Additional Questions - Chapter 6 Gaseous State 11th Chemistry Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Additional Questions Solved
I. Choose the correct answer.
Question 1.
For one mole of a gas, the ideal gas equation is
(a) $\mathrm{PV}=\frac{1}{2} \mathrm{RT}$
(b) $\mathrm{PV}=\mathrm{RT}$
(c) $\mathrm{PV}=\frac{3}{2} \mathrm{RT}$
(d) $\mathrm{PV}=\frac{5}{2} \mathrm{RT}$
Answer:
(b) $\mathrm{PV}=\mathrm{RT}$
Question 2.
The average kinetic energy of the gas molecule is
(a) inversely proportional to its absolute temperature
(b) directly proportional to its absolute temperature
(c) equal to the square of its absolute temperature
(d) All of the above
Answer:
(b) directly proportional to Its absolute temperature
Question 3.
Which of the following is the correct mathematical relation for Charles' law at constant pressure?
(a) $\mathrm{V} \propto \mathrm{T}$
(b) $\mathrm{V} \propto \mathrm{t}$
(c) $\mathrm{V} \propto-\frac{1}{T}$
(d) all of above
Answer:
(a) $\mathrm{V} \propto \mathrm{T}$

Question 4.
At constant temperature, the pressure of the gas is reduced to one-third, the volume
(a) reduce to one-third
(b) increases by three times
(c) remaining the same
(d) cannot be predicted
Answer:
(b) increases by three times
Question 5 .
With rise in temperature, the surface tension of a liquid
(a) decreases
(b) increases
(c) remaining the same
(d) none of the above
Answer:
(a) decreases
Question 6.
Viscosity of a liquid is a measure of
(a) repulsive forces between the liquid molecules
(b) frictional resistance
(c) intermolecular forces between the molecules
(d) none of the above
Answer:
(b) frictional resistance
Question 7.
The cleansing action of soaps and detergents is due to
(a) internal friction
(b) high hydrogen bonding
(c) viscosity
(d) surface tensions
Answer:
(d) surface tensions
Question 8 .
In Vander Waals equation of state for a non-ideal gas the net force of attraction among the molecules is given by
(a) $\frac{\mathrm{an}^2}{\mathrm{~V}^2}$
(b) $\mathrm{P}+\frac{a n^2}{\mathrm{~V}^2}$

(c) $P-\frac{a n^2}{V^2}$
(d) $-\frac{\mathrm{an}^2}{\mathrm{~V}^2}$
Answer:
(a) $\frac{\mathrm{an}^2}{\mathrm{~V}^2}$
Question 9.
The compressibility factor, $z$ for an ideal gas is
(a) zero
(b) less than one
(c) greater than one
(d) equal to one
Answer:
(d) equal to one
Question 10.
Which of the following gases will have the lowest rate of diffusion?
(a) $\mathrm{H}_2$
(b) $\mathrm{N}_2$
(c) $\mathrm{F}_2$
(d) $\mathrm{O}_2$
Answer:
(c) $\mathrm{F}_2$
Question 11.
Which of the following is a mono atomic gas in nature?
(a) Oxygen
(b) Hydrogen
(c) Helium
(d) Ozone
Answer:
(c) Helium
Question 12 .
Which of the following is a diatomic gas in nature?
(a) Oxygen
(b) Ozone
(c) Helium
(d) Radon
Answer:
(a) Oxygen

Question 13.
Which one of the following is not a monoatomic gas?
(a) Neon
(b) Xenon
(c) Argon
(d) Oxygen
Answer:
(d) Oxygen
Question 14 .
Among the following groups which contains monoatomic gases?
(a) Group 17
(b) Group 18
(c) Group 1
(d) Group 15
Answer:
(b) Group 18
Question 15 .
Which of the following is a tri atomic gas at room temperature?
(a) Oxygen
(b) Helium
(c) Ozone
(d) Nitrogen
Answer:
(c) Ozone
Question 16.
Which of the following gas is essential for our survival?
(a) $\mathrm{N}_2$
(b) $\mathrm{H}_2$
(c) $\mathrm{O}_2$
(d) $\mathrm{He}$
Answer:
(c) $\mathrm{O}_2$

Question 17.
Among the following, which is deadly poison?
(a) $\mathrm{CO}_2$
(b) $\mathrm{HCN}$
(c) $\mathrm{HCl}$
(d) $\mathrm{NH}_3$
Answer:
(b) $\mathrm{HCN}$
Question 18 .
Which of the following is not chemically inert?
(a) Helium
(b) Oxygen
(c) Argon
(d) Krypton
Answer:
(b) Oxygen
Question 19.
Match the List-I and List-II using the correct code given below the list.

