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A first order reaction takes 25 minutes ...

A first order reaction takes 25 minutes for `25%` decomposition. Calculate `t_(1//2)`.

`" "["Give ":log 2=0.3010,log3=0.4771,log4=0.6021]`

Text Solution

Verified by Experts

Apply the relation :
`k=(2.303)/(t)"log"([R]_(0))/([R])`
`25%` decomposition means `[R]=0.75[R]_(0)` and `t=25` minutes Substituting the values in the equation above,, we have
`k=(2.303)/(25)"log"([R]_(0))/(0.75[R]_(0))`
`=(2.303)/(25)"log"4/3`
`=(2.303)/(25)[log4-log3]`
`=(2.303)/(25)[0.6021-0.4771]`
`=(2.303)/(25)xx0.1250=0.011515" minutes"^(-1)`
`t_(1//2)=(0.693)/(k)`
`=(0.693)/(0.011515" minutes"^(-1))`
`=60.18" minutus"`
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