To solve this problem, we need to understand the principles of chemical equilibrium and the effect of temperature changes on the equilibrium constant, Keq, particularly when the reaction is exothermic.
### Step-by-Step Solution:
1. Identify the Characteristics of the Reaction:
- The given chemical reaction is:
[tex]\[
2 NO _2(g) \rightleftharpoons N _2 O _4(g) \quad \Delta H ^{\circ} _{rxn} < 0
\][/tex]
- The reaction is exothermic, as indicated by [tex]\(\Delta H ^{\circ} _{rxn} < 0\)[/tex]. This means that heat is released during the reaction.
2. Effect of Temperature on Exothermic Reactions:
- According to Le Chatelier's Principle, if a system at equilibrium is disturbed by an external change (such as temperature), the system will react in such a way as to counteract the disturbance and restore a new equilibrium.
- For an exothermic reaction ([tex]\(\Delta H < 0\)[/tex]), heat can be considered a product. Increasing the temperature adds heat to the system, effectively increasing the concentration of the 'heat' product.
- The system will respond by shifting the equilibrium to the left, towards the reactants, in order to absorb the added heat and reduce its effect.
3. Impact on the Equilibrium Constant (Keq):
- When the equilibrium shifts towards the reactants to counteract the increased temperature, the concentrations of the reactants will increase while the concentration of the products will decrease.
- Since Keq is the ratio of the concentrations of products to reactants at equilibrium, in the form:
[tex]\[
K_{eq} = \frac{[N _2 O _4]}{[NO _2]^2}
\][/tex]
with the shift in equilibrium toward the reactants, [tex]\([N _2 O _4]\)[/tex] will decrease and [tex]\([NO _2]\)[/tex] will increase.
- Therefore, the value of Keq will decrease as the equilibrium shifts to favor the formation of reactants.
### Conclusion:
Given that the temperature increase causes the equilibrium to shift towards the reactants for an exothermic reaction, the equilibrium constant Keq will decrease.
Thus, the correct answer is:
B. decrease