Answer:
(a) 3142
Question 20.
Pressure of a gas is equal to
(a) $\frac{F}{a}$
(b) $\mathrm{F} \times$
(c) $\frac{a}{F}$
(d) $\mathrm{F}-\mathrm{a}$
Answer:
(a) $\frac{F}{a}$
Question 21.
The SI unit of pressure is
(a) $\mathrm{Nm}^{-2} \mathrm{Kg}^{-1}$
(b) Pascal
(c) bar
(d) atmosphere
Answer:
(b) Pascal
Question 22.
Statement-I: The pressure cooker takes more time for cooking at high altitude.
Statement-II: Air is subjected to Earth's gravitational force. The pressure of air gradually decreases from the surface of the Earth to higher altitude.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(e) Statement-I is wrong but Statement-II is correct
(ð) Statement-I is correct but Statement-II is wrong
Answer:
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I

Question 23.
The instrument used for measuring the atmospheric pressure is
(a) lactometer
(b) barometer
(c) electrometer
(d) ammeter
Answer:
(b) barometer
Question 24 .
The standard atmospheric pressure at sea level at $0^{\circ} \mathrm{C}$ is equal to
(a) $1 \mathrm{~mm} \mathrm{Hg}$
(b) $76 \mathrm{~mm} \mathrm{Hg}$
(c) $760 \mathrm{~mm} \mathrm{Hg}$
(d) $680 \mathrm{~mm} \mathrm{Hg}$
Answer:
(c) $760 \mathrm{~mm} \mathrm{Hg}$
Question 25.
Mathematical expression of Boyle's law is
(a) $P_1 V_1=P_2 V_2$
(b) $\frac{P}{V}=$ Constant
(c) $\frac{V}{T}=$ Constant
(J) $\frac{P}{T}=$ Constant
Answer:
(a) $P_1 V_1=P_2 V_2$
Question 26.
Statement-I: If the volume of a fixed mass of a gas is reduced to half at constant temperature the gas pressure doubles.
Statement-II: If the volume is halved, the density of the gas is doubled.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-II is wrong
(d) Statement-I is wrong but Statement-II is correct
Answer:
(a) Statement-I and liare correct and Statement-II is the correct explanation of Statement-I
Question 27.
Which one of the following represents the Charles' law?
(a) $\mathrm{PV}=$ Constant
(b) $\frac{V}{T}=$ Constant
(c) VT Constant
(d) $\frac{T}{V}=\mathrm{R}$
Answer:
(b) $\frac{V}{T}=$ Constant

Question 28.
Which one of the following is absolute zero?
(a) $293 \mathrm{~K}$
(b) $273 \mathrm{~K}$
(c) $-273.15^{\circ} \mathrm{C}$
(d) $0^{\circ} \mathrm{C}$
Answer:
(c) $-273.15^{\circ} \mathrm{C}$
Question 29.
$\frac{P}{T}=$ Constant is known as
(a) Boyle's law
(b) Charles' law
(c) Gay Lussac's law
(d) Dalton's law
Answer:
(c) Gay Lussac's law
Question 30.
The ideal gas equation is
(a) PV = RT for 1 mole
(b) $\mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2$
(c) $\frac{P}{T}=\mathrm{R}$
(d) $\mathrm{P}=\mathrm{P}_2+\mathrm{P}_2+\mathrm{P}_2$
Answer:
(a) PV = RT for 1 mole
Question 31.
The value of Universal gas constant in a ideal gas equation is equal to
(a) $8.314 \mathrm{KJ}$
(b) $0.082057 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
(c) 1 Pascal
(d) $8.314 \times 10^{-2}$ Pascal
Answer:

(b) $0.082057 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$

Question 32.
Mathematical expression of Graham's law is
(a) $\frac{\mathrm{r}_{\mathrm{A}}}{r_{\mathrm{B}}}=\frac{\mathrm{M}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{A}}}$
(b) $\frac{\mathrm{r}_{\mathrm{A}}}{r_{\mathrm{B}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{A}}}{\mathrm{M}_{\mathrm{B}}}}$
(c) $\frac{\mathrm{r}_{\mathrm{A}}}{r_{\mathrm{B}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{A}}}}$
(d) $\sqrt{\frac{\mathrm{r}_{\mathrm{A}}}{r_{\mathrm{B}}}}=\mathrm{M}_{\mathrm{A}} \cdot \mathrm{M}_{\mathrm{B}}$
Answer:
(c) $\frac{\mathrm{r}_{\mathrm{A}}}{r_{\mathrm{B}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{A}}}}$
Question 33.
Which law is used in the isotopic separation of deuterium and protium?
(a) Boyle's law
(b) Charles' law
(c) Graham's law
(d) Gay Lussac's law
Answer:
(c) Graham's law

