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A second order reaction requires 70 min ...

A second order reaction requires `70 min` to change the concentration of reactants form `0.08 M` to `0.01 M`. The time required to become `0.04 M = 2x min`. Find the value of `x`.

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The correct Answer is:
5
For second order reaction:
`[R]_("initial") = 0.08, M, [R]_("initial") = 0.01M`
`x = 0.08 - 0.01 = 0.07M`
`:. (a-x) = 0.08 - 0.07 = 0.01 M`
`k_(2) = (1)/(t).(x)/(a(a-x))`
`= (1)/(70 min) xx (0.07 M)/(0.08M xx 0.01 M)` …(i)
Now, time required to become concentration `= 0.04 M`.
i.e., `x = 0.04 M`
`k_(2) = (1)/(t) xx (0.04 M)/(0.08 M xx (0.08-0.04)M)` ...(ii)
form Eqs. (i) and (ii)
`(0.07)/(70 xx 0.08 xx 0.01) = (0.04)/(t xx 0.08 xx 0.04)`
`t = 10 min = 2x min`
`:. x = 5 min`
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