Homework 15.61

[arif_latif_2G]

Can someone help me through this question:
The rate constant of the fi rst-order reaction 2 N2O(g) S
2 N2(g) -> O2(g) is 0.76 s1
at 1000. K and 0.87 s1
at 1030. K.
Calculate the activation energy of the reaction.

[Michael Torres 4I]

To solve this problem, you need to use the equation ln(k2/k1)=((activation energy)/R)((1/T1)-(1/T2)).

The problem gives you the values for two different rate constants and their respective temperatures. Therefore, you can plug 0.76 s^-1 into k2 and 1000. K into T2. After that, you can plug 0.87 s^-1 into k1 and 1030. K into T1. (Note that you could have plugged what the values you plugged into k2 and T2 into k1 and T1 and vice versa as long as they remained in that format of 1's and 2's aligning with each other.) After this, plug in 8.3145 J*K^-1*mol^-1 into R since it is the gas constant.

Once you plug all these values into your equation, solve for the activation energy. You should get 39 kilojoules per mole.

The significance of this problem is that it asks you to find the activation energy of some reaction given what its rate constants would be at different temperatures. With this information, you are able to find how much energy the reaction requires to proceed in order to form products.