Question

Prove that T755=2T505 for first order reaction

Answer 1

Explanation:

For a first order reaction, we have

t=

t

2.303

log

[A]

[A]

0

Let a M be the initial concentration.

When reaction is 99% complete,

[A]=a−

100

99a

=0.01a

t

99

=

k

2.303

log

0.01a

a

t

99

=

k

2.303

×2 ......(1)

When reaction is 90% complete,

[A]=a−

100

90a

=0.1a

t

90

=

k

2.303

log

0.1a

a

t

90

=

k

2.303

×1 ......(2)

Divide equation (1) by (2), we get

t

90

t

99

=2 ⟹t

99

=2t

90