Question 34.
The value of compression factor $Z$ is equal to
(a) $\frac{n R T}{P V}$
(b) $\frac{P V}{R T}$
(c) PV $\mathrm{PRRT}$
(d) $\frac{P V}{n R T}$
Answer:
(d) $\frac{P V}{n R T}$
Question 35 .
The value of critical volume is equal in terms of Vander Waals constant is
(a) $3 \mathrm{~b}$
(b) $\frac{8 a}{27 R b}$
(c) $\frac{a}{27 b^2}$
(d) $\frac{2 a}{R b}$
Answer:
(a) $3 \mathrm{~b}$
Question 36.
The value of critical temperature of carbon dioxide is
(a) $273 \mathrm{~K}$
(b) $303.98 \mathrm{~K}$
(c) $373 \mathrm{~K}$
(d) $-80^{\circ} \mathrm{C}$
Answer:
(b) $303.98 \mathrm{~K}$
Question 37.
Match the List-I and List-II using the correct code given below the list.

Answer:
(a) 3142
Question 38.
The value of critical pressure of $\mathrm{CO}_2$ is
(a) $173 \mathrm{~atm}$
(b) $73 \mathrm{~atm}$
(c) $1 \mathrm{~atm}$
(d) $22.4 \mathrm{~atm}$
Answer:
(b) $73 \mathrm{~atm}$
Question 39.
The temperature below which a gas obey Joule Thomson effect is called
(a) critical temperature
(b) standard temperature
(c) inversion temperature
(d) normal temperature
Answer:
(c) Inversion temperature
Question 40.
The substance used in adiabatic process of liquefaction is
(a) liquid helium
(b) gadolinium sulphate
(c) iron sulphate
(d) liquid ammonia
Answer:
(b) Gadolinium sulphate
Question 41.
The temperature produced in adiabatic process of liquefaction is
(a) zero kelvin
(b) $-273 \mathrm{~K}$
(c) $10^{-4} \mathrm{~K}$

(d) $10^4 \mathrm{~K}$
Answer:
(c) $10^{-4} \mathrm{~K}$
Question 42.
The molecules of a gas A travel four times faster than the molecules of gas $\mathrm{B}$ at same temperature. The ratio of molecular weight $\mathrm{M}_{\mathrm{A}} / \mathrm{M}_{\mathrm{B}}$ is
(a) $1 / 16$
(b) 4
(c) $1 / 4$
(d) 16
Answer:
(a) $1 / 16$
Question 43.
The compressibility factor for an ideal gas is
(a) 1.5
(b) 2
(c) 1
(d) $\mathrm{x}$
Answer:
(c) 1
Question 44.
Which of the following pair will diffuse at the same rate?
(a) $\mathrm{CO}_2$ and $\mathrm{N}_2 \mathrm{O}$
(b) $\mathrm{CO}_2$ and $\mathrm{NO}$
(c) $\mathrm{CO}_2$ and $\mathrm{CO}$
(d) $\mathrm{N}_2 \mathrm{O}$ and $\mathrm{NO}$
Answer:
(a) $\mathrm{CO}_2$ and $\mathrm{N}_2 \mathrm{O}$
Question 45.
The value of Vander Waals constant "a" is maximum for
(a) helium
(b) nitrogen
(c) methane
(d) ammonia
Answer:
(d) Ammonia
Question 46.
A person living in Shimla observed that cooking food with using pressure cooker takes more time. The reason for this observation is that at high altitude ............
(a) pressure increases
(b) temperature decreases
(c) pressure decreases

(a) temperature decreases
Answer:
(c) pressure decreases
Question 47.
Statement-I : At constant temperature PV vs $\mathrm{V}$ plot for real gases is not a straight line.
Statement-II : At high pressure, all gases have $Z>1$, but at intermediate pressure most gases have $Z<1$.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-Il is wrong
(d) Statement-I is wrong but Statement-Il is correct .
Answer:
(a) Statement-I and liare correct and Statement-II is the correct explanation of Statement-I
Question 48 .
Statement-I: Gases do not liquefy above their critical temperature, even on applying high press ure.
Statement-II: Above critical temperature, the molecular speed is high and intermolecular attractions cannot hold the molecules together because they escape because of high speed.
(a) Statement-I and II are correct and Statement-II is the correct explanation of Statement-I
(b) Statement-I and II are correct but Statement-II is not the correct explanation of Statement-I
(c) Statement-I is correct but Statement-II is wrong
(d) Statement-I is wrong but Statement-II is correct
Answer:
(c) Statement-I and II are correct and Statement-IIs the correct explanation of Statement-I
Question 49.
The rate of diffusion of a gas is
(a) directly proportional to its density
(b) directly proportional to its molecular mass
(c) directly proportional to its square root of its molecular mass
(d) inversely proportional to its square root of its molecular mass
Answer:
(d) inversely proportional to its square root of its molecular mass
Question 50 .
In a closed flask of 5 liters, $1.0 \mathrm{~g}$ of $\mathrm{H}_2$ is heated from 300 to $600 \mathrm{~K}$, which statement is not correct'?
(a) pressure of the gas increases

(b) the rate of the collusion increase
(c) the number of moles of gas increases
(d) the energy of gaseous molecules increases
Answer:
(c) the number of moles of gas increases
Question 51 .
Match the List-I and List-II using the correct code given below the list.

