Q: The gas with the highest critical temperature is

Critical temperature \$\left( T \right) \$ is the measure of intermolecular forces of attraction. The order of the critical temperature of the given gases is as\$\begin{matrix} \quad \\ { T }_{ c }\left( K \right) \end{matrix}\begin{matrix} C{ O }_{ 2 } \\ 304.2K \end{matrix}\begin{matrix} > \\ \quad \end{matrix}\begin{matrix} { O }_{ 2 } \\ \left( 154.3K \right) \end{matrix}\begin{matrix} > \\ \quad \end{matrix}\begin{matrix} { N }_{ 2 } \\ \left( 126.2K \right) \end{matrix}\begin{matrix} > \\ \quad \end{matrix}\begin{matrix} { H }_{ 2 } \\ \left( 33.2K \right) \end{matrix}\begin{matrix} > \\ \quad \end{matrix}\begin{matrix} He \\ \left( 5.2K \right) \end{matrix}\$

Q: At 100\$^0\$C and 1 atm, if the density of liquid water is \$1.0\ g\ { cm }^{ -3 }\$ and that of water vapour is \$0.0006\ g\ { cm }^{ -3 }\$, then the volume occupied by water molecules in one litre of steam at that temperature is :

Density of liquid water \$={1gcm}^{-3}\$Density of water vapour \$={0.0006gcm}^{-3}\$Mass of \$1000\ ml\$ stream \$=1000\times 0.0006=0.6g\$\$\because\$ Volume of liquid water \$=\cfrac {\text{mass of 1000ml stream}}{\text{density of liquid water}}\$\$V=\cfrac {0.6g}{1\ g.cm^{-3}}\$\$V=0.6cm^3\$\$\therefore\$ The answer is option C.

Q: The ratio of Boyle's temperature and critical temperature for a gas is:

\$\displaystyle T_B= \dfrac {a}{bR}\$\$\displaystyle T_C= \dfrac {8}{27} \dfrac {a}{bR}\$\$\displaystyle T_C =\dfrac {8}{27}T_B\$\$\displaystyle \dfrac {T_B}{T_C}=\dfrac {27}{8}\$The ratio of Boyle's temperature and critical temperature for gas is \$\displaystyle \dfrac {27}{8}\$.Hence, option B is correct.

Q: The relationship between \$P_c, V_c\$ and \$T_c\$ is:

\$T_c=\$ Temperature at and above which the vapour state can not be further liquified. \$P_c=\$ Pressure of gas in its critical state\$V_c=\$ Volume of gas in its critical state. relation with the van der waals constants -\$T_c = 8a / 27 Rb\$ So \$a=27T_cRb/8\$\$V_c = 3b\$ So \$b=V_c/3\$ \$P_c = a / 27 b^2\$ ....(1)put the value of a and b in equation (1)\$P_c = \dfrac{27T_c\times R\times b}{8\times 27\times b^2}\$\$P_c = \dfrac{27T_c.R}{8\times 27\times b}= \dfrac{27T_c.R}{8\times 27\times V_c/3}\$\$P_cV_c = \dfrac{3}{8}RT_c\$

Q: Consider the van der Waals constants, \$a\$ and \$b\$, for the following gases.Gas\$Ar\$\$Ne\$\$Kr\$\$Xe\$a/(atm \${dm}^{6}{mol}^{-2}\$1.30.25.14.1b/(\${10}^{-2}{dm}^{3}{mol}^{-1}\$3.21.71.05.0Which gas is expected to have the highest critical temperature?

\$T_C= \dfrac{8a}{27Rb}\$Greater value of \$\cfrac ab\$ higher is \$T_c\$Gas \$\dfrac{a}{b}\$Ar = \$\dfrac {1.3}{3.2}=0.406\$Ne=\$\dfrac{0.2}{1.7}=0.118\$Kr=\$\dfrac{5.1}{1}=5.1\$Xe=\$\dfrac{4.1}{5}=0.82\$\$\because T_c\$ has order: \$Kr>Xe>Ar>Ne\$

Question 1

$T_C$ and $ P_c$ of a gas are 400 K and 41 atm respectively. The $V_c$ is:

Accepted Answer

The critical temperature is the temperature above which a gas cannot be liquified. It is denoted as $T_c$.$P_c$ is the Critical pressure, $V_c$ is the critical molar volume$V_c = 3b$  (from Ideal gas law)&#8203;and $b = \dfrac{RT_c}{8p_c}=\dfrac{R \times 400}{8\times 41}=\dfrac{50R}{41}$ $V_c = 3 \times \dfrac{50R}{41} = \dfrac{150R}{41}$Hence, option $B$ is correct.

Question 2

Which among the following gases can be liquified easily?

Accepted Answer

A gas can be liquified when its temperature is below the critical temperature, by cooling or compressing it.Gases which have high critical temperatures (such as ${Cl}_{2}, N{H}_{3}, C{O}_{2}, S{O}_{2}$ etc.,) can be liquified by applying a suitable pressure alone. Permanent gases (such as ${H}_{2},  {N}_{2},  {O}_{2}$ etc.,) cannot be liquified by the action of pressure and cooling.Hence, option A is correct.

