Question

The half life period of a zero order reaction was found to be 10 minutes when the initial concentration was
1.0 mole per litre. What will be the half life period if the initial concentration is made 2 moles per litre?​

Answer 1

Answer:

For a zero order reaction we have the following condition:

rate = k [A]^0 = k

Now, the rate can also be written as:

rate = -ΔAΔt = k

if the intervals are small then we would write:

rate = -δAδt = k

We can rearrange this equation to be:

δ A = -k δt

integrating both sides we obtain:

Af - Ai = -k (tf - ti) = -kΔ t

For a half-life, Af = 1/2 Ai so that:

1/2 Ai - Ai = - k t1/2

This reduces to:

-1/2 Ai = - k t1/2

solving for t1/2 we get:

t1/2 = Ai2k

This is the half-life equation for a zero order reaction. We can now solve the problem. We must solve for k.

10 min = 1(M)2k

k = 0.05

Therefore, if the concentration is 2 (M), the half-life would be:

t1/2 = 2(M)2(0.05) = 20 min