1

### NEET 2013 (Karnataka)

What is the density of N2 gas 227oC and 5.00 atm. pressure? (R = 0.082 L atm K$-$1 mol$-$1)
A
1.40 g/mL
B
2.81 g/mL
C
3.41 g/mL
D
0.29 g/mL

## Explanation

PV = nRT

$\Rightarrow$ PV = ${W \over M}RT$

$\Rightarrow$ $P = {W \over M} \times {{RT} \over V}$

$\Rightarrow$$P = {{dRT} \over M}$   [Density = ${{Mass} \over {Volume}}$]

$\Rightarrow d = {{PM} \over {RT}} = {{5 \times 28} \over {0.0821 \times 500}} = 3.41\,g/ml$
2

### 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 = ${3 \over 2}R$

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

### 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
4

### 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 = ?

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

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