Real Gases

Q. At high pressure, van der Waals' equation becomes:

1. $PV=RT+Pb$
2. $PV=RT$
3. $PV=RT+\frac{a}{V}$
4. $PV=RT-\frac{a}{V}$

Q. For different ideal gases $\left(d/P\right)$ versus $P$ variations at definite temperature is:

1. 
2. 
   
3. 
4. 

Q. The van der Waals’ constant ‘$b$’ of helium is $24{\text{mL mol}}^{-1}$. Find the molecular diameter of helium.

1. $1.335\times {10}^{-10}\text{cm}$
2. $1.335\times {10}^{-8}\text{cm}$
3. $2.670\times {10}^{-8}\text{cm}$
4. $4.340\times {10}^{-8}\text{cm}$

Q.

Write short notes on the behavior of real gases.

Q.

Calculate the pressure exerted by 5 mol of $C{O}_2$ in 1 L vessel at ${47}^{\circ }C$ using van der Waals equation. Also, calculate the pressure for an ideal gas. Given $a=3.592atm{L}^{2}mo{l}^{-2}$, b = 0.0427 L $mo{l}^{-1}$ .

1. 131.2 , 77.01

2. 69.83, 126.22

3. 77.01, 131.2

4. 114 , 122

Q. Which of the following gases will have a density of $1.8{\text{g L}}^{-1}$ at 760 torr pressure and ${27}^{\circ }\text{C}$?

1. $O_2$
2. $C{O}_2$
3. $N{H}_3$
4. $S{O}_2$

Q. A real gas obeying van der Waal equation will resemble ideal gas if the

1. a is large and b is small
2. constants a and b are large
3. a is small and b is large
4. constants a and b are negligibly small

Q. 1 mole of an aliphatic compound $C_3{H}_8$ is completely burnt in an excess of $O_2$. The reacted moles of oxygen are:

1. $5\text{mol}$
2. $2\text{mol}$
3. $8\text{mol}$
4. $3\text{mol}$

Q.

When is deviation more in the behaviour of a gas from the ideal gas equation PV=nRT

1. At high temperature and low pressure

2. At low temperature and high pressure

3. At high temperature and high pressure

4. At low temperature and low high pressure

Q.

Van der waals constant "b" of helium is $24mLmo{l}^{-1}$. Find molecular diameter of helium.

1. $1.335\times {10}^{-10}cm$

2. $1.35\times {10}^{-8}cm$

3. $2.67\times {10}^{-8}cm$

4. $4.34\times {10}^{-8}cm$

Q. Gases $X,Y,Z,P$ and $Q$ have their van der Waals' constants ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ (in CGS units) as shown below:
$\begin{array}{cccccc}& X& Y& Z& P& Q\\ a& 6& 6& 20& 0.05& 30\\ b& 0.025& 0.15& 0.1& 0.02& 0.2\end{array}$
The gas with the highest critical temperature is:

1. $P$
2. $Q$
3. $Y$
4. $Z$
5. $X$

Q.

If v is the volume of one molecule of a gas under given conditions then va der Waals' constant b is

1. $4v$

2. $152$

3. $\frac{N_0}{4v}$

4. $4v{N}_0$

Q.

Which of the following graphs correctly represents the variation of $\beta$ = - $(\frac{\frac{dV}{dP}}{V}{)}_{\gamma }$ with P for an ideal gas at constant temperature.

1. 

2. 

3. 

4. 

Q. 1 mole of each of $X_1,X_2$ and $X_3$, with van der Waals’ constant ‘$a$’ (in $\left({\text{atm L}}^2{\text{mol}}^{(-2)}\right)$ 1.0, 3.8 and 2.1, respectively are kept separately in three different vessels of equal volume at the same temperature. Their pressures are observed to be $P_1,P_2$, and $P_3$ respectively. On the basis of this data alone, select the correct option (neglect the effect of ‘$b$’):

1. $P_1<P_2<P_3$
2. $P_2<P_1<P_3$
3. $P_2<P_3<P_1$
4. $P_1=P_2=P_3$

Q. 1 mole of a gaseous compound $C_5{H}_{10}$ is completely burnt in excess of $O_2$. The moles of $C{O}_2$ formed are:

1. $5\text{mol}$
2. $7\text{mol}$
3. $3\text{mol}$
4. $2\text{mol}$

Q.

Give any two examples of gases.

Q.

Gas deviates from ideal gas nature because molecules

1. Are colourless

2. Attract each other

3. Contain covalent bond

4. Show Brownian movement

Q. For different ideal gases $\left(d/P\right)$ versus $P$ variations at definite temperature is:

1. 
2. 
3. 
   
4. 

Q.