Answer:
(a) 314
Question 52.
Consider the following statements.
(i) All the gases have higher densities than liquids and solids.
(ii) All gases occupy zero volume at absolute zero.
(iii) At very low pressure all gases exhibit ideal behaviour.
Which of the above statement is/are not correct?
(a) (i) only
(b) (ii) only
(c) (iii) only
(d) (ii) and (iii) only
Answer:
(a) (i) only
Question 53.
Which of the following gas is present maximum in atmospheric air?
(a) $\mathrm{O}_2$
(b) $\mathrm{N}_2$
(c) $\mathrm{H}_2$
(d) radon
Answer:
(b) $\mathrm{N}_2$
Question 54 .
Which law is used in the process of enriching the isotope of $U^{235}$ from other isotopes?
(a) Boyle's law
(b) Dalton's law of partial pressure
(c) Graham's law of diffusion
(d) Charles' law
Answer:
(c) Graham's law of diffusion

2 - Mark Questions
Question 1.
Identify the elements that are in gaseous state under normal atmospheric conditions.
Answer:
- Hydrogen, nitrogen, oxygen, fluorine and chlorine exist as gaseous diatomic molecules.
- Another form of oxygen namely ozone tr iatomic molecule exist as a gas at room temperature.
- Noble gases namely helium, neon, argon, krypton, xenon and radon are mono atomic gases.
Question 2.
Distinguish between a gas and a vapour.
Answer:
- Gas : A substance that is normally in a gaseous state at ordinary temperature and pressure. .,e.g., Hydrogen.
- Vapou $r$ : The gaseous form of any substance that is a liquid or solid at normal temperature and pressure. e.g., At $298 \mathrm{~K}$ and $1 \mathrm{~atm}$, water exist as water vapour.
Question 3.
Define pressure. Give its units.
Answer:
- Pressure is defined as the force exerted by a gas on unit area of the wall. Force $F$
- Pressure $=\frac{\text { Force }}{\text { Area }}=\frac{F}{a}$
- The SI unit of pressure is Pascal $(\mathrm{Pa})$
Question 4.
Define atmospheric pressure. What is its value?
Answer:
- The pressure exerted on a unit area of Earth by the colunm of air above it is called atmospheric pressure.
- The standard atmospheric pressure $=1 \mathrm{~atm}$.
- $1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$.
Question 5.
Deep sea divers ascend slowly and breath continuously by time they reach the surface. Give reason.

Answer:
- For every $10 \mathrm{~m}$ of depth, a diver experiences an additional $1 \mathrm{~atm}$ of pressure due to the weight of water surrounding him.
- At $20 \mathrm{~m}$, the diver experiences a total pressure of $3 \mathrm{~atm}$. So the most important rule in diving is never hold breath.
- Divers must ascend slowly and breath continuously allowing the regulator to bring the air pressure in their lungs to $1 \mathrm{~atm}$ by the time they reach the surface.
Question 6.
Most aeroplanes cabins are artificially pressurized. Why?

Answer:
The pressure decreases with the increase in altitude because there are fewer molecules per unit volume of air. Above $9200 \mathrm{~m}(30,000 \mathrm{ft})$, for example, where most commercial aeroplanes fly, the pressure is so low
that one could pass out for lack of oxygen. For this reason most aeroplanes cabins arc artificially pressurized.
Question 7.
What is the reason behind the cause of ear pain while climbing a mountain? How it can be rectified?

Answer:
- When one ascends a mountain in a plain, the external pressure drops while the pressure within the air cavities remains the same. This creates an imbalance.
- The greater internal pressure forces the eardrum to bulge outward causing pain.
- With time and with the help of a yawn or two, the excess air within your ear's cavities escapes thereby equalizing the internal and external pressure and relieving the pain.
Question 8 .
State Charles' law.
Answer:
Charles' law:
For a fixed mass of a gas constant pressure, the volume is directly proportional to temperature (K).
Mathematically $\mathrm{V}-\mathrm{T}$ at constant $\mathrm{P}$ and $\mathrm{n}$. (or) $\frac{V}{T}=$ Constant (or) $\frac{V_1}{T_1}=\frac{V_2}{T_2}=$ Constant
Question 9.
What are the applications of Charles' law?
Answer:
- A hot air inside the balloon rises because of its decreased density and causes the balloon to float inside the balloon rises because of its decreased density and causes the balloon to float.
- If you take a helium balloon outside on a chilly day, the balloon will crumble. Once you get back into warm area, the balloon will return to its original shape. This is because, in accordance with Charles' law, a gas like helium takes up more space when it is warm.

