The rate of a first order reaction is 0.04mol/L/s at10minutes and 0.03mol/L/s at 20minutes after initiation. Find the half life of the reaction.

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Solution

Reaction type : 1st order reaction

Formula used :
k =( 2.303/t2-t1) log([R1]/[R2])

Given :
T1 = 10 min and T2 = 20 min therefore T2-T1 = 10 min

[R1] = 0.04 mol/L and [R2] = 0.03 mol/L

Substituting the values in the above equation

k =( 2.303/10) log( 0.04/0.03)

k = 0.2303 [log(0.04) - log (0.03)]

k = 0.2303 [-1.3979 - (-1.5228)]

k = 0.02876 /min

For the first order reaction half life t1/2 is given by

t1/2 = 0.693/k

We know, k = 0.02876 we get

t1/2 = 0.693/0.02876

t1/2 = 24.096 min

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