Calculate the pressure exerted by 5 mol of $C{O}_2$ in 1 L vessel at ${47}^{\circ }C$ using van der Waals equation. Also, calculate the pressure for an ideal gas. Given $a=3.592atm{L}^{2}mo{l}^{-2}$, b = 0.0427 L $mo{l}^{-1}$ .

1. 131.2 , 77.01

2. 69.83, 126.22

3. 77.01, 131.2

4. 114 , 122

Q.

Which of the given sets of temperature and pressure will cause a gas to exhibit the greatest deviation from ideal gas behavior

1. 100${}^{\circ }$ C and 4 atm

2. 100${}^{\circ }$ C and 2 atm

3. -100${}^{\circ }$ C and 4 atm

4. 0${}^{\circ }$ C and 2 atm

Q.

A real gas most closely approaches the behaviour of an ideal gas at

1. 15 atm and 200 K

2. 1 atm and 273 K

3. 0.5 atm and 500 K

4. 15 atm and 500 K

Q. $\begin{array}{cc}\text{Column -I}& \text{Column -II}\\ \left(A\right)P{V}^{(}\gamma )\text{Constant}& \text{(p)Expansion of ideal gas in vacuum}\\ \left(B\right)\Delta T=0& \text{(q)}Z=1-\frac{a}{V_{m}RT}\\ \text{(C) For}{H}_2\text{and He at}{0}^{\circ }C& \text{(r) Adiabatic reversible process}\\ \text{(C) At low density of gas}& \left(s\right)Z=1+\frac{pb}{RT}\end{array}$

1. $A\to R$, $B\to P$, $C\to S$, $D\to Q$
2. $A\to Q$, $B\to R$, $C\to S$, $D\to P$
3. $A\to P$, $B\to R$, $C\to S$, $D\to Q$
4. $A\to Q$, $B\to P$, $C\to S$, $D\to R$

Q. Positive deviation from ideal gas behavior takes place because of

1. Molecular interaction and $\frac{PV}{nRT}>1$
2. Molecular interaction and $\frac{PV}{nRT}<1$
3. Finite atomic size and $\frac{PV}{nRT}>1$
4. Finite atomic size and $\frac{PV}{nRT}<1$

Q. An element crystallises into a structure which may be described by a cubic unit cell having one atom at each corner of the cube and two atoms on one of its diagonals. If the volume of this unit cell is $24\times {10}^{-24}{\text{cm}}^3$ and density of element is $7.2{\text{g/cm}}^3$. Calculate the number of atoms present in $200\text{g}$ of the element.

Q. 1 mole of each of $X_1,X_2$ and $X_3$, with van der Waals’ constant ‘$a$’ (in $\left({\text{atm L}}^2{\text{mol}}^{(-2)}\right)$ 1.0, 3.8 and 2.1, respectively are kept separately in three different vessels of equal volume at the same temperature. Their pressures are observed to be $P_1,P_2$, and $P_3$ respectively. On the basis of this data alone, select the correct option (neglect the effect of ‘$b$’):

1. $P_1<P_2<P_3$
2. $P_2<P_1<P_3$
3. $P_2<P_3<P_1$
4. $P_1=P_2=P_3$

Q. Which of the following statement(s) is/are true regarding Freundlich adsorption isotherm?

Q. $50\text{ml}$ of a mixture of $N{H}_3$ and $H_2$ was completely decomposed by sparking into nitrogen and hydrogen. $40\text{ml}$ of oxygen was added and the mixture was sparked again. After cooling to the room temperature, the mixture was shaken with alkaline pyrogallol solution and a contraction of $6\text{ml}$ was observed. Calculate the % by volume of $N{H}_3$ in the original mixture.

1. 36%
2. 54%
3. 27%
4. 72%

Q. For a gas, the deviation from ideal behavior is maximum at:

1. $0^{\circ }\text{C and}1.0\text{atm}$
2. ${100}^{\circ }\text{C and}2.0\text{atm}$
3. $-{13}^{\circ }\text{C and}1.0\text{atm}$
4. $-{13}^{\circ }\text{C and}2.0\text{atm}$

Q. 1.25 moles of a gas A and y moles of a gas B exert a pressure of 300 Pa in a container of volume $10m^3$ at $1000K$. Find the value of y in terms of R (where R is the gas constant in $J{K}^{-1}mo{l}^{-1}$ )

1. $\frac{12}{5R}$
2. $\frac{3}{R}$
3. $\frac{12-5R}{4R}$
4. $\frac{15-4R}{5R}$

Q.

At high temperature, van der Waal’s equation can be expressed as

1. $PV=RT$

2. $PV=nRT$

3. $Bothaandb$

4. $(P+\frac{a{n}^2}{v^2})(V-nb)=nRT$