Liquefaction of Gases and Critical Constants

Q.

Calculate the number of moles of gas present in the container of volume $10L$ at $300K$. If the manometer containing glycerin shows $5\text{m}$ difference in level as shown in the diagram. calculate your answers up to two decimal points.

(Given: $d_{\text{glycerin}}=2.72\text{g/mL};d_{\text{mercury}}=13.6\text{g/mL}\text{Tale}R=0.08Latmmo{l}^{-1}{K}^{-1}$)

Q. $T_c$ and $P_c$ of a gas are $400\text{K}$ and $41$ atm respectively, $V_c$ is:

1. $\frac{400R}{41}$
2. $\frac{150R}{41}$
3. $\frac{300R}{41}$
4. $\frac{41R}{400}$

Q. The van der Waals’ constants for a gas are; $a=3.6{\text{atm L}}^2{\text{mol}}^2$, $b=0.6{\text{L mol}}^{-1}$. If $R=0.08{\text{L atm K}}^{-1}$. If the Boyle's temperature $\left(K\right)$ of this gas is $T_B$, then what is the value of $\frac{T_B}{15}$?

Q. Which of the following is not correct for critical temperature?

1. It is the highest temperature at which liquid and vapour can
   co-exist.
2. Beyond this temperature, a gas cannot be liquefied by compression.
3. At this temperature, the surface tension of the system is zero.
4. At this temperature, the gas and the liquid phases have different critical densities.

Q. The value of $\frac{RT}{PV}$ for a gas at critical condition is how many times of $\frac{RT}{PV}$ at normal condition?

1. $\frac{8}{3}$
2. $\frac{3}{8}$
3. $3$
4. $\frac{1}{3}$

Q. Which of the following gases will have a density of $1.9{\text{g L}}^{-1}$ at 1520 torr pressure and $87{}^{\circ }\text{C}$?

1. $O_2$
2. $S{O}_2$
3. $N_2$
4. $C{O}_2$

Q. Critical temperature and critical pressure values of four gases are given

$\begin{array}{ccc}\text{Gas}& \text{C. Temp (K)}& \text{C. Pressure (atm)}\\ P& 5.1& 2.2\\ Q& 33& 13\\ R& 126& 34\\ S& 135& 40\end{array}$

Which of the gas/gases cannot be liquefied at a temperature of 100 K and a pressure of 50 atmospheres?

1. S only
2. P only
3. R and S
4. P and Q

Q. 400 mL of hydrogen gas at a pressure of 300 mm $Hg$ and 200 mL of hydrogen chloride gas at a pressure of 600 mm $Hg$ are mixed in a one litre evacuated flask. Calculate the resulting pressure (in $\text{mm Hg}$) of the mixture at the same temperature.

Q. The vapours of phosphine gas at ${27}^{\circ }\text{C}$ and 3 bar pressure has a density of:

1. $4.09{\text{g mL}}^{-1}$
2. $4.14{\text{g L}}^{-1}$
3. $4.14{\text{kg L}}^{-1}$
4. $2.04{\text{g L}}^{-1}$

Q. For Argon, the critical point occurs at a pressure $P_C=4.83mPa$ and temperature $T_c=151K$

Estimate the diameter of an Ar atom.

Q. The vapours of phosphine gas at ${27}^{\circ }\text{C}$ and 3 bar pressure has a density of:

1. $4.14{\text{g L}}^{-1}$
2. $4.14{\text{kg L}}^{-1}$
3. $2.04{\text{g L}}^{-1}$
4. $4.09{\text{g mL}}^{-1}$

Q.

The critical temperature of ammonia and hydrogen are 405.5K and 33.2K respectively. Ammonia can be liquefied at room temperature just by compression of the gas at high pressure. Liquifaction of hydrogen , on the other hand, requires cooling as well as compression. (True/False)

1. True

2. False

Q.

The van der Waals' parameters for gases W, X, Y and Z are

$\begin{array}{ccc}Gas& a(litr{e}^2-atom/mo{l}^2)& b\left(litre/mol\right)\\ W& 4.0& 0.027\\ X& 8.0& 0.030\\ Y& 6.0& 0.032\\ Z& 12.0& 0.027\end{array}$

Which one of these gases has the highest critical temperature?

1. W

2. X

3. Y

4. Z

Q. An ideal gas obeying kinetic theory of gases can be liquefied if:

1. Its temperature is more than critical temperature $T_c$
2. Its pressure is more than critical pressure $P_c$
3. Its pressure is more than $P_c$ at a temperature less than $T_c$
4. It cannot be liquefied at any value of P and T

Q. At critical point in Andrews isotherm which of the following is a correct statement:

1. Liquid - vapor equilibrium exist
2. Substance may change from liquid to gas phase
3. Substance may change from gas to liquid phase
4. All of the above

Q. Which of the following is not correct for critical temperature?

1. It is the highest temperature at which liquid and vapour can
   co-exist.
2. Beyond this temperature, a gas cannot be liquefied by compression.
3. At this temperature, the surface tension of the system is zero.
4. At this temperature, the gas and the liquid phases have different critical densities.

