The rate constant increases 50% when temperature is increased from 298 K to 308 K. THe value of ΔH⁰ is 15 kJ mol. Calculate the activation energies Ea^f and Ea^r.

Solution

The rate constant at 298 K = k.
When the temperature is raised from 298 k to 308 k.
Increase in rate constant

   $= k \times \frac{50}{100} = 0.5 k$
By using the equation

   $In [k_{2} / k_{1}] = [{E_{a}}^{f} / R] [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$

We have,

$In (1.5 k / k) = [{E_{a}}^{f} / R] [\frac{1}{298 k} - \frac{1}{308 k}] = [{E_{a}}^{f} / R] [\frac{10}{298 \times 208}] \log (2.303 \times 1.5) = \frac{E_{a}^{f}}{8.314} \times \frac{10}{298 \times 308} \log 3.4545 = \frac{E_{a}^{f}}{8.314} \times \frac{10}{298 \times 308} 0.4460 = \frac{E_{a}^{f}}{8.314} \times \frac{10}{298 \times 308} E_{a}^{f} = \frac{0.4460 \times 8.314 \times 298 \times 308}{10} = 34.03 kJ / mol$

   $∆ rH ° = 15 kJ {mol}^{- 1}$

but $∆ rH ° = {E_{a}}^{f} - {E_{a}}^{r}$

   $∴$    ${E_{a}}^{f} = (34.03 - 15) kJ mol = 19.03 kJ {mol}^{- 1}$

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

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Chemical Kinetics

The rate constant increases 50% when temperature is increased from 298 K to 308 K. THe value of ΔH⁰ is 15 kJ mol. Calculate the activation energies Ea^f and Ea^r.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

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NCERT Sample Papers

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Chemical Kinetics

The rate constant increases 50% when temperature is increased from 298 K to 308 K. THe value of ΔH0 is 15 kJ mol. Calculate the activation energies Eaf and Ear.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The rate constant increases 50% when temperature is increased from 298 K to 308 K. THe value of ΔH⁰ is 15 kJ mol. Calculate the activation energies Ea^f and Ea^r.