States of Matter · JEE Main previous year questions

One mole each of $\mathrm{He}$ and $\mathrm{A}(\mathrm{g})$ are taken in a $10\mathrm{L}$ closed flask and heated to $400\mathrm{K}$ to establish the following equilibrium. $\mathrm{A}(\mathrm{g})\rightleftharpoons \mathrm{B}(\mathrm{g})$ ${\mathrm{K}}_{\mathrm{c}}$ for this reaction at $400\mathrm{K}$ is $4.0$. The partial pressures (in $\mathrm{atm}$) of $\mathrm{He}$ and $\mathrm{B}(\mathrm{g})$ are respectively (at equilibrium) (Assume $\mathrm{He}$, $\mathrm{A}(\mathrm{g})$ and $\mathrm{B}(\mathrm{g})$ behave as ideal gases) (Given : $\mathrm{R}=0.082\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$)

1. A.3.28, 2.624
2. B.2.624, 3.28
3. C.3.28, 0.656
4. D.0.656, 6.56

$20.0\mathrm{d}{\mathrm{m}}^3$ of an ideal gas ' X ' at $600\mathrm{K}$ and $0.5\mathrm{MPa}$ undergoes isothermal reversible expansion until pressure of the gas is $0.2\mathrm{MPa}$ . Which of the following option is correct? (Given: $\log 2=0.3010$ and $\log 5=0.6989$ )

1. A.$w=-9.1\mathrm{kJ}$, $\Delta U=0$, $\Delta H=0$, $q=9.1\mathrm{kJ}$
2. B.$w=9.1\mathrm{J}$, $\Delta U=9.1\mathrm{J}$, $\Delta H=0$; $q=0$
3. C.$w=-3.9\mathrm{kJ}$, $\Delta U=0$, $\Delta H=0$; $q=3.9\mathrm{kJ}$
4. D.$w=+4.1\mathrm{kJ}$, $\Delta U=0$, $\Delta H=0$; $q=-4.1\mathrm{kJ}$

Consider the following equilibrium, $\mathrm{CO}(\mathrm{g})+2{\mathrm{H}}_2(\mathrm{g})\rightleftharpoons {\mathrm{CH}}_3\mathrm{OH}(\mathrm{g})$ $0.1\text{ mol}$ of CO along with a catalyst is present in a $2{\text{ dm}}^3$ flask maintained at $500\text{ K}$. Hydrogen is introduced into the flask until the pressure is $5\text{ bar}$ and $0.04\text{ mol}$ of ${\mathrm{CH}}_3\mathrm{OH}$ is formed. The $K_p^{\theta }$ is _________ $\times 10^{-3}$ (nearest integer). $\text{Given : }\mathrm{R}=0.08{\text{ dm}}^3{\text{ bar K}}^{-1}{\text{ mol}}^{-1}$ Assume only methanol is formed as the product and the system follows ideal gas behaviour.

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :

1. A.$\mathrm{q}=0,\Delta \mathrm{T}=0,\mathrm{w}=0$
2. B.$\mathrm{q}=0,\Delta \mathrm{T}\ne 0,\mathrm{w}=0$
3. C.$\mathrm{q}\ne 0,\Delta \mathrm{T}=0,\mathrm{w}=0$
4. D.$\mathrm{q}=0,\Delta \mathrm{T}<0,\mathrm{w}\ne 0$

A certain quantity of real gas occupies a volume of $0.15{\text{ dm}}^3$ at $100\text{ atm}$ and $500\text{ K}$ when its compressibility factor is 1.07 . Its volume at $300\text{ atm}$ and $300\text{ K}$ (When its compressibility factor is 1.4 ) is ___________ $\times 10^{-4}{\text{ dm}}^3$ (Nearest integer)

Four gases A, B, C and D have critical temperatures $5.3$, $33.2$, $126.0$ and $154.3\text{ K}$ respectively. For their adsorption on a fixed amount of charcoal, the correct order is:

1. A.$\mathrm{D}>\mathrm{C}>\mathrm{B}>\mathrm{A}$
2. B.$\mathrm{C}>\mathrm{B}>\mathrm{D}>\mathrm{A}$
3. C.$\mathrm{D}>\mathrm{C}>\mathrm{A}>\mathrm{B}$
4. D.$\mathrm{C}>\mathrm{D}>\mathrm{B}>\mathrm{A}$

Arrange the following gases in increasing order of van der Waals constant 'a' A. $\mathrm{Ar}$ B. $\mathrm{C}{\mathrm{H}}_4$ C. ${\mathrm{H}}_2\mathrm{O}$ D. ${\mathrm{C}}_6{\mathrm{H}}_6$ Choose the correct option from the following.

