The presence of a catalyst provides a reaction pathway in which the activation energy of a certain reaction is reduced from 192 kJ·mol-1 to 72 kJ·mol-1.

(a) By what factor does the rate of the reaction increase at 281 K, all other factors being equal?


(b) By what factor would the rate change if the reaction were carried out at 343 K instead?


What equation do i use to solve this???

shut the heck up

Your mother is a fat wore

To solve this problem, we can use the Arrhenius equation, which is an equation that relates the rate constant of a reaction to the activation energy and temperature. The Arrhenius equation is given as:

k = A * exp(-Ea / (R * T))

Where:
k = rate constant of the reaction
A = pre-exponential factor, also known as the frequency factor
Ea = activation energy
R = gas constant (8.314 J/(mol·K))
T = temperature in Kelvin

Now, let's address each part of the question:

(a) By what factor does the rate of the reaction increase at 281 K?

To calculate the factor by which the rate of the reaction will increase, we need to compare the rate constant at 281 K with and without the catalyst.

First, let's calculate the rate constant without the catalyst using the given activation energy (Ea = 192 kJ·mol-1). We'll assume a typical value for the A factor.

k1 = A * exp(-Ea / (R * T1))

Now, let's calculate the rate constant with the catalyst using the reduced activation energy (Ea = 72 kJ·mol-1) and the same temperature (T2 = 281 K).

k2 = A * exp(-Ea / (R * T2))

Finally, we can determine the factor by which the rate of the reaction increases:

Factor = k2 / k1

(b) By what factor would the rate change if the reaction were carried out at 343 K instead?

To calculate the factor by which the rate of the reaction would change at 343 K, we can follow a similar approach as in part (a). However, we need to recalculate the rate constant with the new temperature (T3 = 343 K) while keeping the activation energy constant at 72 kJ·mol-1.

k3 = A * exp(-Ea / (R * T3))

Factor = k3 / k1

By substituting the appropriate values into the equations and performing the necessary calculations, you will be able to determine the factors by which the rate of the reaction increases or changes at different temperatures.

Use the Arrhenius equation. You can solve for k1/k2 for each activation energy, then compare them.

For part A, I'm plugging into the Arrhenius equation, ignoring A, and then dividing the 2 rates for each activation energy. I'm getting 1.027 for my particular set of numbers (Ea = 120 & 56) @ 293K. This isn't correct though.

If any clarification is needed on the question, it wants to know the difference between the rates with an Ea of 192 at T=281K and an Ea of 72 at T=281K.

Use the rearranged Arrhenius like DrBob suggested: k=Ae^(-Ea/RT)

Take k2/k1 and you get your answer. If you want to check your answers, my numbers were 178 kJ·mol-1 to 54 kJ·mol-1 with the reaction carried out at 333K. My rate changed by a factor of 2.82774e19