At 25 ∘ C 25∘C, 0.11 mol 0.11 mol of N 2 O 4 N2O4 reacts to form 0.10 mol 0.10 mol of N 2 O 4 N2O4 and 0.02 mol 0.02 mol of N O 2 NO2. At 90 ∘ C 90∘C, 0.11 mol 0.11 mol of N 2 O 4 N2O4 forms 0.050 mol 0.050 mol of N 2 O 4 N2O4 and 0.12 mol 0.12 mol of N O 2 NO2. From these data, it can be concluded that

A. N 2 O 4 N2O4 molecules react by a second order rate law.
B. N 2 O 4 N2O4 molecules react by a first order rate law.
C. N 2 O 4 N2O4 molecules react faster at 25 ∘ C 25∘C than at 90 ∘ C 90∘C.
D. the equilibrium constant for the reaction above increases with an increase in temperature.

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To determine the answer to this question, let's analyze the given data and the information provided.

We are given the following reactions at two different temperatures:

At 25 °C:
0.11 mol of N2O4 reacts to form 0.10 mol of N2O4 and 0.02 mol of NO2.

At 90 °C:
0.11 mol of N2O4 forms 0.050 mol of N2O4 and 0.12 mol of NO2.

Now, let's consider the rate of the reaction at both temperatures. According to the given data, the amount of N2O4 consumed and the amount of NO2 formed are different at both temperatures for the same initial amount of N2O4. This indicates that the rate of the reaction is affected by the temperature.

At 25 °C, 0.11 mol of N2O4 reacts to form 0.10 mol of N2O4 and 0.02 mol of NO2.
At 90 °C, 0.11 mol of N2O4 forms 0.050 mol of N2O4 and 0.12 mol of NO2.

Comparing these values, we can see that at 25 °C, less N2O4 is converted to NO2 compared to the reaction at 90 °C. This suggests that the reaction is slower at 25 °C and faster at 90 °C.

Based on this information, we can conclude that the rate of the reaction increases with an increase in temperature. Therefore, the correct answer is:

D. The equilibrium constant for the reaction above increases with an increase in temperature.