In a pseudo first order hydrolysis of ester in water the following results were obtained :
`{:("Time t(s)",0,30,60),("Ester (mol "L^(-1)")",0.55,0.31,0.17):}`
Calculate the pseudo first order rate constant

Explanation

Case I :
`[R]_0=0.55" mol L"^(-1),[R]=0.31" mol L"^(-1)`
t=30 s, k=?
`k=(2.303)/(t)log(0.55)/(0.31)`
`=(2.303)/(30s)log(0.55)/(0.31)`
`k=(2.303)/(30 s)log1.774`
`=(2.303xx0.2490)/(30s)`
`=1.91xx10^(-2)s^(-1)`
Case II :
`[R]_0=0.55" mol L"^(-1),[R]=0.17" mol L"^(-1)` t=60 s, k=?
`k=(2.303)/(60s)log(0.55)/(0.17)`
`=(2.303)/(60s)log3.235`
`=(2.303xx0.5099)/(60)s^(-1)`
Average value of
`k=1/2(1.91xx10^(-2)+1.96xx10^(-2))s^(-1)`
`=1.935xx10^(-2)s^(-1)`