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The rate of a first order reaction is 0....

The rate of a first order reaction is 0.04 mol `"litre"^(-1)s^(-1)` after 10 minutes and 0.03 mol `"litre"^(-1)s^(-1)` after 20 minutes. Find the half life period of the reaction.

Text Solution

Verified by Experts

For a first order reaction, `Ato"Products, for concentration of the reactant at two different times,"`
`k=(2.303)/(t_(2)-t_(1))log""([A]_(1))/([A]_(2))`
But as rate `=k[A]," therefore, "(("rate")_(1))/((rate)_(2))=([A]_(1))/([A]_(2))`
Hence, `k=(2.303)/(t_(2)-t_(1))log""(("rate")_(1))/(("rate")_(2))=(2.303)/((20-10)min)log""(0.04)/(0.03)=2.88xx10^(-2)min^(-1)`
`:.t_(1//2)=(0.693)/(k)=(0.693)/(2.88xx10^(-2)min^(-1))=24.06" min "=1443.6 s.`
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