Dalton's Law of Partial Pressures

Q. For the reaction, $2HI\left(g\right)\rightleftharpoons H_2\left(g\right)+I_2\left(g\right)$ the degree of dissociation $\left(\alpha \right)$ of $HI$(g) is related to the equilibrium constant, $K_P$ by expression

1. $\alpha =\sqrt{\frac{2K_P}{1+2K_P}}$
2. $\alpha =\frac{2\sqrt{K_P}}{1+2\sqrt{K_P}}$
3. $\alpha =\sqrt{\frac{1+2K_P}{2}}$
4. $\alpha =\frac{1+2\sqrt{K_P}}{2\sqrt{K_P}}$

Q. Assume that you have a sample of a gas containing $H_2,HD$ and $D_2$ that you want to separate into pure components $(H={}^{1}H\text{and}D={}^{2}H)$. What are the relative rates of diffusion of the three gases according to Graham’s law?

1. $H_2>HD>D_2$
2. $D_2>HD>H_2$
3. $D_2>H_2>HD$
4. All have same rate

Q.

If a mixture of $C{O}_{2}and{N}_2$ in equal amount exert a total pressure of 1 atm, the partial pressure of $N_2$ in the mixture is –

1. 0.56 atm

2. 1 atm

3. 1.52 atm

4. 0.75 atm

Q.

Find total pressure observed after opening the stopcock . [neglecting the volume of the tube connecting the two bulbs]

1. 1.33 atm

2. 3 atm

3. 0.3 atm

4. 0.75 atm

Q. Two containers $C_1$ and $C_2$ are kept at a constant temperature T=300 K. Container $C_1$ has a volume of 2 litres and it contains Helium gas at a pressure of 10 atm while container $C_2$ has a volume of 8 litres and that contains Methane $\left(C{H}_4\right)$ gas at a pressure of 5 atm. Assume the effective radius of $C{H}_4$ gas molecule is 4 times that of a He gas molecule.

List-I contains questions related to gases in containers $C_1$ and $C_2$ and List-II contains their answer(s).

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \left(I\right)\text{When both the containers are connected with}& \left(P\right)4\\ \text{a thin tube, the final pressure will be (in atm)}& \\ \left(II\right)\text{The mole fraction of He gas when both}& \left(Q\right)\frac{1}{4}\\ \text{containers are connected with the thin tube}& \\ \left(III\right)\text{The ratio of the mean fee path of}C{H}_4\text{to He}& \left(R\right)\frac{1}{8}\\ \text{before connecting the containers}& \\ \left(IV\right)\text{The ratio of collision frequency of He to}C{H}_4& \left(S\right)\frac{2}{3}\\ \text{before connecting the containers}& \\ & \left(T\right)\frac{1}{3}\\ & \left(U\right)6\end{array}$

Which of the following options has the correct combination considering questions of List-I and answers of List-II

1. (I), (P) and (III), (Q)
2. (II), (S) and (I), (P)
3. (I), (U) and (III), (R)
4. (IV), (R) and (II), (T)

Q.

$n_1$ and $n_2$ moles of two ideal gases (mol. wt. $M_1$ and $M_2$) respectively at temperature $T_1$K and $T_2$K are mixed. Assuming that no loss of energy, the temperature of mixture becomes -

1. $\frac{n_1{T}_1+n_2{T}_2}{T_1+T_2}$

2. $n_1{T}_1+n_2{T}_2$

3. $\frac{n_1{T}_1+n_2{T}_2}{n_1+n_2}$

4. $\frac{n_1\times T_2}{n_1\times n_2}$

Q. 10 moles of a mixture of gases has three gases A, B and C at a total pressure of 10 atm. The partial pressures of A and B are 3 atm and 1 atm respectively. If C has a molecular weight of 2g /mol, then the weight of C present in the mixture will be:

1. 8 g
2. 12 g
3. 3 g
4. 6 g

Q.

A sample of $O_2$ gas is collected over water at ${23}^{\circ }$ C at a barometric pressure of 751 mm Hg (vapour pressure of water at ${23}^{\circ }$ C is 21 mm Hg). The partial pressure of $O_2$ gas in the sample collected is ......

1. 21 mm Hg

2. 751 mm Hg

3. 0.96 atm

4. 1.02 atm

Q. The pressure of a $1:4$ mixture by moles of dihydrogen and dioxygen enclosed in a vessel is one bar. What will be the partial pressure of dioxygen?

