Chemical Kinetics — Page 5 | NEET Chemistry

Q41

For the reaction A + B

\to

products, it is observed that (i) on doubling the initial concentration of A only, the rate of reaction is also doubled and (ii) on doubling the initial concentration of both A and B, there is a change by a factor of 8 in the rate of the reaction. The rate of this reaction is given by

A rate = k[A] 2 [B] 2

B rate = k[A] [B] 2

C rate = k[A] [B]

D rate = k[A] 2 [B]

Correct Answer

Option B

Solution

R = k[A] m [B] n ... (i) 2R = k[2A] m [B] n ... (ii) 8R = k[2A] m [2B] n ... (iii) from (i), (ii) and (iii), m = 1, n = 2 So, rate = k[A][B] 2

Q42

Half-life period of a first order reaction is 1386 seconds. The specific rate constant of the reaction is

A 0.5

\times

10

-

2 s

-

1

B 0.5

\times

10

-

3 s

-

1

C 5.0

\times

10

-

2 s

-

1

D 5.0

\times

10

-

3 s

-

1 .

Correct Answer

Option B

Solution

Specific rate constant k =

{{0.693} \over {{t_{1/2}}}}

=

{{0.693} \over {1386}}

= 0.5 $\times$ 10 -3 sec -1

Q43

The rate constants k 1 and k 2 for two different reactions are 10 16

\cdot

e

-

2000/T and 10 15

\cdot

e

-

1000/T , respectively. The temperature at which k 1 = k 2 is

A 2000 K

B

{{1000} \over {2.303}}K

C 1000 K

D

{{2000} \over {2.303}}K

Correct Answer

Option B

Solution

k 1 = 10 16

{e^{ - {{2000} \over T}}}

k 2 = 10 15

{e^{ - {{1000} \over T}}}

On taking log of both the equations, we get

\log {k_1} = 16 - {{2000} \over {2.303T}}

\log {k_2} = 15 - {{1000} \over {2.303T}}

As k 1 = k 2

16 - {{2000} \over {2.303T}}

=

15 - {{1000} \over {2.303T}}

$\Rightarrow$ T =

{{1000} \over {2.303}}K

Q44

The reaction of hydrogen and iodine monochloride is given as : H 2(g) + 2ICl (g)

\to

2HCl (g) + I 2(g) This reaction is of first order with respect to H 2(g) and ICl (g) , following mechanisms were proposed. Mechanism A : H 2(g) + 2ICl (g)

\to

2HCl (g) + I 2(g) Mechanism B : H 2(g) + ICl (g)

\to

HCl (g) + HI (g) ; slow HI (g) + ICl (g)

\to

HCl (g) + I 2(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

Correct Answer

Option D

Solution

The slow step is the rate determining step and it involves 1 molecule of H 2 (g) and 1 molecule of ICl(g) .

Hence the rate will be, r = k[H 2 (g)] [ICl(g)] $\therefore$ The reaction is 1 st order with respect to H 2 (g) and ICl(g).

Q45

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}}

Correct Answer

Option C

Solution

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}

Q46

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

Correct Answer

Option A

Solution

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.

Q47

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}}

Correct Answer

Option B

Solution

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}}

Q48

Consider the reaction : N 2(g) + 3H 2(g)

\to

2NH 3(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}}

Correct Answer

Option C

Solution

N 2(g) + 3H 2(g) $\to$ 2NH 3(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}}

Q49

For a first order reaction A

\to

B the reaction rate a reactant concentration of 0.01 M is found to be 2.0

\times

10

-

5 mol L

-

1 s

-

1 . The half-life period of the reaction is

A 30 s

B 220 s

C 300 s

D 347 s

Correct Answer

Option D

Solution

Given [A] = 0.01 M Rate = 2.0 × 10 –5 mol L –1 S –1 For a first order reaction Rate = k[A] k =

{{2 \times {{10}^{ - 5}}} \over {0.01}} = 2 \times {10^{ - 3}}

$\Rightarrow$

{t_{1/2}} = {{0.693} \over {2 \times {{10}^{ - 3}}}} = 347\,\sec

Q50

The rate of reaction between two reactions A and B decreases by a factor of 4 if the concentration of reactant B is doubled. The order of this reaction with respect to reactant B is

A 2

B

-

2

C 1

D

-

1

Correct Answer

Option B

Solution

A + B $\to$ Product Rate $\propto$ [A] x [B] y .......(

1) The rate of the reaction decreases by a factor of 4 if the concentration of reactant B is doubled.

{r \over 4}

$\propto$ [A] x [2B] y ......(2) From equation (1) and (2), we get

{\left( {{1 \over 2}} \right)^y} = 4

$\Rightarrow$ y = -2 $\therefore$ Order of this reaction with respect to reactant B is -2.