Question 10 .
State Avogadro's hypothesis.
Answer:
Equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. Mathematically $\mathrm{V} \propto \mathrm{n}$
$
\frac{V_1}{n_1}=\frac{V_2}{n_2}=\text { Constant }
$
Question 11.
Define Dalton's law of partial pressure.
Answer:
Dalton's law of partial pressure:
It states that the total pressure of a mixture of gases is the sum of partial pressures of the gases present.
$
\mathrm{P}_{\text {total }}=\mathrm{P}_1+\mathrm{P}_2+\mathrm{P}_3
$
Question 12 .
What are the applications of Dalton's law of partial pressure?
Answer:
1. Physicians report the pressure of the patient's gases in blood, analyzed by hospital lab, the values are reported as partial pressures.
Gas - Normal range
$
\begin{aligned}
& \mathrm{P}_{\mathrm{CO}_2} 35-45 \mathrm{~mm} \text { of } \mathrm{Hg} \\
& \mathrm{P}_{\mathrm{O}_2} 80-100 \mathrm{~mm} \text { of } \mathrm{Hg}
\end{aligned}
$
2. When gas is collected by downward displacement of water, the pressure of dry vapour collected is computed using Dalton's law
$
\mathrm{P}_{\text {dry gas collected }}=\mathrm{P}_{\text {Total }}-\mathrm{P}_{\text {water vapour }}
$
$P_{\text {water vapour }}=$ Aqueous tension

Question 13.
How can you identify a heavy smoker with the help of Dalton's law?
Answer:
Physicians report the pressure of the patient's gases in blood, analyzed by hospital lab. The values are reported as partial pressures.
Gas Normal range
$\mathrm{p}_{\mathrm{O}_2} \quad 80-100 \mathrm{~mm}$ of $\mathrm{Hg}$
$\mathrm{p}_{\mathrm{CO}_2} \quad 35-45 \mathrm{~mm}$ of $\mathrm{Hg}$
A heavy smoker may be expected to have low $\mathrm{O}_2$ and huge $\mathrm{CO}_2$ partial pressures.
Question 14 .
Define Graham's law of diffusion.
Answer:
Graham's law of diffusion:
The rate of diffusion or effusion is inversely proportional to the square root of molecular mass of a gas through an orifice.
$
\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{B}}}{\mathrm{M}_{\mathrm{A}}}}
$
$\mathrm{r}_{\mathrm{A}} \mathrm{r}_{\mathrm{B}}=$ rate of diffusion of gases $\mathrm{A}, \mathrm{B}$
$\mathrm{M}_{\mathrm{A}}, \mathrm{M}_{\mathrm{B}}=$ Molecular mass of gases $\mathrm{A}, \mathrm{B}$
Question 15.
Helium diffuses more than air. Give reason.
Answer:
Take two balloons, one is filled with air and another with helium. After one day, the helium balloon was shrunk, because helium being lighter diffuses out faster than the air
Question 16.
Explain about the applications of Graham's law of diffusion.
Answer:
- Graham's law of diffusion is useful to determine the molecular mass of the gas if the rate of diffusion is known.
- Graham's law forms the basis of the process of enriching the isotopes of $\mathrm{U}^{235}$ from other isotopes and also useful in isotopic separation of deuterium and protium.
Question 17.
What is compression factor?
Answer:
The deviation of real gases from ideal behaviour is measured in terms of a ratio of $\mathrm{PV}$ to $\mathrm{nRT}$.

This is termed as compression factor.
Compression factor $=\mathrm{Z}=\frac{P V}{n R T}$
For ideal gases $\mathrm{Z}=1$ at all temperature and pressures.
Question 18.
1. Define critical temperature.
2. What is the critical temperature of $\mathrm{CO}_2$ gas?
Answer:
1. The temperature below which a gas can be liquefied by application of pressure is known as critical temperature.
2. The critical temperature of $\mathrm{CO}_2$ gas is $303.98 \mathrm{~K}$.
Question 19.
1. Define critical pressure.
2. What is the critical pressure of $\mathrm{CO}_2$ gas?
Answer:
1. Critical temperature $\left(\mathrm{P}_{\mathrm{C}}\right)$ of a gas is defined as the minimum pressure required to liquefy.
2. The critical pressure of $\mathrm{CO}_2$ is $73 \mathrm{~atm}$.
Question 20.
$\mathrm{CO}_2$ gas cannot be liquefied at room temperature. Give reason.
Answer:
Only below the critical temperature, by the application of pressure, a gas can be liquefied. $\mathrm{CO}_2$ has critical temperature as $303.98 \mathrm{~K}$. Room temperature means $(30+273 \mathrm{~K}) 3 \mathrm{O}_3 \mathrm{~K}$. At room temperature, (critical temperature) even by applying large amount of pressure $\mathrm{CO}_2$ cannot be liquefied. Only below the critical temperature, it can be liquefied. At room temperature, $\mathrm{CO}_2$ remains as gas.
Question 21.
What is meant by Joule-Thomson effect?
Answer:
The phenomenon of lowering of temperature when a gas is made to expand adiabatically form a region of high pressure into a region of low pressure is known as Joule-Thomson effect.
Question 22.
Define inversion temperature.
Answer:
The temperature below which a gas obey Joule-Thomson effect is called inversion temperature $\left(T_i\right)$.
$
\mathrm{T}_1=\frac{2 a}{R b}
$

