IIT JEE Advanced 2011 Paper 2

For the given first-order reaction, the rate equation is

−d[N2O5]

dt

= k[N2O5]
The concentration of the reactant at any time t is given by
t = (

2.303

k

)‌log‌

a

a−x

where a = 100 and a – x = 100 – 99.6 = 0.4. Hence, concentration of N2O5 decreases exponentially with time.
Half-life period for first-order reaction
t

1

2

=

ln2

k

=

0.693

k

It is independent of the concentration of the reactant. We know that k increases with increase in temperature (according to Arrhenius equation) and since t

1

2

is inversely proportional to k, so t

1

2

decreases, when k increases with increase in temperature. When the reaction is 99.6% complete, then
t99.6 = (

2.303

k

)‌log‌

100

0.4

t99.6 = (

2.303

k

)2.4 = 8×

0.693

k

= 8t

1

2