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Questions
The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.
The rate of reaction becomes four times when the temperature changes from 293 K to 313 K.
Calculate the energy of activation (Ea) of the reaction assuming that it does not change with temperature.
(R = 8.314 J K–1 mol–1)
The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction, assuming that it does not change with temperature.
[Given: log 4 = 0.602, log 2 = 0.301, R = 8.314 J K–1mol]
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Solution
Given: T1 = 293 K
T2 = 313 K
k2 = 4 × k1
R = 8.314 × 10−3 kJ K−1 mol−1
According to the Arrhenius equation,
`log_10 k_2/k_1 = E_a/(2.303 R) [1/T_1 - 1/T_2]`
⇒ `log_10 (4 xx k_1)/k_1 = E_a/(2.303 xx 8.314 xx 10^-3) xx [1/293 - 1/313]`
⇒ log10 (4) = `E_a/0.0191 xx (313 - 293)/(293 xx 313)`
⇒ 0.6021 = `E_a/0.0191 xx 20/(293 xx 313)`
⇒ Ea = `(0.6021 xx 0.0191 xx 293 xx 313)/20`
= `1054.66/20`
= 52.73 kJ mol−1
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