A first order reaction has rate constants of 4.6 x 10-2 s-1 and 8.1 x 10-2 s-1 at 0ºC and 20ºC, respectively. What is the value for the activation energy?
A.
0.566 J/mol
B.
2.5 x 10-4 J/mol
C.
2260 J/mol
D.
18,800 J/mol
E.
1.76 J/mol

D.  18,800 J/mol

Explanation:

We need to use the Arrhenius equation to solve for this problem:

, where k is the rate constant, A is the frequency factor, is the activation energy, R is the gas constant, and T is the temperature in Kelvins.

We want to find the value of , so let's plug some of the information we have into the equation. The gas constant we can use here is 8.31 J/mol-K.

At 0°C, which is 0 + 273 = 273 Kelvins, the rate constant k is . So:

At 20°C, which is 20 + 273 = 293 Kelvins, the rate constant k is . So:

We now have two equations and two variables to solve for. We just want to find Ea, so let's write the first equation for A in terms of Ea:

Plug this in for A in the second equation:

After some troublesome manipulation, the answer should come down to be approximately:

Ea = 18,800 J/mol

The answer is thus D.

a. energy is absorbed in the reaction.

if in a given reaction the energy of products is greater than the energy of reactants it means that reaction is endothermic and during the reaction, the energy is absorbed by reactants. in an endothermic reaction, the products have more stored chemical energy than the reactants. and in this reaction the reactants are more stable than products before the compounds with less energy are always more stable.