1. $0.8\times {10}^4\text{bar}$
2. $0.008N{m}^{-2}$
3. $8\times {10}^{4}N{m}^{-2}$
4. $0.08\text{bar}$

Q. A gaseous mixture containing $CO$, $C{H}_4$ and $N_2$ gas has total volume of 40 $mL$. This mixture is exploded with excess of oxygen, on cooling 30 $mL$ of contraction is observed and when this mixture is treated with aqueous $KOH$ a further contraction of 30 $mL$ is observed. Find the composition of the mixture in $mL$.

1. $CO=20,C{H}_4=10,N_2=10$
2. $CO=15,C{H}_4=15,N_2=10$
3. $CO=10,C{H}_4=15,N_2=15$
4. $CO=20,C{H}_4=15,N_2=5$

Q.

An empty container was filled with equal masses of methane and hydrogen gases. The fraction of total pressure exerted by hydrogen is____.

1. $\frac{1}{2}$

2. $\frac{8}{9}$

3. $\frac{1}{9}$

4. $\frac{16}{17}$

Q. What is the density of wet air (in $\text{g/L}$) that has the partial pressure of water of $22.5$ torr at $1$ atm and $300\text{K}$?
$($Given: vapour pressure of $H_{2}O$ is $30$ torr and the average molar mass of air is $29\text{g/mol})$

1. $1.164\text{g/L}$
2. $2.164\text{g/L}$
3. $3.164\text{g/L}$
4. $4.164\text{g/L}$

Q.

A mixture containing 1.6 g of $O_2$, 1.4 g of $N_2$ and 0.4 g of $He$ occupies a volume of $10L$ at ${27}^{\circ }C$. Calculate the partial pressure of each component of the mixture.

1. $P_{N_2}=0.500atm$
   $P_{O_2}=0.25atm$
   $P_{He}=0.25atm$
   
   

2. $P_{N_2}=0.246atm$
   $P_{O_2}=0.246atm$
   $P_{He}=0.492atm$
   
   

3. $P_{N_2}=0.123atm$
   $P_{O_2}=0.123atm$
   $P_{He}=0.246atm$

4. $P_{N_2}=1atm$
   $P_{O_2}=1.123atm$
   $P_{He}=2.246atm$
   

Q.

If a mixture of $C{O}_{2}and{N}_2$ in equal amount exert a total pressure of 1 atm, the partial pressure of $N_2$ in the mixture is –

1. 0.56 atm

2. 1 atm

3. 1.52 atm

4. 0.75 atm

Q.

An empty container was filled with equal masses of methane and hydrogen gases. The fraction of total pressure exerted by hydrogen is____.

1. $\frac{1}{2}$

2. $\frac{8}{9}$

3. $\frac{1}{9}$

4. $\frac{16}{17}$

Q. $O_2$ and $S{O}_2$ gases are filled in ratio of $1:3$ by moles in a closed container of $3\text{L}$ at temperature of ${27}^{\circ }\text{C}$. If the partial pressure of $O_2$ is $0.54\text{atm}$, then the concentration of $S{O}_2\left({\text{in mol L}}^{-1}\right)$ would be $(R=0.082{\text{L atm K}}^{-1}mo{l}^{-1})$

1. $0.66$
2. $0.066$
3. $6.6$
4. $66$

Q. When $N{O}_2$ is cooled to room temperature, some of it reacts to form a dimer $N_2{O}_4$ through the reaction,
$2N{O}_2\left(g\right)\to N_2{O}_4\left(g\right)$
In the reaction, $15.2\text{g}$ of $N{O}_2$ is placed in a $10.0\text{L}$ flask at high temperature and the flask is cooled to ${25}^{\circ }\text{C}$. The total pressure is measured to be $0.500\text{atm}$. Thus, the partial pressure of $N{O}_2$ is found to be:

1. 0.31 atm
2. 0.19 atm
3. 0.10 atm
4. 0.40 atm

Q. 10 moles of a mixture of gases has three gases A, B and C at a total pressure of 10 atm. The partial pressures of A and B are 3 atm and 1 atm respectively. If C has a molecular weight of 2g /mol, then the weight of C present in the mixture will be:

1. 8 g
2. 12 g
3. 3 g
4. 6 g

Q.

A sample of air contains nitrogen, oxygen and saturated with water vapour under a total pressure of 640 mm. If the vapour pressure of water at that temperature is 40 mm and the molecular ratio of $N_2:O_2$ is 3 : 1. Find the partial pressure of nitrogen in the sample.