1. A.D, C, B and A
2. B.A, B, C and D
3. C.B, C, D and A
4. D.C, D, B and A

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: Amongst $\text{He},\text{Ne},\text{Ar}$ and $\text{Kr}$; $1\text{g}$ of activated charcoal adsorbs more of $\text{Kr}$. Reason R: The critical volume ${\text{V}}_c\left({\text{cm}}^3{\text{ mol}}^{-1}\right)$ and critical pressure ${\text{P}}_c\text{ (atm)}$ is highest for Krypton but the compressibility factor at critical point $Z_c$ is lowest for Krypton. In the light of the above statements, choose the correct answer from the options given below

1. A.Both A and R are true and R is the correct explanation of A
2. B.A is false but R is true
3. C.Both A and R are true but R is NOT the correct explanation of A
4. D.A is true but R is false

The total pressure of a mixture of non-reacting gases $\mathrm{X}(0.6\text{ g})$ and $\mathrm{Y}(0.45\text{ g})$ in a vessel is $740\text{ mm of Hg}$. The partial pressure of the gas $\mathrm{X}$ is ___________ $\text{mm of Hg}$. (Nearest Integer) (Given : molar mass $\mathrm{X}=20$ and $\mathrm{Y}=45{\text{ g mol}}^{-1}$)

A $300\text{ mL}$ bottle of soft drink has $0.2\text{ M}$ ${\mathrm{CO}}_2$ dissolved in it. Assuming ${\mathrm{CO}}_2$ behaves as an ideal gas, the volume of the dissolved ${\mathrm{CO}}_2$ at STP is ___________ $\text{mL}$. (Nearest integer) Given : At STP, molar volume of an ideal gas is $22.7{\text{ L mol}}^{-1}$

1. A.$1+\frac{b}{V}$
2. B.$1-\frac{a}{RTV}$
3. C.$1+\frac{a}{RTV}$
4. D.$1-\frac{b}{V}$

If ${\mathrm{O}}_2$ gas is bubbled through water at $303\mathrm{K}$, the number of millimoles of ${\mathrm{O}}_2$ gas that dissolve in $1\text{ litre}$ of water is __________. (Nearest Integer) (Given : Henry's Law constant for ${\mathrm{O}}_2$ at $303\mathrm{K}$ is $46.82\mathrm{k}\mathrm{bar}$ and partial pressure of ${\mathrm{O}}_2=0.920\mathrm{bar}$) (Assume solubility of ${\mathrm{O}}_2$ in water is too small, nearly negligible)

Given below are the critical temperatures of some of the gases: $$\begin{array}{ll}\text{Gas}& \text{Critical temperature (K)}\\ \mathrm{He}& 5.2\\ \mathrm{C}{\mathrm{H}}_4& 190.0\\ \mathrm{C}{\mathrm{O}}_2& 304.2\\ \mathrm{N}{\mathrm{H}}_3& 405.5\end{array}$$ The gas showing least adsorption on a definite amount of charcoal is

1. A.$\mathrm{He}$
2. B.$\mathrm{C}{\mathrm{H}}_4$
3. C.$\mathrm{C}{\mathrm{O}}_2$
4. D.$\mathrm{N}{\mathrm{H}}_3$

'x' g of molecular oxygen (${\mathrm{O}}_2$) is mixed with $200\mathrm{g}$ of neon (Ne). The total pressure of the non-reactive mixture of ${\mathrm{O}}_2$ and Ne in the cylinder is $25\mathrm{bar}$. The partial pressure of Ne is $20\mathrm{bar}$ at the same temperature and volume. The value of 'x' is ____. [Given: Molar mass of ${\mathrm{O}}_2=32\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. Molar mass of $\mathrm{Ne}=20\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$]

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Activated charcoal adsorbs ${\text{SO}}_2$ more efficiently than ${\text{CH}}_4$. Reason R : Gases with lower critical temperatures are readily adsorbed by activated charcoal. In the light of the above statements, choose the correct answer from the options given below.

1. A.Both A and R are correct and R is the correct explanation of A.
2. B.Both A and R are correct but R is NOT the correct explanation of A.
3. C.A is correct but R is not correct.
4. D.A is not correct but R is correct.

For a real gas at $25^{\circ }\mathrm{C}$ temperature and high pressure ($99\mathrm{bar}$) the value of compressibility factor is 2, so the value of van der Waals constant 'b' should be ____ $\times 10^{-2}\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}$ (Nearest integer) (Given $\mathrm{R}=0.083\mathrm{L}\mathrm{bar}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$)

A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is _________ bar. (Nearest Integer)

A sealed flask with a capacity of $2\mathrm{d}{\mathrm{m}}^3$ contains $11\mathrm{g}$ of propane gas. The flask is so weak that it will burst if the pressure becomes $2\mathrm{MPa}$. The minimum temperature at which the flask will burst is ____ ${}^{\circ }\mathrm{C}$. [Nearest integer] (Given : $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$, Atomic masses of C and H are $12\mathrm{u}$ and $1\mathrm{u}$, respectively.) (Assume that propane behaves as an ideal gas.)

1. A.A and C
2. B.B and A
3. C.D and A
4. D.C and D

$100\mathrm{g}$ of an ideal gas is kept in a cylinder of $416\mathrm{L}$ volume at $27^{\circ }\mathrm{C}$ under $1.5\mathrm{bar}$ pressure. The molar mass of the gas is ____ $\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. (Nearest integer) (Given : $\mathrm{R}=0.083\mathrm{L}\mathrm{bar}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$)

1. A.
2. B.
3. C.
4. D.

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density $0.95{\text{ g mL}}^{-1}$ and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in ${\text{g mol}}^{-1}$ is : (Given : $\mathrm{R}=0.082{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}$)

1. A.35
2. B.50
3. C.75
4. D.125