Question

The rate constant for a certain reaction is measured at two different temperatures:

temperature k
376.0 °C 4.8 x 10^8
280.0 °C 2.3 x 10^8

Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy Ea for this reaction.

Answer 1

Answer: The activation energy Ea for this reaction is 22689.8 J/mol

Step-by-step explanation:

According to Arrhenius equation with change in temperature, the formula is as follows.

`ln (k_(2))/(k_(1)) = (-E_(a))/(R)[(1)/(T_(2)) - (1)/(T_(1))]`

`k_1` = rate constant at temperature
`T_1` =
`2.3* 10^8`

`k_2` = rate constant at temperature
`T_2` =
`4.8* 10^8`

`E_a`= activation energy = ?

R= gas constant = 8.314 J/kmol

`T_1` = temperature =
`280.0^0C=(273+280)=553K`

`T_2` = temperature =
`376.0^0C=(273+376)=649K`

Putting in the values ::

`ln (4.8* 10^8)/(2.3* 10^8) = (-E_(a))/(8.314)[(1)/(649) - (1)/(553)]`

`E_a=22689.8J/mol`

The activation energy Ea for this reaction is 22689.8 J/mol