1
MCQ (Single Correct Answer)

AIPMT 2007

In a first-order reaction A $$ \to $$ B, if k is rate constant and initial concentration of the reactant A is 0.5 M, then the half-life is
A
$${{\log 2} \over k}$$
B
$${{\log 2} \over {k\sqrt {0.5} }}$$
C
$${{\ln 2} \over k}$$
D
$${{0.693} \over {0.5k}}$$

Explanation

For first order reaction

k = $${{2.303} \over t}\log {a \over {a - x}}$$

at $${t_{1/2}}$$, x = $${a \over 2}$$

$${t_{1/2}}$$ = $${{2.303} \over k}\log {a \over {a - {a \over 2}}}$$

= $${{\ln 2} \over k}$$
2
MCQ (Single Correct Answer)

AIPMT 2007

If 60% of a first order reaction was completed in 60 minutes, 50% of the same reaction would be completed in approximately
(log 4 = 0.60, log 5 = 0.69)
A
45 minutes
B
60 minutes
C
40 minutes
D
50 minutes

Explanation

For a first order reaction,

k = $${{2.303} \over t}\log {a \over {a - x}}$$

k = $${{2.303} \over {60}}\log {{100} \over {40}}$$

= $${{2.303} \over {60}}\log 2.5$$

= 0.0153

Also, $${t_{1/2}}$$ = $${{2.303} \over k}\log {{100} \over {50}}$$

= $${{2.303} \over {0.0153}}\log 2$$

= 45 min.
3
MCQ (Single Correct Answer)

AIPMT 2006

For the reaction, 2A + B $$ \to $$ 3C + D, which of the following does not express the reaction rate?
A
$$ - {{d\left[ A \right]} \over {2dt}}$$
B
$$ - {{d\left[ C \right]} \over {3dt}}$$
C
$$ - {{d\left[ B \right]} \over {dt}}$$
D
$$ {{d\left[ D \right]} \over {dt}}$$

Explanation

Given,

2A + B $$ \to $$ 3C + D

Rate of reaction =

$$ - {1 \over 2}{{d\left[ A \right]} \over {dt}} = - {{d\left[ B \right]} \over {dt}}$$ = $${1 \over 3}{{d\left[ C \right]} \over {dt}} = {{d\left[ C \right]} \over {dt}}$$

4
MCQ (Single Correct Answer)

AIPMT 2006

Consider the reaction :  N2(g) + 3H2(g) $$ \to $$ 2NH3(g)

The equality relationship between $${{d\left[ {N{H_3}} \right]} \over {dt}}$$ and $$ - {{d\left[ {{H_2}} \right]} \over {dt}}$$ is
A
$${{d\left[ {N{H_3}} \right]} \over {dt}} = - {{d\left[ {{H_2}} \right]} \over {dt}}$$
B
$${{d\left[ {N{H_3}} \right]} \over {dt}} = - {1 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}}$$
C
$$ + {{d\left[ {N{H_3}} \right]} \over {dt}} = - {2 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}}$$
D
$$ + {{d\left[ {N{H_3}} \right]} \over {dt}} = - {3 \over 2}{{d\left[ {{H_2}} \right]} \over {dt}}$$

Explanation

N2(g) + 3H2(g) $$ \to $$ 2NH3(g)

Rate = $${{ - d\left[ {{N_2}} \right]} \over {dt}} = - {1 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {N{H_3}} \right]} \over {dt}}$$

$$ \Rightarrow $$$${{d\left[ {N{H_3}} \right]} \over {dt}} = - {2 \over 3}{{d\left[ {{H_2}} \right]} \over {dt}}$$

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