The Gaseous State and Transport Phenomenon – Chemistry Optional PYQs (2000–2026)

Here are all 40 The Gaseous State and Transport Phenomenon questions asked in UPSC Chemistry Optional Paper I from 2000 to 2026, arranged under the 2 topics of the official syllabus. Within each topic the latest questions come first.

Each question ends with a code such as [2024/15m/3b] – the year, the marks, the word limit (where UPSC set one) and the question number in the paper.

4.1] Real gases and critical phenomena

19 questions

1. One real gas equation is van der Waals equation $(P+\frac{n^{2}a}{V^2})(V-nb)=nRT$ Which parameter in the above equation reflects the intermolecular force of attraction and which one reflects the intermolecular force of repulsion? Give their units in SI system. [2026/5m/1a]

2. A sealed container contains a gaseous sample at 300 K consisting of either pure ethane, or pure neon, or a mixture of the two. The pressure inside the container at this temperature is 1.00 atm. When the container is cooled to 150 K, the pressure is 0.37 atm. What is the composition of the sample; pure ethane, pure neon or a mixture of both? Explain your answer. Given: Vapour pressure of $C_2{H}_6$ at 150 K is 0.10 atm; Critical temperature of neon = 44 K. [2025/5m/1h]

3. The compound dichlorodifluoromethane ($CC{l}_2{F}_2$) has a normal boiling point of –30°C, a critical temperature of 112°C, and a corresponding critical pressure of 40 atm. If the gas is compressed to 18 atm at 20°C, will the gas condense? Give your answer on the basis of graphical presentation. [2024/5m/1d(i)]

4. Arrange Boyle’s temperature of the gases Ar, $C{H}_4$ and $C_6{H}_6$ in increasing order. Give reason(s) for the answer. [2024/5m/3a(ii)]

5. The volume of a certain gas is found to be $5.0\times {10}^{-4}{m}^{3}mo{l}^{-1}$ at 273 K and $3.0\times {10}^6$ Pa. This gas obeys the van der Waals’ equation with $a=0.50m^{6}Pamo{l}^{-2}$. (i) Calculate the other van der Waals’ constant, $b$. (ii) What is the compression factor for this gas at the same temperature and pressure? (iii) Comment on the nature of the molecular interactions of this gas. [2023/20m/4a]

6. By using the following given data, find that under what conditions is $H_2$ in the state corresponding to $N_2$ at 126 K and 1 atm?

Gas	$T_c$/K	$P_c$/atm
$H_2$	33	13
$N_2$	126	39

[2022/10m/4a]

7. The critical temperature and pressure for NO gas are 177 K and 64 atm, respectively, and for $CC{l}_4$, they are 550 K and 45 atm, respectively. Which gas has the smaller values of the van der Waals’ constants, $a$ and $b$? Which is the most nearly ideal in behaviour at 300 K and 10 atm? [2021/10m/4b(ii)]

8. Calculate van der Waals constants for ethylene. Given: critical temperature ($T_c$) = 282 K and critical pressure ($P_c$) = 50 atm. [2020/10m/5b]

9. Account for the difference between vapour and gas on the basis of critical temperature. [2018/5m/4c(ii)]

10. Define Boyle temperature of non-ideal gas. Obtain its expression for van der Waals’ gas. [2017/15m/2a(ii)]

11. Explain “continuity of state” with the help of isotherms of $C{O}_2$. How is it affirmed by van der Waals’ equation? [2016/10m/1d]

12. The van der Waals equation for real gases is given by $P_{obs}=\frac{nRT}{V-nb}-a{\left(\frac{n}{V}\right)}^2$ where $P_{obs}$ is the observed pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the gas constant and $T$ is the temperature. $a$ and $b$ are constants characteristic of a gas. (i) Is $P_{obs}$ greater or less than the pressure expected for an ideal gas? Write a few sentences outlining the reason(s) for your answer. (ii) Consider the halogens $F_2$ (g), $C{l}_2$ (g) and $B{r}_2$ (g). (1) Rank these in order of increasing $a$. Justify your answer. (2) Rank these in order of increasing $b$. Justify your ranking. [2015/10m/1b]

13. Determine expressions for the critical constants ($P_c$, $V_c$, $T_c$) of a Van der Waals gas, defined by the expression $P=\frac{RT}{V_m-b}-\frac{a}{V_m^2}$ where the symbols have their usual meanings. [2013/10m/1c]

