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1

### AIPMT 2012 Mains

Equal volumes of two monoatomic gases, A and B at same temperature and pressure are mixed. The ratio of specific heats (Cp/Cv) of the mixture will be
A
0.83
B
1.50
C
3.3
D
1.67

## Explanation

Cp for monoatomic gas mixture of same volume = $${5 \over 2}R$$

$$\therefore$$ CV = $${3 \over 2}R$$

$$\Rightarrow {{{C_P}} \over {{C_V}}} = {{{5 \over 2}R} \over {{3 \over 2}R}} = {5 \over 3} = 1.67$$
2

### AIPMT 2012 Mains

For real gases van der Waals equation is written as

$$\left( {p + {{a{n^2}} \over {{V^2}}}} \right)$$ (V $$-$$ nb) = n RT
where $$a$$ and $$b$$ are van der Waals constants. Two sets of gases are
(I)  O2, CO2, H2 and He
(II)  CH4. O2 and H2

The gases given in set-I in increasing order of b and gases given in set-II in decreasing order of $$a$$, are arranged below. Select the correct order from the following
A
(I) He < H2 < CO2 < O2   (II) CH4 > H2 > O2
B
(I) O2 < He < H2 < CO2   (II) H2 > O2 > CH4
C
(I) H2 < He < O2 < CO2   (II) CH4 > O2 > H2
D
(I) H2 < O2 < He < CO2   (II) O2 > CH4 > H2

## Explanation

Van der Waal gas constant '$$a$$' represent intermolecular force of attraction of gaseous molecules and Van der Waal gas constant 'b' represent effective size of molecules . Therefore order should be

(I) H2 < He < O2 < CO2   (II) CH4 > O2 > H2
3

### AIPMT 2012 Mains

A certain gas takes three times as long to effuse out as helium. Its molecular mass will be
A
27 u
B
36 u
C
64 u
D
9 u

## Explanation

According to Graham's law of diffusion

$$r \propto {1 \over {\sqrt d }} \propto {1 \over {\sqrt M }}$$

$$\Rightarrow {{{r_1}} \over {{r_2}}} = \sqrt {{{{M_2}} \over {{M_1}}}}$$

Rate of diffusion = $${{Volume\,of\,gas\,diffused\,(V)} \over {Times\,taken\,(t)}}$$

$$\therefore$$ $${{{V_1}/{t_1}} \over {{V_2}/{t_2}}} = \sqrt {{{{M_2}} \over {{M_1}}}}$$

If same volume of two gases diffuse then V1 = V2

$$\Rightarrow$$ $${{{t_1}} \over {{t_2}}} = \sqrt {{{{M_2}} \over {{M_1}}}}$$

Here t2 = 3t, M1 = 4 u, M2 = ?

$$\therefore {{3{t_1}} \over {{t_1}}} = \sqrt {{{{M_2}} \over 4}} \Rightarrow 3 = \sqrt {{{{M_2}} \over 4}}$$

$$\Rightarrow 9 = {{{M_2}} \over 4} \Rightarrow {M_2} = 36\,u$$
4

### AIPMT 2012 Prelims

50 mL of each gas A and of gas B takes 150 and 200 seconds respectively for effusing through a pin hole under the similar conditions. If molecular mass of gas B is 36, the molecular mass of gass A will be
A
96
B
128.74
C
20.25
D
64.42

## Explanation

According to Graham's law of diffusion,

$${{{r_1}} \over {{r_2}}} = \sqrt {{{{d_2}} \over {{d_1}}}} = \sqrt {{{{M_2}} \over {{M_1}}}}$$

$${r_A} = {{{V_A}} \over {{T_A}}},\,{r_B} = {{{V_B}} \over {{T_B}}}$$

$${{{V_A}/{T_A}} \over {{V_B}/{T_B}}} = \sqrt {{{{M_B}} \over {{M_A}}}}$$

$${V_A} = {V_B},\,{T_A} = 150\,\sec$$, TB = 200 sec, MB = 36, MA = ?

$${{{T_B}} \over {{T_A}}} = \sqrt {{{{M_B}} \over {{M_A}}}} \Rightarrow {{200} \over {150}} = \sqrt {{{36} \over {{M_A}}}}$$

$$\Rightarrow {4 \over 3} = \sqrt {{{36} \over {{M_A}}}} \,\,or\,\,{{4 \times 4} \over {3 \times 3}} = {{36} \over {{M_A}}}$$

$$\Rightarrow$$ MA = $${{36} \over {4 \times 4}} \times 3 \times 3 = 20.25$$

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