States of Matter · JEE Main previous year questions

A company dissolves 'x' amount of ${\mathrm{CO}}_2$ at $298\text{ K}$ in $1\text{ litre}$ of water to prepare soda water. $\mathrm{X}=\underline{}\times 10^{-3}\text{ g}$. (nearest integer) (Given : partial pressure of ${\mathrm{CO}}_2$ at $298\text{ K}=0.835\text{ bar}$. Henry's law constant for ${\mathrm{CO}}_2$ at $298\text{ K}=1.67\text{ kbar}$. Atomic mass of $\mathrm{H}$, $\mathrm{C}$ and $\mathrm{O}$ is $1$, $12$, and $16{\text{ g mol}}^{-1}$, respectively)

An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm. In the course of use at ambient temperature, the mass of the cylinder is reduced to 23.0 kg. The final pressure inside of the cylinder is _________ atm. (Nearest integer) (Assume LPG to be an ideal gas)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : $\mathrm{S}{\mathrm{O}}_2(\mathrm{g})$ is adsorbed to a larger extent than ${\mathrm{H}}_2(\mathrm{g})$ on activated charcoal. Reason R : $\mathrm{S}{\mathrm{O}}_2(\mathrm{g})$ has a higher critical temperature than ${\mathrm{H}}_2(\mathrm{g})$. In the light of the above statements, choose the most appropriate answer from the options given below.

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

$2\mathrm{S}{\mathrm{O}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2\mathrm{S}{\mathrm{O}}_3(\mathrm{g})$ The above reaction is carried out in a vessel starting with partial pressure ${\mathrm{P}}_{\mathrm{S}{\mathrm{O}}_2}=250\text{ m bar}$, ${\mathrm{P}}_{{\mathrm{O}}_2}=750\text{ m bar}$ and ${\mathrm{P}}_{\mathrm{S}{\mathrm{O}}_3}=0\text{ bar}$. When the reaction is complete, the total pressure in the reaction vessel is __________ m bar. (Round off of the nearest integer).

$\mathrm{C}{\mathrm{O}}_2$ gas is bubbled through water during a soft drink manufacturing process at 298 K. If $\mathrm{C}{\mathrm{O}}_2$ exerts a partial pressure of 0.835 bar then x m mol of $\mathrm{C}{\mathrm{O}}_2$ would dissolve in 0.9 L of water. The value of x is ____. (Nearest integer) (Henry's law constant for $\mathrm{C}{\mathrm{O}}_2$ at 298 K is $1.67\times 10^3$ bar)

A home owner uses $4.00\times 10^3{\mathrm{m}}^3$ of methane ($\mathrm{C}{\mathrm{H}}_4$) gas, (assume $\mathrm{C}{\mathrm{H}}_4$ is an ideal gas) in a year to heat his home. Under the pressure of 1.0 atm and 300 K, mass of gas used is $x\times 10^5$ g. The value of x is ____. (Nearest integer) (Given R = 0.083 L atm ${\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$)

A certain gas obeys $P(V_m-b)=RT$. The value of ${\left(\frac{\partial Z}{\partial P}\right)}_T$ is $\frac{xb}{RT}$. The value of x is _________. (Integer answer) (Z : compressibility factor)

1. A.II
2. B.III
3. C.I
4. D.IV

Consider the following table : | Gas | $a/(\mathrm{k}\mathrm{Pa}\mathrm{d}{\mathrm{m}}^6\mathrm{mo}{\mathrm{l}}^{-1})$ | $b/(\mathrm{d}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1})$ | |---|---|---| | A | 642.32 | 0.05196 | | B | 155.21 | 0.04136 | | C | 431.91 | 0.05196 | | D | 155.21 | 0.4382 | a and b are van der Waals constants. The correct statement about the gases is :

1. A.Gas C will occupy more volume than gas A; gas B will be more compressible than gas D
2. B.Gas C will occupy lesser volume than gas A; gas B will be more compressible than gas D
3. C.Gas C will occupy lesser volume than gas A; gas B will be lesser compressible than gas D
4. D.Gas C will occupy more volume than gas A; gas B will be lesser compressible than gas D

Consider the van der Waals constants, a and b, for the following gases. $$\begin{array}{lcccc}\text{Gas}& \text{Ar}& \text{Ne}& \text{Kr}& \text{Xe}\\ a/(\mathrm{atm}\mathrm{d}{\mathrm{m}}^6\mathrm{mo}{\mathrm{l}}^{-2})& 1.3& 0.2& 5.1& 4.1\\ b/(10^{-2}\mathrm{d}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1})& 3.2& 1.7& 1.0& 5.0\end{array}$$ Which gas is expected to have the highest critical temperature?