Question 3

The gas with the highest critical temperature is

Accepted Answer

Critical temperature $\left( T \right) $ is the measure of &#10;intermolecular forces of attraction. The order of the critical &#10;temperature of the given gases is as$\begin{matrix} \quad  \ { T &#10;}_{ c }\left( K \right)  \end{matrix}\begin{matrix} C{ O }_{ 2 } \ &#10;304.2K \end{matrix}\begin{matrix} > \ \quad &#10; \end{matrix}\begin{matrix} { O }_{ 2 } \ \left( 154.3K \right) &#10; \end{matrix}\begin{matrix} > \ \quad  \end{matrix}\begin{matrix} { N&#10; }_{ 2 } \ \left( 126.2K \right)  \end{matrix}\begin{matrix} > \ &#10;\quad  \end{matrix}\begin{matrix} { H }_{ 2 } \ \left( 33.2K \right) &#10; \end{matrix}\begin{matrix} > \ \quad  \end{matrix}\begin{matrix} He&#10; \ \left( 5.2K \right)  \end{matrix}$

Question 4

At 100$^0$C and 1 atm, if the density of liquid water is $1.0\ g\ { cm }^{ -3 }$ and that of water vapour is $0.0006\ g\ { cm }^{ -3 }$, then the volume occupied by water molecules in one litre of steam at that temperature is :

Accepted Answer

Density of liquid water $={1gcm}^{-3}$Density of water vapour $={0.0006gcm}^{-3}$Mass of $1000\ ml$ stream $=1000\times 0.0006=0.6g$$\because$ Volume of liquid water $=\cfrac {\text{mass of 1000ml stream}}{\text{density of liquid water}}$$V=\cfrac {0.6g}{1\ g.cm^{-3}}$$V=0.6cm^3$$\therefore$ The answer is option C.

Question 5

The ratio of Boyle's temperature and critical temperature for a gas is:

Accepted Answer

$\displaystyle T_B= \dfrac {a}{bR}$$\displaystyle T_C= \dfrac {8}{27} \dfrac {a}{bR}$$\displaystyle T_C =\dfrac {8}{27}T_B$$\displaystyle \dfrac {T_B}{T_C}=\dfrac {27}{8}$The ratio of Boyle's temperature and critical temperature for gas is $\displaystyle \dfrac {27}{8}$.Hence, option B is correct.

Question 6

The relationship between $P_c, V_c$ and $T_c$ is:

Accepted Answer

$T_c=$ Temperature at and above which the vapour state can not be further liquified. $P_c=$ Pressure of gas in its critical state$V_c=$ Volume of gas in its critical state. relation with the van der waals constants -$T_c = 8a / 27 Rb$ So $a=27T_cRb/8$$V_c = 3b$ So $b=V_c/3$ $P_c = a / 27 b^2$ ....(1)put the value of a and b in equation (1)$P_c = \dfrac{27T_c\times R\times b}{8\times 27\times b^2}$$P_c = \dfrac{27T_c.R}{8\times 27\times b}= \dfrac{27T_c.R}{8\times 27\times V_c/3}$$P_cV_c = \dfrac{3}{8}RT_c$

Question 7

Consider the van der Waals constants, $a$ and $b$ , for the following gases.

Gas $A r$ $N e$ $K r$ $X e$
a/(atm $d m^{6} m o l^{- 2}$ 1.3 0.2 5.1 4.1
b/( $10^{- 2} d m^{3} m o l^{- 1}$ 3.2 1.7 1.0 5.0
Which gas is expected to have the highest critical temperature?

Accepted Answer

$T_C= \dfrac{8a}{27Rb}$Greater value of $\cfrac ab$  higher is $T_c$Gas $\dfrac{a}{b}$Ar = $\dfrac {1.3}{3.2}=0.406$Ne=$\dfrac{0.2}{1.7}=0.118$Kr=$\dfrac{5.1}{1}=5.1$Xe=$\dfrac{4.1}{5}=0.82$$\because T_c$ has order: $Kr>Xe>Ar>Ne$

Question 8

Critical temperature of $H_2O, NH_3, CO_2$ and $O_2$ are $647 K, 405.6 K, 304.10 K$ and $154.2 K$ respectively. If the cooling starts from $500 \,K$ to their temperature, the gas that liquefies first is:

Accepted Answer

Critical Temperature of the gas in critical state, above which it cannot be liquefied  by pressure. Here, cooling starts from 500 K to critical temperature. So, $H_{2} O$ will liquefied first due to it's maximum critical temperature value.

Question 9

Critical temperature for carbon dioxide and methane are $31.1^{\circ}C$ and $-81.9^{\circ}C$ respectively. Which of these has stronger intermolecular forces and why?

