1
MCQ (Single Correct Answer)

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 = ?

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

$$ \Rightarrow 9 = {{{M_2}} \over 4} \Rightarrow {M_2} = 36\,u$$
2
MCQ (Single Correct Answer)

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 = $${{36} \over {4 \times 4}} \times 3 \times 3 = 20.25$$
3
MCQ (Single Correct Answer)

AIPMT 2011 Prelims

In Duma's method of estimation of nitrogen 0.35 g of an organic compound gave 55 mLof nitrogen collected at 300 K temperature and 715 mm pressure. The percentage composition of nitrogen in the compound would be (aqueous tension at 300 K = 15 mm).
A
15.45
B
16.45
C
17.45
D
14.45

Explanation

Given V1 = 55 mL, V2 = ?

P1 = 715 – 15 = 700 mm, P2 = 760 mm

T1 = 300 K, T2 = 273 K

General gas equation,

$${{{P_1}{V_1}} \over {{T_1}}} = {{{P_2}{V_2}} \over {{T_2}}}$$

$$ \Rightarrow $$ $${{700 \times 55} \over {300}} = {{760 \times {V_2}} \over {273}}$$

$$ \Rightarrow $$ V2 = 46.098 mL

Now, 22400 mL of nitrogen = 1 mole

$$ \therefore $$ 46.098 mL of nitrogen = $${{1 \times 46.098} \over {22400}}$$ mol

Weight of nitrogen = $${{1 \times 46.098} \over {22400}}$$ $$ \times $$ 28 = 0.057 g

Percent composition of nitrogen in 0.35 g of compound

= $${{0.0576} \over {0.35}} \times 100$$ = 16.45 %
4
MCQ (Single Correct Answer)

AIPMT 2011 Prelims

Two gases A and B having the same volume diffuse through a porous partition in 20 and 10 seconds respectively. The molecular mass of A is 49 u. Molecular mass of B will be
A
50.00 u
B
12.25 u
C
6.50 u
D
25.00 u

Explanation

We know that $${{{r_A}} \over {{r_B}}} = {{v/{t_A}} \over {v/{t_B}}} = \sqrt {{{{M_B}} \over {{M_A}}}} $$

$$ \Rightarrow {{{t_A}} \over {{t_B}}} = \sqrt {{{{M_B}} \over {{M_A}}}} \Rightarrow {{10} \over {20}} = \sqrt {{{{M_B}} \over {49}}} $$

$$ \Rightarrow {\left( {{{10} \over {20}}} \right)^2} = {{{M_B}} \over {49}} \Rightarrow {{100} \over {400}} = \,{{{M_B}} \over {49}}$$

$$ \Rightarrow {M_B} = {{49 \times 100} \over {400}} = 12.25$$ u

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