Question

1.) The decomposition of phosphine (PH₃) is a 1st order reaction.

A.) If the half life of the reaction is 35.0s, what is the rate constant?

B.) How long will it take for 75% of the phosphine to decompose?

Answer 1

for first order reaction rate and concentration are related as - dc/dt= kc (1)

where K= rate constant and c= concentratino at any time

Eq.1 upon integration gives -ln (1-XA)= kt (2) where XA= 1-CA/CAO

CA= cocentration at any time t and CAO= initital concentratin

for half lfe, the cocentratino CA should drop down to 50% of its inital value CA=0.5CAO and XA=0.5

from Eq.2 -ln (1-0.5)= k*35

k= 0.693/35 sec-1=0.0198 sec-1

b) for 75% conversion , i.e XA=0.75 and from eq.2 -ln (1-0.75)= 0.0198*t

t= time taken

t= 1.386/0.0198 =70 sec