14. With the help of P – V diagram of $N{H}_3$ explain the critical temperature. [2012/12m/5d]

15. State the van der Waals equation of state and justify briefly the appearance of the parameters $a$ and $b$ in the equation. Given that for Xe, $a=4.191bard{m}^{6}mo{l}^{-2}$, $b=5.16\times {10}^{-2}d{m}^{3}mo{l}^{-1}$, determine the pressure exerted by 1 mol of Xe in a container of volume 20 $d{m}^3$ at 300 K. How does the pressure compare with that predicted by the perfect gas law? Explain. ($R=0.083bard{m}^{3}mo{l}^{-1}{K}^{-1}$) [2011/15m/1c]

16. Derive the Van der Waal s equation of state for real gases. What are the units of Van der Waals constants? [2007/20m/2b]

17. Define the terms critical temperature, critical pressure and critical volume. How are these constants determined experimentally? [2007/20m/2c]

18. What do you understand by liquefaction of gases? Explain critical temperature and critical pressure. Draw schematic diagram for liquefaction of air. [2006/15m/6c]

19. State and explain the law of corresponding states. For large number of substances, the quantity $R{T}_c/P_c{V}_c$ lies between 3.4 and 3.7. Comment on the fact. [2000/20m/2c]

4.2] Kinetic theory and transport

21 questions

1. The Maxwell distribution of molecular speed of a gaseous system is $d{N}_c=4\pi N{\left(\frac{M}{2\pi RT}\right)}^{3/2}{c}^2{e}^{-M{c}^2/2RT}dc$ (Symbols have their usual meanings) Plot $(\frac{1}{N}\times \frac{d{N}_c}{dc})$ against c— (i) at two different temperatures $T_1$ and $T_2$; $T_2>T_1$; (ii) at two molar masses $M_1$ and $M_2$; $M_2>M_1$. Justify your plots. [2026/15m/2a]

2. Two sheets of copper of area $1.50m^2$ are separated by 10 cm. What is the rate of transfer of heat by conduction from the warm sheet (50°C) to the cold sheet (–10°C)? What is the rate of loss of heat? (Assume the space between the two sheets is filled with air) Given: Coefficient of thermal conductivity of air $=2.4\times {10}^{-2}J{s}^{-1}{m}^{-1}{K}^{-1}$ [2025/5m/1d]

3. Calculate the number of collisions that oxygen makes per second on $1.00c{m}^2$ of the surface of the vessel containing them if the pressure is $1.00\times {10}^{-6}$ atm and the temperature is 25°C. [2025/10m/3a]

4. The ${}^{235}U$ isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from more abundant ${}^{238}U$ isotope, U is first converted to $U{F}_6$, which is easily vaporized above room temperature. The mixture of ${}^{235}U{F}_6$ and ${}^{238}U{F}_6$ gases is then subjected to many stages of effusion. Calculate the separation factor, that is enrichment of ${}^{235}U$ relative to ${}^{238}U$ after one stage of effusion. [2024/5m/1b(i)]

5. Calculate the coefficient of viscosity of air at temperatures: (I) 298 K and (II) 0 K. Assume that the collision cross-section ($\pi {\sigma }^2$) of air is $0.28{\left(nm\right)}^2$ and average molar mass of air is $29gmo{l}^{-1}$. [2024/10m/3a(i)]

6. Find the temperature at which the water molecules can have the root-mean-square speed of $719m{s}^{-1}$. [2023/5m/1d(i)]

7. What is the root-mean-square velocity of water molecules at 473 K? [2023/5m/1d(ii)]

8. The graph above shows the distribution of molecular speeds for Argon and Helium at the same temperature. (i) Which curve, 1 or 2 better represents the behavior of Argon? (ii) Which curve represents the gas that effuses more slowly? (iii) Which curve more closely represents the behavior of fluorine gas? Explain.

