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1

### NEET 2013

What is the activation energy for a reaction if its rate doubles when the temperature is raised from 20oC to 35oC?
(R = 8.314 J mol$$-$$1 K$$-$$1)
A
34.7 kJ mol$$-$$1
B
15.1 kJ mol$$-$$1
C
342 kJ mol$$-$$1
D
269 kJ mol$$-$$1

## Explanation

$$\log {{{k_2}} \over {{k_1}}} = {{{E_a}} \over {2.303R}}\left( {{1 \over {{T_1}}} - {1 \over {{T_2}}}} \right)$$

Initial temperature, T1 = 20 + 273 = 293 K

Final temperature, T2 = 35 + 273 = 308 K

R = 8.314 JK–1 mol–1

As rate becomes double on raising temperature

$$\therefore$$ r2 = 2r1

As rate constant, k $$\infty$$ r

k2 = 2k1

$$\therefore$$ $$\log 2 = {{{E_a}} \over {2.303 \times 8.314}}\left( {{1 \over {293}} - {1 \over {308}}} \right)$$

$$\Rightarrow$$ $$0.301 = {{{E_a}} \over {19.147}} \times {{15} \over {293 \times 308}}$$

$$\Rightarrow$$ E$$a$$ = 34673 J mol–1 = 34.7 kJ mol–1
2

### NEET 2013 (Karnataka)

For a reaction between A and B the order with respect to A is 2 and the other with respect to B is 3. The concentrations of both A and B are doubled, the rate will increase by a factor of
A
12
B
16
C
32
D
10

## Explanation

Rate1 = k[A]2[B]3

when concentrations of both A and B are doubled then

Rate2 = k[2A]2[2B]3 = 32 k[A]2[B]3

$$\therefore$$ Rate will increase by a factor of 32.
3

### AIPMT 2012 Prelims

In a zero-order reaction, for every 10oC rise of temperature, the rate is doubled. If the temperature is increased from 10oC to 100oC, the rate of the reaction will become
A
256 times
B
512 times
C
64 times
D
128 times

## Explanation

For energy 10° rise in temperature the rate of reaction doubles. So, rate = 2n
when, n = 1 rate = 21 = 2

when, temperature is increased from 10°C to 100°C change in temperature = 100 – 10 = 90°C

i.e., n = 9

So, rate = 29 = 512 times
4

### AIPMT 2012 Prelims

In a reaction, A + B $$\to$$ product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentration of both the reactants (A and B) are doubled, rate law for the reaction can be written as
A
rate = k[A][B]2
B
rate = k[A]2[B]2
C
rate = k[A][B]
D
rate = k[A]2[B]

## Explanation

Rate of reaction for A + B $$\to$$ Product

Rate = k[A]x[B]y …(1)

where, x and y are order w.r.t. A and B respectively. When the concentration of only B is doubled, the rate is doubled, so

R’ = k [A]x [2B]y = 2R …(2)

If concentration of both the reactants A and B are doubled then the rate increases by a factor of 8 so

R’’ = k[2A]x[2B]y = 8R ...(3)

= k2x 2y [A]x [B]y = 8R …(4)

From equation (1) and (2), we get

$${{2R} \over R} = {{{{\left[ A \right]}^x}{{\left[ {2B} \right]}^y}} \over {{{\left[ A \right]}^x}{{\left[ B \right]}^y}}}$$

$$\Rightarrow$$ 2 = 2y

$$\Rightarrow$$ y = 1

From equation (1) and (4), we get

$${{8R} \over R} = {{{2^x}{2^y}{{\left[ A \right]}^x}{{\left[ B \right]}^y}} \over {{{\left[ A \right]}^x}{{\left[ B \right]}^y}}}$$

$$\Rightarrow$$ 8 = $${{2^x}{2^y}}$$

Substituting the value of y gives

$${{2^x}{2^1}}$$ = 8

$$\Rightarrow$$ $${{2^x}}$$ = 4

$$\Rightarrow$$ x = 2

By replacing the values of x and y in

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

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