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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)=3h`. What fraction of sample of sucrose remains after 8h?

Text Solution

Verified by Experts

For first order reactions,
`k = (0.693)/( t_(1//2) ) = (0.693)/( (3.0 h) )`
or ` t= (2.303)/( k) log"" ([A]_0)/([A])`
or `log"" ([A]_0)/([A]) = (k xx t)/( 2.303)`
`log"" ([A]_0)/([A])= (0.693)/(3h) xx (8h)/( 2.303) = 0.8024`
`([A]_0)/([A]) =" antilog" 0.8024 = 6.345`
`[A]_0= 1M`,
`[A] = ([A]_0)/( 6.345) = (1M)/( 6.345) = 0.1576M`
After 8 h, sucrose left `=0.1576` M
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