Question

Hydrogen peroxide `H_(2)O_(2)` (aq) decomposes to `H_(2)O`(l) and `O_(2)`(g) in a reaction that is first order in `H_(2)O_(2)` and has a rate constant `k=1.06xx10^(3) min^(-1)`
(i) How long will it takes for 15% of a sample of `H_(2)O_(2)` to decompose?
(ii) How long will it take for 87.5% of the sample to decompose?

Answer 1

(i) `t=(2.303)/(k)log[(A)]/[(A)]`
Given `k=1.06xx10^(-3) min^(-1) [A]/[A]=100/85`
`t=(2.303)/(1.06xx10^(-3)min^(-1)log100/85`
`t=(2303)/(1.06)[2 log 10 -log85]min`
`t=(2303)/(1.06)[2xx1-1.9294]=(2303xx0.0706)/(1.06)`
t=153.39 min =153.4 min
(ii) Given `k= 1.06xx10^(-3)min^(-1) [A]/[A]=100/15`
`t=(2.303)/(1.06)(10^(-3)min^(-1)log(100))/(15)`
`=(2303)/(1.06)[2log 10-log15]min =(2303)/(1.06)[2xx1-1.1761]`
`=(2303xx0.8231)/(1.06)`min
t=1790 min