What is the value of delta H for a reaction the value of K doubles when the temerature is increased from 25 deg C to 35 deg C?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem provides the condition that `k_35 = 2k_25` , hence you should come up with the substitution `k_35 = k_1`  and `k_25 = k_2` .

You may use the following equation such that:

`ln k_1 = ln A - E_a/(RT_1)`

`ln k_2 = ln A - E_a/(RT_2)`

You need to subtract `ln k_2 = ln A - E_a/(RT_2)`  from `ln k_1 = ln A - E_a/(RT_1)`  such that:

`ln k_1 - ln k_2= ln A - E_a/(RT_1) - ln A+ E_a/(RT_2)`

Using the laws of logarithms and reducing like terms yields:

`ln(k_1/k_2) = (E_a/R)(1/T_2 - 1/T_1)`

`E_a = (RT_1*T_2)/(T_2-T_1)*ln(k_1/k_2)`

You need to convert Celsius degrees to Kelvin such that:

`T_1 = 25 + 273 = 298`

`T_2 = 35 + 273 = 308`

`E_a = (8.314*298*308)/(308-298)*ln(2k_2/k_2)`

`E_a = 76309.2176*0.6931`

`E_a = 52889.918`

`E_a ~~ 53 (kJ)/(mol)`

Hence, evaluating the energy of activation yields entalpy `Delta H = 53 (kJ)/(mol)` .

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