Consider the reaction: At a certain temperature, Kc = 8.5 * 10-3. A reaction mixture at this temperature containing solid NH4HS has [NH3] = 0.166 M and [H2S] = 0.166 M. Will more of the solid form, or will some of the existing solid decompose as equilibrium is reached?

Understanding the equilibrium constant (\( K_c \)) helps us predict the direction and extent of a chemical reaction. It is specific to a particular reaction at a given temperature. The value of the equilibrium constant reflects the ratio of the concentrations of the products to the reactants when the reaction has reached a steady state where the concentrations no longer change with time.

For the dissociation of ammonium hydrogen sulfide (\( NH_4HS \) decomposes into ammonia (\( NH_3 \) and hydrogen sulfide (\( H_2S \)), the expression for the equilibrium constant based on a balanced chemical equation is given by:
\[ K_c = [NH_3][H_2S] \].
The numerical value of the equilibrium constant tells us about the position of equilibrium. If it is a large number, products are favored at equilibrium; if it is small, reactants are favored. In the given problem, the equilibrium constant for the dissociation of solid ammonium hydrogen sulfide is provided as \( 8.5 \times 10^{-3} \), indicating a reaction that favors the formation of reactants at equilibrium.

The reaction quotient (\( Q \)) is a crucial concept that tells us about the progress of a reaction. It is calculated in the same way as the equilibrium constant but is not fixed and changes as the reaction progresses. Q is found using the concentrations of the reactants and products at any given time before the reaction reaches equilibrium.

To calculate the reaction quotient for the dissociation of ammonium hydrogen sulfide, we use the formula:\[ Q = [NH_3][H_2S] \].
In the exercise, we are given the concentrations of ammonia and hydrogen sulfide, both at 0.166 M. Therefore:
\[ Q = (0.166)(0.166) = 0.02756 \].
We then compare Q to the equilibrium constant to determine the direction in which the reaction will proceed to reach equilibrium. If \( Q < K_c \), the reaction will move forward, shifting toward products. If \( Q > K_c \), the reaction shifts toward reactants. This comparison is pivotal for predicting how the system will change over time to achieve equilibrium.

The dissociation of ammonium hydrogen sulfide (\( NH_4HS \) into ammonia (\( NH_3 \) and hydrogen sulfide (\( H_2S \) is portrayed in the balanced chemical reaction:\[ NH_4HS(s) \rightleftharpoons NH_3(g) + H_2S(g) \].
This reaction showcases a dynamic equilibrium where the rate of the forward reaction (dissociation of the solid) equals the rate of the reverse reaction (formation of the solid) at equilibrium. In the given situation, with both products having the same concentration upon mixing, we use the predetermined Kc value to predict whether solid will form or decompose as the system reaches equilibrium.

After calculating the reaction quotient, we found \( Q \) to be lower than \( K_c \). This suggests that, to reach equilibrium, the reaction will shift in the direction that increases the production of gases, which means that more of the solid NH4HS will decompose. This knowledge is essential when anticipating the behavior of the system under different concentration conditions and can be extrapolated to various other equilibrium reactions in chemistry.