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Questions
In the Arrhenius equation for a first order reaction, the values of ‘A’ of ‘Ea’ are 4 × 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]
In the Arrhenius equation for a certain reaction, the value of A and Ea (activation energy) are 4 × 1013 sec−1 and 98.6 kJ mol−1 respectively. If the reaction is of first order, at what temperature will its half-life period be ten minutes?
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Solution
The value of k, corresponding to t1/2 = 10 min = 600 s, is given by
k = `0.693/t_(1//2)`
= `0.693/600`
= 1.155 ×10−3 s−1.
Given that A = 4 × 1013 sec−1 and Ea = 98.6 kJ mol−1.
According to the Arrhenius equation,
k = `e^(-E_a//RT)`
Taking logarithm, we get
loge k = `log_e A - E_a/(RT)`
or, log10 k = `log_10 A - E_a/(2.303 RT)`
Substituting the values, we get
log10 1.155 × 10−3 = `log_10 4 xx 10^13 - 98.6/(2.303 xx 8.314 xx 10^-3 xx 7`
or, −2.9374 = `13.6021 - 5149.6/7`
or, `5149.6/T` = 13.6021 + 2.9374 = 16.5395
or, T = `5149.6/16.5395`
= 311.35 K
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