[Figure: Maxwell speed-distribution plot: vertical axis “Relative number of molecules”, horizontal axis “Molecular speed” (arrow →). Both curves start at the origin. Curve 1 rises steeply to a tall, narrow maximum at low speed and falls almost to zero at moderate speed; Curve 2 is low and broad, with its maximum at a higher speed than that of Curve 1, and tails off slowly to high speeds. No numerical values] [2022/10m/3c]

9. A certain closed cell foam used as an insulating material is initially filled with polyatomic gas of molecular weight ~60. Later, the gas diffuses out of the foam and is replaced by dry air (mean molecular weight ~30). Assuming that insulating property arises largely from the thermal conductivity of the gas, explain the factors which influence the thermal conductivity of the gas. For each factor, make an argument whether insulating ability increases or decreases. What is the overall effect upon the insulating ability? [2021/10m/4b(i)]

10. What does most probable speed ($C_{mp}$), average speed ($C_{av}$) and root mean square speed ($C_{rms}$) mean? Indicate these speeds on a Maxwell distribution curve. What does the area under the Maxwell distribution curve represent? [2020/10m/6a]

11. Write Maxwell’s distribution of molecular velocities for gases. What is the effect of temperature on the distribution? Represent graphically. [2019/10m/1e]

12. Discuss the effect of temperature on the viscosity of liquids and gases. [2018/5m/2b(ii)]

13. One side of glass cylinder is initially filled with $H_2$ at a pressure P and other side with $N_2$ at a pressure 2P. This glass cylinder is closed at both ends and a glass filter in the middle of the cylinder divides it into two compartments of equal volume. Describe what happens, starting at time, t = 0 at constant temperature and assuming that the pores of filter have a diameter much smaller than the mean free paths of the gases. [2018/10m/4c(i)]

14. For an ideal gas, the distribution law of molecular speed is, $d{N}_c=4\pi N{\left(\frac{m}{2\pi k_{B}T}\right)}^{3/2}{c}^2{e}^{-m{c}^2/2k_{B}T}dc,$ where, $d{N}_c$ = Number molecules within the speed range $c$ and $(c+dc)$. $N$ = Total number of molecules. $m$ = Molecular mass. $T$ = Temperature in Kelvin scale. Derive the expression of most probable speed of this gaseous system. [2017/10m/1b]

15. What is the dimension of viscosity co-efficient? What is its unit in SI system? The temperature effect on viscosity co-efficient of ideal gas is positive. Explain. [2017/10m/2a(i)]

16. The viscosity of gases increases with temperature, but the viscosity of liquids decreases with temperature. Explain. [2015/10m/3d]

17. The molecular speeds are distributed according to the Maxwell distribution, $f\left(v\right)=4\pi {\left(\frac{M}{2\pi RT}\right)}^{3/2}{v}^2{e}^{-M{v}^2/2RT}$ (i) Sketch f(v) for He and for $N_2$. (ii) Show that f(v) is normalized, i.e. ${\int }_0^{\infty }f\left(v\right)dv=1$ (iii) Show that the most probable molecular speed $v_{mp}$, is given by $v_{mp}=\sqrt{\frac{2RT}{M}}$ [2013/15m/2b]

18. Evaluate most probable speed and average speed from Maxwell’s relation for distribution of speed in a gas. Given: $\frac{dNc}{N}=4\pi {\left(\frac{m}{2\pi KT}\right)}^{3/2}{c}^2{e}^{-\frac{m{c}^2}{2KT}}dc$ and ${\int }_0^{\infty }{e}^{-a{x}^2}\cdot x^{2}dx=\frac{1}{2a^2}$ [2012/15m/4a]

19. According to the kinetic model of gases, the pressure and volume of a gas are related through the root mean square molecular speed, $c=⟨v^2{⟩}^{1/2}$, by $pV=\frac{1}{3}nM{c}^2$ where $M=m{N}_A$ is the molecule’s molar mass, and $n$ is the number of moles of gas present. (i) According to the ‘equipartition theorem’ of classical mechanics, the average energy per molecule for three-dimensional transitional motion is $\frac{3}{2}{k}_{B}T$, where $k_B$ is the Boltzmann’s constant. Use this and the above equation to derive the ideal gas law. (ii) Show that the root mean square molecular speed is given by $c=\sqrt{\frac{3RT}{M}}$ (iii) Calculate c for $O_2$ at room temperature (298 K). (iv) Calculate the ratio of c for He to that for $O_2$ at 298 K. ($R=8.314J{K}^{-1}mo{l}^{-1}$) [2011/25m/2b]

20. Derive an expression to estimate the frequency of collisions of gas molecules with a surface. Describe the relaxation method for studying fast reactions. [2009/20m/2c]

21. State and explain Maxwells law of distribution of velocities of molecules of a gas at a definite temperature. What is meant by most probable velocity? [2008/20m/2c]

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Last updated: 30 October 2026