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1

### AIPMT 2007

The reaction of hydrogen and iodine monochloride is given as :
H2(g) + 2ICl(g) $$\to$$ 2HCl(g) + I2(g)
This reaction is of first order with respect to H2(g) and ICl(g),
following mechanisms were proposed.

Mechanism A :
H2(g) + 2ICl(g) $$\to$$ 2HCl(g) + I2(g)
Mechanism B :
H2(g) + ICl(g) $$\to$$ HCl(g) + HI(g) ; slow
HI(g) + ICl(g) $$\to$$ HCl(g) + I2(g) ; fast

Which of the above mechanism(s) can be consistent with the given information about the reaction?
A
A and B both
B
Neither A nor B
C
A only
D
B only

## Explanation

The slow step is the rate determining step and it involves 1 molecule of H2(g) and 1 molecule of ICl(g) . Hence the rate will be,

r = k[H2(g)] [ICl(g)]

$$\therefore$$ The reaction is 1st order with respect to H2(g) and ICl(g).
2

### 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 = $${a \over 2}$$

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

= $${{\ln 2} \over k}$$
3

### 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.
4

### 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 =

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

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