Question 23.
State and explain Boyle's law. Represent the law graphically.
Answer:
It states that, the pressure of a fixed mass of a gas is inversely proportional to its volume if temperature is kept constant.
$
\begin{aligned}
& \mathrm{P}-\frac{1}{V} \\
& \mathrm{PV}=\text { Constant (n and } \mathrm{T} \text { are constant) } \\
& \mathrm{P}_1 \mathrm{v}_1=\mathrm{P}_2 \mathrm{~V}_2
\end{aligned}
$
Graphical Representation:

Question 24.
Give an expression for the van der Waals equation. Give the significance of the constants used in the equation. What are their units?
Answer:
$
\left(P+\frac{n^2 a}{V^2}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}
$
Where $n$ is the number of moles present and ' $a$ ' $b$ ' are known as van der Waals constants.
Significance of Van der Waals constants:
Van der Waals constant ' $a$ ':
' $a$ ' is related to the magnitude of the attractive forces among the molecules of a particular gas. Greater the
value of'a', more will be the attractive forces.
Unit of'a' $=\mathrm{L}^2 \mathrm{~mol}^{-2}$
Van der Waals constant 'b':
'b' determines the volume occupied by the gas molecules which depends upon size of molecule.
Unit of ' $\mathrm{b}$ ' $=\mathrm{L} \mathrm{mol}^{-1}$
Question 25.
What are ideal and real gases? Out of $\mathrm{CO}_2$ and $\mathrm{NH}_3$ gases, which is expected to show more deriation from the ideal gas behaviour?
Answer:
Ideal gas:
A gas that follows Boyle's law, Charles' law and Avogadro law strictly is called an ideal gas. It is assumed that intermolecular forces are not present between the molecules of an ideal gas.
Real gases:
Gases which deviate from ideal gas behaviour are known as real gases. $\mathrm{NH}_3$ is expected to show more deviation. Since $\mathrm{NH}_3$ is polar in nature and it can be liquefied easily.
3-Mark Questions
Question 1.
Explain the graphical representation of Boyle's law.
Answer:
Boyle's law states that at a given temperature the volume occupied by a fixed mass of a gas is inversely proportional to its pressure. $V \propto(T$ and $\mathrm{n}$ are fixed) .

If the pressure of the gas increases, volume will decrease and if the pressure of the gas decreases, the volume will increase. So $\mathrm{PV}=$ Constant.

Question 2.
What are the consequences of Boyle's law?
Answer:
1. if the volume of a fixed mass of a gas is reduced to half at constant temperature the gas pressure doubles.
2. Boyle's law also helps to relate pressure to density.
$\mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_3 \mathrm{~V}_3$ (Boyle's law)
$P_1 \frac{m}{d_1}=P_2 \frac{m}{d_2}$
Where ' $m$ ' is the mass, $d_1$ and $d_2$ are the densities of gases at pressure $P_1$ and $P_2$. The density of the gas is directly proportional to pressure.
Question 3.
Explain Charles' law with an experimental illustration.
Answer:
Charles' law states that for a fixed mass of a gas at constant pressure, the volume is directly proportional to temperature $(\mathrm{K})$.
$
\mathrm{V} \propto \mathrm{T} \text { (or) } \frac{V}{T}=\text { Constant }
$

Volume vs Temperature:
If a balloon is moved from an ice water bath to a boiling water bath, the gas molecules inside move faster due to increased temperature and hence the volume increases.
Question 4.
Explain the graphical representation of Charles' law.
Answer:
1. Variation of volume of the gas sample with temperature at constant pressure.
2. Each line (iso bar) represents the variation of volume with temperature at certain pressure. The pressure increases from $P_1$ to $\mathrm{P}_5$.
3. i.e. $P_1 4. All gases are becoming liquids, if they are cooled to sufficiently low temperatures.
5. In other words, all gases occupy zero volume at absolute zero. So the volume of a gas can be measured over only a limited temperature range.

Question 5.
Explain graphicl representation of Gay Lussac's law

Answer:
Gay Lussac's law
At constant volume, the pressure of a fixed mass of a gas is directly proportional to temperature. $\mathrm{P}-\mathrm{T}$ (or) $\frac{P}{T}=$ Constant
It can be graphically represented as shown here:
Lines in the pressure vs temperature graph are known as isochores (constant volume) of a gas.