1. A.Ne
2. B.Kr
3. C.Xe
4. D.Ar

At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as $p=\frac{RT}{V-b}$ at T. Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vs p?

1. A.Xe
2. B.Ne
3. C.Ar
4. D.Kr

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

Given | Gas | ${\mathrm{H}}_2$ | $\mathrm{C}{\mathrm{H}}_4$ | $\mathrm{C}{\mathrm{O}}_2$ | $\mathrm{S}{\mathrm{O}}_2$ | | :--- | :--- | :--- | :--- | :--- | | Critical Temperature / K | 33 | 190 | 304 | 630 | On the basis of data given above, predict which of the following gases shows least adsorption on a definite amount of charcoal ?

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

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

An open vessel at $27^{\circ }\mathrm{C}$ is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is -

1. A.750 K
2. B.$500^{\circ }\mathrm{C}$
3. C.$750^{\circ }\mathrm{C}$
4. D.500 K

Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl = 35.5 u)

1. A.1.46
2. B.0.46
3. C.1.64
4. D.0.64

1. A.$-5\text{kJ}{\text{mol}}^{-1}$
2. B.$+5\text{kJ}{\text{mol}}^{-1}$
3. C.$18\text{kJ}{\text{mol}}^{-1}$
4. D.$-18\text{kJ}{\text{mol}}^{-1}$

An ideal gas undergoes isothermal expansion at constant pressure. During the process :

1. A.enthalpy increases but entropy decreases.
2. B.enthalpy remains constant but entropy increases.
3. C.enthalpy decreases but entropy increases.
4. D.Both enthalpy and entropy remain constant.

1. A.$2p_i\left(\frac{T_2}{T_1+T_2}\right)$
2. B.$2p_i\left(\frac{T_1{T}_2}{T_1+T_2}\right)$
3. C.$p_i\left(\frac{T_1{T}_2}{T_1+T_2}\right)$
4. D.$2p_i\left(\frac{T_1}{T_1+T_2}\right)$

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

1. A.$Z=1+\frac{RT}{Pb}$
2. B.$Z=1-\frac{a}{VRT}$
3. C.$Z=1-\frac{Pb}{RT}$
4. D.$Z=1+\frac{Pb}{RT}$

A transition metal $M$ forms a volatile chloride which has a vapour density of 94.8. If it contains $74.75\%$ of chlorine the formula of the metal chloride will be

1. A.$\mathrm{MC}{\mathrm{l}}_3$
2. B.$\mathrm{MC}{\mathrm{l}}_2$
3. C.$\mathrm{MC}{\mathrm{l}}_4$
4. D.$\mathrm{MC}{\mathrm{l}}_5$

For $1\mathrm{mol}$ of an ideal gas at a constant temperature $T$, the plot of $(\log P)$ against $(\log V)$ is a ($P$ : Pressure, $V$ : Volume)

1. A.Straight line parallel to $x$-axis.
2. B.Straight line with a negative slope.
3. C.Curve starting at origin.
4. D.Straight line passing through origin.

An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_i$ is the initial temperature and $T_f$ is the final temperature, which of the following statements is correct?

1. A.$(T_f{)}_{\mathrm{irrev}}>(T_f{)}_{\mathrm{rev}}$
2. B.$(T_f{)}_{\mathrm{rev}}=(T_f{)}_{\mathrm{irrev}}$
3. C.$T_f>T_i$ for reversible process but $T_f=T_i$ for irreversible process
4. D.$T_f=T_i$ for both reversible and irreversible processes

An ideal gas expands in volume from $1\times 10^{-3}{\mathrm{m}}^3$ to $1\times 10^{-2}{\mathrm{m}}^3$ at 300 K against a constant pressure of $1\times 10^5\mathrm{N}{\mathrm{m}}^{-2}$. The work done is :

1. A.-900 J
2. B.900 kJ
3. C.270 kJ
4. D.-900 kJ

In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure of

1. A.intermolecular repulsions
2. B.intermolecular collisions per unit volume
3. C.Volume occupied by the molecules
4. D.intermolecular attraction