The equilibrium concentrations for the reaction \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftarrows \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) are \(\left[\mathrm{CS}_{2}\right]=6.10 \times 10^{-3} \mathrm{M},\left[\mathrm{H}_{2}\right]=1.17 \times 10^{-3} \mathrm{M},\left[\mathrm{CH}_{4}\right]=2.35 \times 10^{-3} \mathrm{M},\left[\mathrm{H}_{2} \mathrm{~S}\right]=2.93 \times\) \(10^{-3}\) M. Calculate \(K_{\mathrm{eq}}\) for this reaction.

In chemistry, chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate, leading to constant concentrations of the reactants and products over time. This state doesn't mean that the reactants and products are equal in concentration, but rather that their concentrations have stabilized at a particular ratio. The point at which this occurs is known as the equilibrium point.

For the reaction
\[\mathrm{CH}_{4}(g) + 2 \mathrm{H}_{2}S(g) \rightleftarrows \mathrm{CS}_{2}(g) + 4 \mathrm{H}_{2}(g)\]
the system reaches equilibrium when the rate at which the reactants combine to form the products is equal to the rate at which the products decompose back into the reactants. Although the macroscopic properties, such as concentration, remain constant at equilibrium, it's important to recognize that chemical equilibrium is a dynamic process where individual molecules continue to react.

To understand how a reaction system is behaving at any given moment, chemists use the reaction quotient Qc, which has the same form as the equilibrium constant expression but uses the concentrations of the reactants and products at any point in time, not just at equilibrium.

For example, for the given reaction
\[\mathrm{CH}_{4}(g) + 2 \mathrm{H}_{2}S(g) \rightleftarrows \mathrm{CS}_{2}(g) + 4 \mathrm{H}_{2}(g)\]
the reaction quotient is given by:\[Q_c = \frac{[\mathrm{CS}_{2}] \cdot [\mathrm{H}_{2}]^4}{[\mathrm{CH}_{4}] \cdot [\mathrm{H}_{2}S]^2}\]
Comparing the value of \(Q_c\) to \(K_{eq}\), the equilibrium constant, we can predict the direction in which the reaction will proceed to reach equilibrium. If \(Q_c < K_{eq}\), the forward reaction is favored, producing more products. If \(Q_c > K_{eq}\), the reverse reaction is favored, to produce more reactants.

The term equilibrium concentrations refers to the concentrations of the reactants and products at equilibrium. These concentrations do not change as long as the system's conditions remain constant. Understanding and calculating these concentrations are essential for predicting the outcome of a reaction and for designing chemical processes.

Let's revisit the reaction:
\[\mathrm{CH}_{4}(g) + 2 \mathrm{H}_{2}S(g) \rightleftarrows \mathrm{CS}_{2}(g) + 4 \mathrm{H}_{2}(g)\]
The given equilibrium concentrations were:

• \([\mathrm{CS}_{2}] = 6.10 \times 10^{-3} \mathrm{M}\)
• \([\mathrm{H}_{2}] = 1.17 \times 10^{-3} \mathrm{M}\)
• \([\mathrm{CH}_{4}] = 2.35 \times 10^{-3} \mathrm{M}\)
• \([\mathrm{H}_{2}S] = 2.93 \times 10^{-3} \mathrm{M}\)

With these concentrations, we can calculate the equilibrium constant, \(K_{eq}\), which provides valuable insight into the ratio of product to reactant concentrations for this reaction.

Le Chatelier's Principle is a fundamental concept in chemistry that predicts how a change in conditions will affect the position of equilibrium in a chemical reaction. According to this principle, if an external condition (such as concentration, temperature, or pressure) is changed, the equilibrium will shift to counteract the change and re-establish equilibrium.

For instance, if additional \(\mathrm{CH}_{4}\) were introduced into the system for the reaction
\[\mathrm{CH}_{4}(g) + 2 \mathrm{H}_{2}S(g) \rightleftarrows \mathrm{CS}_{2}(g) + 4 \mathrm{H}_{2}(g)\]
Le Chatelier's Principle suggests that the equilibrium would shift to the right, favoring the formation of \(\mathrm{CS}_{2}\) and \(\mathrm{H}_{2}\) to reduce the added \(\mathrm{CH}_{4}\). Conversely, an increase in the concentration of a product would shift the reaction to the left, promoting the formation of reactants. Understanding this principle helps chemists to control and optimize reactions by carefully adjusting the conditions to steer the equilibrium in the desired direction.