Question 6.
Explain the graphical representation of Arogadro's hypothesis.
Answer:
Arogadros hypothesis states that equal volumes of all gases under the same conditions of temperature and pressure contain equaLnumbr of molecules.
$\mathrm{V} \propto \mathrm{n}$
$\frac{V_1}{n_1}=\frac{V_2}{n_2}=$ Constant.
Where $V_1$ and are the volume and number 10- of moles of a gas and $V_2$ and $n_2$ are the different set of values of volume and number of moles of the same gas.

A better example to iflustrate Arogadro's Number of Moles (n) hypothesis is to observe the effect of pumping more gas into a balloon. When more gas molecules (particularly $\mathrm{CO}_2$ ) are passed, the volume of the balloon increases. The pressure and temperature stay constant as the balloon inflates, so the increase in volume is due to the increase in the quantity of gas inside the balloon.
Question 7.
Derive ideal gas equation.
Answer:
The gaseous state is described completely using the following four variables $T, P, V$ and $n$. Each gas law relates one variable of a gaseous sample to another while the other two variables are held constant.
Therefore, combining all equations into a single equation will enable to account for the change in any or all of the variables.
Boyle's law: $\mathrm{V} \propto \frac{1}{P}$
Charles' law: $\mathrm{V} \propto \mathrm{T}$
Avogadro's law: $V \propto \mathrm{n}$
We can combine these equations into the following general equation that describes the physical behaviour of all gases.
$\mathrm{V} \propto \frac{n T}{P}$
$\mathrm{V}=\frac{n R T}{P}$
$\mathrm{V}=$, where $\mathrm{R}=$ Proportionately constant
The above equation can be rearranged to give $\mathrm{PV}=\mathrm{nRT}$ - Ideal gas equation. Where, $\mathrm{R}$ is also known as Universal gas constant.
Question 8.
Derive the various values of $R$, gas constant.
Answer:
1. For standard conditions in which $P$ is $1 \mathrm{~atm}$, volume $22.414 \mathrm{dm}^3$ for 1 mole at $273.15 \mathrm{~K}$.
$
\begin{aligned}
& \mathrm{R}=\frac{1 \mathrm{~atm} \times 22.414 \mathrm{dm}^3}{1 \mathrm{~mole} \times 273.15 \mathrm{~K}} \\
& =0.082057 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}
\end{aligned}
$
2. Where $P=10^5$ Pascal, $V=22.71 \times 10^{-3} \mathrm{~m}^3$ for $\mathrm{I}$ mole of a gas at $273.15 \mathrm{~K}$.
$
\begin{aligned}
& \mathrm{R}=\frac{10^5 \mathrm{pa} \times 22.71 \times 10^{-3} \mathrm{~m}^3}{1 \mathrm{~mole} \times 273.15 \mathrm{~K}} \\
& =8.314 \mathrm{pa} \mathrm{m}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \\
& =8.314 \times 10^{-2} \mathrm{bar} \mathrm{dm}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \\
& \mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}
\end{aligned}
$
Question 9.
What is meant by Boyle temperature (or) Boyle point? How is it related with compression point?
Answer:
(1) Over a range of low pressures, the real gases can behave ideally at a particular temperature called as Boyle temperature or Boyle point.
(2) The Boyle point varies with the nattirc of the gas.
(3) Above the Boyle point, the compression point $Z>1$ for real gases i.e. real gases show positive deviation.
(4) Below the Boyle point, the real gases first show a decrease for $Z$, reaches a minimum and then increase with increase in pressure. So, it is clear that at low pressure and at high temperature, the real gases behave
as ideal gases.
(5) Hence $\mathrm{Z}=\frac{\mathrm{PV}_{\text {real }}}{\mathrm{nRT}}$
$\mathrm{PV}_{\text {ideal }}=\frac{\mathrm{nRT}}{\mathrm{P}}$
So, $Z=\frac{V_{\text {real }}}{V_{\text {ideal }}}$
Question 10.
Explain the different methods used for liquefaction of gases.
Answer:
- Linde's method: Joule-Thomson effect is used to get liquid air or any other gas.
- Claude's process: In addition to Joule-Thomson effect, the gas is allowed to perform mechanical work so that more cooling is produced.
- Adiabatic process: This method of cooling is produced by removing the magnetic property of magnetic material e.g. Gadolinium sulphate. By this method, a temperature of $10^{-4} \mathrm{~K}$ i.e. as low as zero Kelvin can be achieved.
5 - Mark Question
Question 1.
How $\mathrm{CH}_4 \mathrm{He}$ and $\mathrm{NH}_3$ are deviating from ideal behaviour? (or) Explain how real gases deviate from ideal behaviour.
Answer:
1. The gases which obeys gas equation $\mathrm{PV}=\mathrm{nRT}$ are known as ideal gases. The gases which do not obey $\mathrm{PV}=\mathrm{nRT}$ are known as real gases.
2. The gas laws and the kinetic theory are based on the assumption that molecules in the gas phase occupy negligible volume (assumption 1) and that they do not exert any force on one another either attractive or repulsive (assumption 2). Gases whose behaviour is consistent with these assumptions are said to exhibit ideal behaviour.

