What is the rate constant as we increase the temperature?Given that A = 2.4 X 10^29 L / (mol x s) and activation energy is 325 kJ/mol calculate the change in the rate constant from 10 to 20 °C. 

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mlsiasebs | College Teacher | (Level 1) Associate Educator

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To find the relationship between the rate constant and temperature we need to use the Arrhenius equation.  Given that we need the ratio of the k values, we can use the two-point form

ln (k2/k1) = Ea/R (1/T1 - 1/T2)

Since the activation energy is in kJ/mol and R includes J, we need to convert the activation energy to J/mol by multiplying by 1000. We must also convert the temperatures from Celsius to Kelvin by adding 273.  Plug in the values we know

ln (k2/k1) = (3.25 x 10^5 J/mol / 8.314 J/molK) (1/283 - 1/293)

and solve for ln (k2/k1)

ln (k2/k1) = 4.71

Now to get rid of the k, we take both sides to the power of e which cancels out with the ln function so we get

k2/k1 = e^4.71


k2/k1 = 111

therefore, the rate constant changes by a factor of 111.