Real Gas Equation

Q. $1$ mole of real gas $(a=1.4)$ occupies a volume of $0.1\text{L}$ at $300\text{K}$, then what will be the pressure of gas?

1. $2460\text{atm}$
2. $2320\text{atm}$
3. $106\text{atm}$
4. $212\text{atm}$

Q. Match the Van der Waal's for one $\text{mole}$ of gas given in column $2$ to the conditions in column $1$.
$$\begin{array}{cccc}& \text{Column 1}& & \text{Column 2}\\ A& \text{At low pressure}& i& P(V-b)=RT\\ B& \text{At high pressure}& ii& (P+\frac{a}{V^2})V=RT\\ C& \text{At low pressure and high temperature}& iii& PV=RT\\ D& \text{At room temperature and pressure}& iv& (P+\frac{a}{V^2})(V-b)=RT\end{array}$$

1. $A-\left(i\right);B-\left(ii\right);C-\left(iii\right);D-\left(iv\right)$
2. $A-\left(ii\right);B-\left(i\right);C-\left(iii\right);D-\left(iv\right)$
3. $A-\left(iv\right);B-\left(iii\right);C-\left(ii\right);D-\left(i\right)$
4. $A-\left(iii\right);B-\left(ii\right);C-\left(i\right);D-\left(iv\right)$

Q. Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

1. $2060$
2. $2500$
3. $3000$
4. $3200$

Q. At S.T.P, the volume of $1\text{mole}$ of gas is measured to be $25\text{litres}$ then nature of gas and type of force dominating are

1. Real gas with + ve deviation, repulsive force.
2. Real gas with -ve deviation, attractive force.
3. Real gas with +ve deviation, attractive force.
4. Real gas with -ve deviation, repulsive force.

Q. Which of the following gases can be most easily liquified? Given, the value of $a$ in van der Waals equation for $N{H}_3=4.17,C{O}_2=3.59,S{O}_2=6.71\&C{l}_2=6.49$

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

Q. For one mole of a van der Waals gas for which $b=0$ and $T=300\text{K}$, the $PV\text{vs}\frac{1}{V}$ plot is shown below. The value of the van der Waals constant $a$ (in ${\text{atm L mol}}^{-2}$) is:

1. $1.0$
2. $4.5$
3. $1.5$
4. $3.0$

Q. At relatively high pressure, van der Waals equation reduces to

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

Q. The value of ${}^{\prime }{a}^{\prime }$ in Van der Waal's equation for the gases $O_2,N_2,N{H}_3$ and $C{H}_4$ are $1.35,1.38,4.16$ and $2.25$ respectively. The gas which can most easily be liquified is

1. $O_2$
2. $N_2$
3. $N{H}_3$
4. $C{H}_4$

Q. Under which of the following conditions is the law $PV=RT$ obeyed most closely by a real gas?

1. High pressure and high temperature
2. Low pressure and low temperature
3. Low pressure and high temperature
4. Double the temperature, double the pressure

Q. Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

1. $2060$
2. $2500$
3. $3000$
4. $3200$

Q. Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

1. $2060$
2. $2500$
3. $3000$
4. $3200$

Q. $1$ mole of real gas $(a=1.4)$ occupies a volume of $0.1\text{L}$ at $300\text{K}$, then what will be the pressure of gas?

1. $2460\text{atm}$
2. $2320\text{atm}$
3. $106\text{atm}$
4. $212\text{atm}$

Q.

The Bat Life: Batman is undercover, and to prevent anyone from recognizing his voice (or Bruce Wayne's) he inhales a very dilute Helium gas (search YouTube for "voice after helium” to see the effects). The helium is stored ina cylindrical chamber as shown.

During a fight one of the steel balls gets dislodged. What will happen to the piston?

1. It will move down

2. It will move up

3. It will remain in the same place

4. Not enough information, only Batman will know