3. The following graph shows RT plotted against $P$ for three real gases and an ideal gas at a given temperature.
4. According to ideal gas equation, $P V / R T$ is equal to $n$. Plot $P V / R T$ versus $P$ for ' $n$ ' moles oigas at $0^{\circ} \mathrm{C}$. Forl mole of an ideal gas PV/ RT is equal to 1 irrespective of the pressure of the gas.
5. For real gases, we observe various deviations from ideal behaviour at high pressure. At very low pressure, all gases exhibit ideal behaviour, ie. PV/RT values all converge to $\mathrm{n}$ as $\mathrm{P}$ approaches zero.

6. For real gases, this is true only at moderate low pressures. $(\leq 5 \mathrm{~atm})$ significant variation occurs as the pressure increases. Attractive forces operate among molecules at relatively short deviation.
7. At atmospheric pressure, the molecules in a gas are far apart and attractive forces arc negligible. At high pressure, the density of the gas increases and the molecules are much closer to one another. Intermolecular forces can be significant enough to affect the motion of the molecules and the gas will not behave ideally.
Question 2.
Derive Van der Waals equation of state.
Answer:
1. Consider the effect of intermolecular forces on the pressure exerted by a gas form the following explanation.
2. The speed of a molecule that is moving toward the wall of a container is reduced by the attractive forces exerted by its neighbours. Hence, the measured gas pressure is $Q$ lower than the pressure the gas would exert, if it behave ideally.

Where ' $\mathrm{a}$ ' is the proportionality constant and depends on the nature of the gas and $\mathrm{n}$ and $\mathrm{V}$ are the number of moles and volume of the container and respectively $\mathrm{an}^2 / \mathrm{V}^2$ is the correction term.
3. The frequency of encounters increases with the square of the number of molecules per unit volume $\mathrm{n}^2 /$ $\mathrm{V}^2$. Therefore $\mathrm{an}^2 / \mathrm{V}^2$ represents the intermolecular interaction that causes non-ideal behaviour.
4. Another correction is concerned with the volume ¿ccupied by the gas molecules. ' $V$ ' represents the volume of the container. As every individual molecule of a real gas occupies certain volume, the effective volume $\mathrm{V}$ - $\mathrm{nb}$ which is the actually available for the gas, $n$ is the number of moles and $\mathrm{b}$ is a constant of gas.
5. Hence Van der Waals equation of state for real gases are given as $\left(P+\frac{a n^2}{V^2}\right)(\mathrm{V}-\mathrm{nb})=\mathrm{nRT}$ Where a and $\mathrm{b}$ are Van der Waals constants.
Question 3.
Explain about Andrew's experimental isotherms of $\mathrm{CO}_2$ gas.
Answer:
1. Andrew plotted isotherms of carbon dioxide at different temperatures. it is then proved that many real gases behave in a similar manner like $\mathrm{CO}_2$.
2. At a temperature of $303.98 \mathrm{~K}, \mathrm{CO}_2$ remains as a gas. Below this temperature, $\mathrm{CO}_2$, turns into liquid $\mathrm{CO}_2$ at $73 \mathrm{~atm}$. It is called the critical temperature of $\mathrm{CO}_2$.

3. At $303.98 \mathrm{~K}$ and 73 atm pressure, $\mathrm{CO}_3$,, becomes a liquid but remains a gas at higher temperature.
4. Below the critical temperature, the behaviour of $\mathrm{CO}_2$ is different. For example, consider an isotherm of $\mathrm{CO}_2$ at $294.5 \mathrm{~K}$, it is a gas until the point $\mathrm{B}$, is reached. At $\mathrm{B}$, a liquid separates along the line $\mathrm{BC}$, both the liquid and gas co-exist. At $\mathrm{C}$, the gas is completely condensed.
5. If the pressure is higher than at $\mathrm{C}$, only the liquid is compressed so, a steep rise in pressure is observed. Thus, there exist a continuity of state.
6. A gas below the critical temperature can be liquefied by applying pressures.
Activity - 1
The table below contains the values of pressure measured at different temperatures for 1 moie of an ideal gas. Plot the values in a graph and verify the Gay Lussac's law. [Lines in the pressure vs temperature graph
are known as iso chores (constant volume) of a gas]

Solution:
Gay Lussac's law at constant volume $=\frac{P_1}{T_1}=\frac{P_2}{T_2}$

If temperature increases, pressure also increases.
So $\frac{P_1}{T_1}=\frac{P_2}{T_2}$