equation. Commonly, the units are expressed as (L^2 * atm/mol^2) or (m^6 * Pa/mol^2) in the SI system. These units are necessary to ensure that ‘a’ has the correct dimensions to match the pressure term in the equation.
‘b’ (Van der Waals constant for molecular volume exclusion)
Physical Significance: ‘b’ represents the volume excluded by one mole of gas molecules. It accounts for the finite size of gas molecules, which reduces the available volume for gas particles to move around. Smaller ‘b’ values indicate that the gas molecules occupy less space relative to their actual size.
Units: The units of ‘b’ also depend on the units used for pressure, volume, and the number of moles in the van der Waals equation. In the SI system, common units for ‘b’ are (L/mol) or (m^3/mol).
In summary, ‘a’ represents the strength of attractive forces between gas molecules, and ‘b’ represents the volume excluded by the gas molecules. Both constants are specific to a particular gas and must be determined experimentally. These constants are crucial in the van der Waals equation to describe the behavior of real gases, especially at conditions where deviations from ideal behavior are significant.