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Question
In the Arrhenius equation for a first order reaction, the values of ‘A’ of ‘Ea’ are 4 x 1013 sec-1 and 98.6 kJ mol-1 respectively. At what temperature will its half life period be 10 minutes?
[R = 8.314 J K-1 mol-1]
Solution
Given: Frequency factor (A) = 4 x 1013 sec–1
Energy of activation (Ea) = 98.6 kJ mol–1
Half life period (t1/2) = 10 minutes = 10 x 60 = 600 sec.
`-> k=0.693/t_(1/2)`
`k=0.693/600=11.55xx10^-4 sec^-1`
`log_10k=log_10A-E_a/(2.303RT)`
`log_10 11.55 xx10^-4 =log_10 4xx10^13-(98.6xx10^3)/(2.303xx8.314xxT)`
`-2.937=13.602-(98.6xx10^3)/(2.303xx8.314xxT)`
`-2.937=13.602-(5149.632)/T`
`(5149.632)/T=13.602+2.937`
`T=(5149.632)/16.539`
T=311.36K or 38.36°
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