1. 480 mm

2. 600 mm

3. 450 mm

4. 160 mm

Q. The pressure of $1\text{g}$ of an ideal gas $A$ at $300\text{K}$ is found to be 2 bar. When $2\text{g}$ of another ideal gas $B$ is introduced in the same flask at the same temperature, the pressure becomes 3 bar. Which of the following is correct?
($m_A$ = mass of gas A; $m_B$ = mass of gas B)

1. $m_B=4m_A$
2. $m_A=3m_B$
3. $m_B=3m_A$
4. $m_A=m_B$

Q. Consider the following equilibrium in a closed container:
$PC{l}_5\left(g\right)\rightleftharpoons PC{l}_3\left(g\right)+C{l}_2\left(g\right)$
$PC{l}_5$ gas at a certain pressure is introduced in the container at $27{}^{o}C$. However, the total pressure at equilibrium at $207{}^{o}C$ was found to be double the initial value. The % dissociation of $PC{l}_5$ at $207{}^{o}C$ is: %

Q. $O_2$ and $S{O}_2$ gases are filled in ratio of $1:3$ by moles in a closed container of $3\text{L}$ at temperature of ${27}^{\circ }\text{C}$. If the partial pressure of $O_2$ is $0.54\text{atm}$, then the concentration of $S{O}_2\left({\text{in mol L}}^{-1}\right)$ would be $(R=0.082{\text{L atm K}}^{-1}mo{l}^{-1})$

1. $0.66$
2. $0.066$
3. $6.6$
4. $66$

Q. A gaseous mixture containing $CO$, $C{H}_4$ and $N_2$ gas has total volume of 40 $mL$. This mixture is exploded with excess of oxygen, on cooling 30 $mL$ of contraction is observed and when this mixture is treated with aqueous $KOH$ a further contraction of 30 $mL$ is observed. Find the composition of the mixture in $mL$.

1. $CO=10,C{H}_4=15,N_2=15$
2. $CO=15,C{H}_4=15,N_2=10$
3. $CO=20,C{H}_4=15,N_2=5$
4. $CO=20,C{H}_4=10,N_2=10$

Q. A jar contains a gas and a few drops of water. The pressure in the jar is 830 mm of Hg. The temperature of the jar is reduced by $1\%$. The vapour pressure of water at two different temperatures is 30 and 25 mm Hg respectively. Calculate the new pressure in the jar.

1. 792 mm of Hg
2. 817 mm of Hg
3. 800 mm of Hg
4. 840 mm of Hg

Q. 10 moles of a mixture of gases has three gases A, B and C at a total pressure of 10 atm. The partial pressures of A and B are 3 atm and 1 atm respectively. If C has a molecular weight of 2g /mol, then the weight of C present in the mixture will be:

1. 8 g
2. 12 g
3. 3 g
4. 6 g

Q. A jar contains a gas and a few drops of water. The pressure in the jar is 830 mm of Hg. The temperature of the jar is reduced by $1\%$. The vapour pressure of water at two different temperatures is 30 and 25 mm Hg respectively. Calculate the new pressure in the jar.

1. 792 mm of Hg
2. 817 mm of Hg
3. 800 mm of Hg
4. 840 mm of Hg

Q.

A sample of $O_2$ gas is collected over water at ${23}^{\circ }$ C at a barometric pressure of 751 mm Hg (vapour pressure of water at ${23}^{\circ }$ C is 21 mm Hg). The partial pressure of $O_2$ gas in the sample collected is ......

1. 21 mm Hg

2. 751 mm Hg

3. 0.96 atm

4. 1.02 atm

Q.

$N_2$ is found in a litre flask under 100kPa pressure and $O_2$ is found in another 3 litre flask under 320 kPa pressure. If the two flasks are connected, the resultant pressures is

1. 310 kPa

2. 210 kPa

3. 420 kPa

4. 365 kPa

5. 265 kPa

Q. What is the density of wet air (in $\text{g/L}$) that has the partial pressure of water of $22.5$ torr at $1$ atm and $300\text{K}$?
$($Given: vapour pressure of $H_{2}O$ is $30$ torr and the average molar mass of air is $29\text{g/mol})$

1. $1.164\text{g/L}$
2. $2.164\text{g/L}$
3. $3.164\text{g/L}$
4. $4.164\text{g/L}$