1
MCQ (Single Correct Answer)

AIPMT 2008

The dissociation equilibrium of a gass AB2 can be represented as :
2AB2(g) $$\rightleftharpoons$$ 2AB(g) + B2(g)
The degree of dissociation is x and is small compared to 1. The expression relating the degree of dissociation (x) with equilibrium constant Kp and total pressure P is
A
(2Kp/P)1/2
B
(Kp/P)
C
(2Kp/P)
D
(2Kp/P)1/3

Explanation

2AB2(g) ⇌ 2AB(g) + B2(g)
Initial mole 2 0 0
At equilibrium 2(1 - x) 2x x


Amount of moles at equilibrium = 2(1 – x) + 2x + x = 2 + x

$${K_p} = {{{{\left[ {{p_{AB}}} \right]}^2}\left[ {{p_{{B_2}}}} \right]} \over {{{\left[ {{p_{A{B_2}}}} \right]}^2}}}$$

= $${{{{\left[ {{{2x} \over {2 + x}} \times P} \right]}^2}\left[ {{x \over {2 + x}} \times P} \right]} \over {{{\left[ {{{2\left( {1 - x} \right)} \over {2 + x}} \times P} \right]}^2}}}$$

= $${{\left[ {{{4{x^3}} \over {2 + x}} \times P} \right]} \over {4{{\left( {1 - x} \right)}^2}}}$$

$$ \Rightarrow $$ Kp = $${{{4{x^3} \times P} \over 2} \times {1 \over 4}}$$

($$ \because $$ 1 – x ≈ 1 and 2 + x ≈ 2)

$$ \Rightarrow $$ x = $${\left( {{{8{K_p}} \over {4P}}} \right)^{{1 \over 3}}}$$

$$ \Rightarrow $$ x = $${\left( {{{2{K_p}} \over P}} \right)^{{1 \over 3}}}$$
2
MCQ (Single Correct Answer)

AIPMT 2007

Calculate the pOH of a solution at 25oC that contains 1 $$ \times $$ 10$$-$$10 M of hydronium ions, i.e. H3O+.
A
4.000
B
9.000
C
1.000
D
7.000

Explanation

Given, [H3O+.] = 1 $$ \times $$ 10$$-$$10

$$ \Rightarrow $$ pH = 10

Also we know, pH + pOH = 14

$$ \Rightarrow $$ pOH = 14 - pH = 14 - 10 = 4
3
MCQ (Single Correct Answer)

AIPMT 2007

A weak acid, HA, has a Ka of 1.00 $$ \times $$ 10$$-$$5. If 0.100 mol of this acid is dissolved in one litre of water, the percentage of acid dissociated at equilibrium is closest to
A
1.00%
B
99.9%
C
0.100%
D
99.0%

Explanation

For weak acid degree of dissociation,

$$\alpha $$ = $$\sqrt {{{{K_a}} \over C}} $$

= $$\sqrt {{{1 \times {{10}^{ - 5}}} \over {0.1}}} = {10^{ - 2}}$$ = 1.00 %
4
MCQ (Single Correct Answer)

AIPMT 2007

The equilibrium constants of the following are

N2 + 3H2 $$\rightleftharpoons$$ 2NH3;     K1

N2 + O2 $$\rightleftharpoons$$ 2NO;     K2

H2 + $${1 \over 2}$$O2 $$\rightleftharpoons$$ H2O;     K3

The equilibrium constant (K) of the reaction :

2NH3 + $${5 \over 2}$$ O2 $$\rightleftharpoons$$ 2NO + 3H2O will be
A
K2K33/K1
B
K2K3/K1
C
K23K3/K1
D
K1K33/K2

Explanation

2NH3 $$\rightleftharpoons$$ N2 + 3H2;     $${1 \over {{K_1}}}$$

N2 + O2 $$\rightleftharpoons$$ 2NO;     K2

3H2 + $${3 \over 2}$$O2 $$\rightleftharpoons$$ 3H2O;     (K3)3

By adding all equations, we get

2NH3 + $${5 \over 2}$$ O2 $$\rightleftharpoons$$ 2NO + 3H2O

$$ \therefore $$ K = $${{{K_2} \times {{\left( {{K_3}} \right)}^3}} \over {{K_1}}}$$

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