Accepted Answer

Higher is the critical temperature, more easily the gas can be liquefied and greater are the intermolecular forces of attraction. Hence, $\displaystyle CO_2$ has stronger intermolecular forces than $\displaystyle H_2O$.

Question 10

Define critical temperature of a gas. Give its expression.

Accepted Answer

Critical temperature of a gas is the temperature at or above which vapor of the gas cannot be liquefied, no matter how much pressure is applied. ${ T }_{ c }=\cfrac { 8a }{ 27Rb } $, $a$ and $b$ are specific constants for each gas.

Revise with Concepts

Liquefaction of Gases

Quick Summary With Stories

Andrews Isotherm of Carbon Dioxide

$T_{C}$ and $P_{c}$ of a gas are 400 K and 41 atm respectively. The $V_{c}$ is:

Which among the following gases can be liquified easily?

The gas with the highest critical temperature is

At 100 $^{0}$ C and 1 atm, if the density of liquid water is $1.0 g c m^{- 3}$ and that of water vapour is $0.0006 g c m^{- 3}$ , then the volume occupied by water molecules in one litre of steam at that temperature is :

The ratio of Boyle's temperature and critical temperature for a gas is:

The relationship between $P_{c}, V_{c}$ and $T_{c}$ is:

Consider the van der Waals constants, $a$ and $b$ , for the following gases.

Gas $A r$ $N e$ $K r$ $X e$
a/(atm $d m^{6} m o l^{- 2}$ 1.3 0.2 5.1 4.1
b/( $10^{- 2} d m^{3} m o l^{- 1}$ 3.2 1.7 1.0 5.0
Which gas is expected to have the highest critical temperature?

Critical temperature of $H_{2} O, N H_{3}, C O_{2}$ and $O_{2}$ are $647 K, 405.6 K, 304.10 K$ and $154.2 K$ respectively. If the cooling starts from $500 K$ to their temperature, the gas that liquefies first is:

Critical temperature for carbon dioxide and methane are $31 . 1^{\circ} C$ and $- 81 . 9^{\circ} C$ respectively. Which of these has stronger intermolecular forces and why?

Define critical temperature of a gas. Give its expression.

Gas	$A r$	$N e$	$K r$	$X e$
a/(atm $d m^{6} m o l^{- 2}$	1.3	0.2	5.1	4.1
b/( $10^{- 2} d m^{3} m o l^{- 1}$	3.2	1.7	1.0	5.0

Revise with Concepts

Liquefaction of Gases

Quick Summary With Stories

Andrews Isotherm of Carbon Dioxide

TC​ and Pc​ of a gas are 400 K and 41 atm respectively. The Vc​ is:

Which among the following gases can be liquified easily?

The gas with the highest critical temperature is

At 1000C and 1 atm, if the density of liquid water is 1.0 g cm−3 and that of water vapour is 0.0006 g cm−3, then the volume occupied by water molecules in one litre of steam at that temperature is :

The ratio of Boyle's temperature and critical temperature for a gas is:

The relationship between Pc​,Vc​ and Tc​ is:

Consider the van der Waals constants, a and b, for the following gases. GasArNeKrXea/(atm dm6mol−21.30.25.14.1b/(10−2dm3mol−13.21.71.05.0Which gas is expected to have the highest critical temperature?

Critical temperature of H2​O,NH3​,CO2​ and O2​ are 647K,405.6K,304.10K and 154.2K respectively. If the cooling starts from 500K to their temperature, the gas that liquefies first is:

Critical temperature for carbon dioxide and methane are 31.1∘C and −81.9∘C respectively. Which of these has stronger intermolecular forces and why?

Define critical temperature of a gas. Give its expression.

$T_{C}$ and $P_{c}$ of a gas are 400 K and 41 atm respectively. The $V_{c}$ is:

At 100 $^{0}$ C and 1 atm, if the density of liquid water is $1.0 g c m^{- 3}$ and that of water vapour is $0.0006 g c m^{- 3}$ , then the volume occupied by water molecules in one litre of steam at that temperature is :

The relationship between $P_{c}, V_{c}$ and $T_{c}$ is:

Consider the van der Waals constants, $a$ and $b$ , for the following gases.

Gas $A r$ $N e$ $K r$ $X e$
a/(atm $d m^{6} m o l^{- 2}$ 1.3 0.2 5.1 4.1
b/( $10^{- 2} d m^{3} m o l^{- 1}$ 3.2 1.7 1.0 5.0
Which gas is expected to have the highest critical temperature?

Critical temperature of $H_{2} O, N H_{3}, C O_{2}$ and $O_{2}$ are $647 K, 405.6 K, 304.10 K$ and $154.2 K$ respectively. If the cooling starts from $500 K$ to their temperature, the gas that liquefies first is:

Critical temperature for carbon dioxide and methane are $31 . 1^{\circ} C$ and $- 81 . 9^{\circ} C$ respectively. Which of these has stronger intermolecular forces and why?