Q.

The temperature at which a real gas obeys the ideal gas law over an appreciable range of pressure is called:

1. Boyle point

2. Boyle temperature

3. Both a and b

4. Neither a nor b

Q. Critical temperature and critical pressure values of four gases are given

$\begin{array}{ccc}\text{Gas}& \text{C. Temp (K)}& \text{C. Pressure (atm)}\\ P& 5.1& 2.2\\ Q& 33& 13\\ R& 126& 34\\ S& 135& 40\end{array}$

Which of the gas/gases cannot be liquefied at a temperature of 100 K and a pressure of 50 atmospheres?

1. S only
2. P only
3. R and S
4. P and Q

Q. For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to liquefaction. Choose the correct statement

1. At $T=500K$, $P=40atm$, the state will be liquid
2. At $T=300K$, $P=50atm$, the state will be gas
3. At $T<300K$, $P=20atm$, the state will be gas
4. At $300K<T<500K,P>50atm$, the state will be liquid

Q.

The temperature to which a gas must be cooled before it can be liquefied by compression is called as___.

1. Boyle's temperature

2. Critical temperature

3. Liquefaction temperature

4. Inversion temperature

Q.

Consider the following statements. The Van der Walls parameters are given as:

Select the correct alternates.

1. A alone

2. A and B

3. A, B and C

4. B and C

Q. Atmospheric pressures recorded in different cities are as follows:

$\begin{array}{ccccc}Cities& Mussorie& Bangalore& Delhi& Goa\\ Pin\left(N/m^2\right)& 1.01\times {10}^5& 1.2\times {10}^5& 1.02\times {10}^5& 1.21\times {10}^5\end{array}$

Consider the above data and mark the place at which liquid will boil first.

1. Mussorie
2. Bangalore
3. Delhi
4. Goa

Q. The vapours of phosphine gas at ${27}^{\circ }\text{C}$ and 3 bar pressure has a density of:

1. $4.09{\text{g mL}}^{-1}$
2. $4.14{\text{g L}}^{-1}$
3. $4.14{\text{kg L}}^{-1}$
4. $2.04{\text{g L}}^{-1}$

Q. The van der Waals’ constants for a gas are; $a=3.6{\text{atm L}}^2{\text{mol}}^2$, $b=0.6{\text{L mol}}^{-1}$. If $R=0.08{\text{L atm K}}^{-1}$. If the Boyle's temperature $\left(K\right)$ of this gas is $T_B$, then what is the value of $\frac{T_B}{15}$?

Q. Assertion (A): Gases do not liquefy above their critical temperature, even on applying high pressure.
Reason (R): Above critical temperature, the molecular speed is high and intermolecular attractions cannot hold the molecules together because they escape because of high speed.

1. Both A and R are true and R is the correct expalanation of A.
2. Both A and R are true but R is not the correct explanation of A.
3. A is true but R is false.
4. A is false but R is true.

Q.

Calculate the volume occupied by 16 gram $O_2$ at 300 K and 8.31 Mpa if $\frac{P_{c}V}{R{T}_c}=\frac{3}{8}and\frac{P_r{V}_r}{T_r}=2.21⟮:R=8.314\frac{Mpa}{K-mol}⟯$

1. 124.31 lit

2. 124.31 mL

3. 248.62 mL

4. 248.62 L

Q.

The critical temperature of a gas is that temperature:

1. Above which it cannot remain a gas

2. Above which it cannot be liquefied by pressure

3. At which it solidifies

4. At which the volume becomes 0

Q. Assertion: Greater the value of van der Waals constant ‘a’ greater is the liquefaction of gas.
Reason: ‘a’ indirectly measures the magnitude of attractive forces between the molecules.

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1. Both assertion and reason are false.
2. Both assertion and reason are true and reason is the correct explanation of assertion.
3. Assertion is true but reason is false.
4. Both assertion and reason are true but reason is not the correct explanation of assertion.

Q. The van der Waal gas constant 'a' is given by which of the following relations?

1. $\frac{V_c}{3}$
2. $\frac{R{T}_c}{8P_c}$
3. $9R{T}_c{V}_c$
4. $3P_c{V}_c^2$

Q. Which of the following statement(s) is/are true:
I - Slope of isotherm at critical point is maximum.
II - Larger the value of $T_c$, easier is the liquefaction of gas.
III - van der Waals' equation of state is applicable below critical temperature at all pressures.

1. Only I
2. I & II
3. II & III
4. Only II