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Sucrose decomposes in acid solution into...

Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with `t_(1//2)=3.00hr.` What fraction of sample of sucrose remains after `8 hr` ?

Text Solution

Verified by Experts

Given : `t_(1//2)=3` hours
t= 8 hours
` k = (0*693)/(t_(1//2))=(0*693)/3 = 0.231 "hr"^(-1)`
From formula,
` k = (2*303)/t log. ([A])/[A]_(t)`
` 0*231 = (2*303)/8 log. ([A]_(0))/([A]_(t))`
` Log. ([A]_(0))/([A]_(t))= 0*8024`
Taking antilog on both sides
` :. ([A]_(0))/([A]_(t))=" Antilog " (0*8024)= 6*345`
` :. ([A]_(0))/([A]_(0)) = 1/(6*345)= 0*158 `
Hence , the fraction of sucrose which will remain after 8 hours is `0*158`.
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