Question

The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy Ea= 50.0 KJ/mol. If the rate constant of this reaction is 0.14M-1 s-1 at -8.0what will the rate constant be at 56.0 ?

Round your answer to significant digits

k=_________ M-1s-1

Answer 1

Answer: The rate constant at 56°C is $11.58M^{-1}s^{-1}$

Explanation:

To calculate rate constant at two different temperatures of the reaction, we use Arrhenius equation, which is:

$\ln(\frac{K_{56^oC}}{K_{-8^oC}})=\frac{E_a}{R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,  

$K_{-8^oC}$ = equilibrium constant at -8°C = $0.14M^{-1}s^{-1}$

$K_{56^oC}$ = equilibrium constant at 56°C = ?

$E_a$ = Activation energy = 50.0 kJ/mol = 50000 J/mol   (Conversion factor:  1 kJ = 1000 J)

R = Gas constant = 8.314 J/mol K

$T_1$ = initial temperature = $-8^oC=[273-8]K=265K$

$T_2$ = final temperature = $56^oC=[273+56]K=329K$  

Putting values in above equation, we get:

$\ln(\frac{K_{56^oC}}{0.14})=\frac{50000J}{8.314J/mol.K}[\frac{1}{265}-\frac{1}{329}]\\\\K_{56^oC}=11.58M^{-1}s^{-1}$

Hence, the rate constant at 56°C is $11.58M^{-1}s^{-1}$