For a certain reaction,the activation energy is 52.1 kJ/mole.By what ratio will the rate constant change if the temperature is decreased from 175°C to 75°C?

Question

Quizplus · Accepted Answer

The ratio of rate constants can be calculated using the Arrhenius equation: 
k2/k1 = exp((Ea/R)(1/T1 - 1/T2))
where k1 and T1 are the original rate constant and temperature, k2 and T2 are the new rate constant and temperature, Ea is the activation energy, and R is the gas constant (8.314 J/mol-K). 
Plugging in the given values, we get:
k2/k1 = exp((52,100 J/mol)/(8.314 J/mol-K) * (1/(448 K) - 1/(348 K))) 
k2/k1 = 0.0179 
Therefore, the rate constant will decrease by a factor of 0.0179, or 1/55.95.

For a Certain Reaction,the Activation Energy Is 52