An 8.00-L reaction vessel at \(491^{\circ} \mathrm{C}\) contains \(0.650\) mole of \(\mathrm{H}_{2}, 0.275\) mole of \(\mathrm{I}_{2}\), and \(3.00\) moles of HI. Assuming that the reaction is at equilibrium, determine the value of \(K_{\text {eq }}\) and comment on where the equilibrium lies. The reaction is: \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)\)

The equilibrium constant, denoted as K_eq, is a number that provides crucial information about the state of a chemical reaction at equilibrium. This constant is derived from the ratio of the concentrations of the products raised to the power of their coefficients to the concentrations of the reactants with the same consideration. The larger the value of K_eq, the more product-favored the reaction is at equilibrium. Conversely, if K_eq is much less than 1, the reaction tends to favor the reactants under the given conditions.

For the reaction in our example, K_eq is calculated using the formula:
\[ K_{eq} = \frac{[HI]^2}{[H_{2}][I_{2}]} \]
The high value of K_eq ≈ 50.35 indicates that the conversion of hydrogen and iodine to hydrogen iodide is highly favored, and at equilibrium, the concentration of hydrogen iodide will be significantly greater than that of either hydrogen or iodine.

The reaction quotient, Q, is similar to the equilibrium constant but focuses on non-equilibrium conditions. It uses the same formula as K_eq but with the initial concentrations of reactants and products. Measuring Q allows us to predict which direction the reaction will proceed to reach equilibrium.

If Q is less than K_eq, the reaction moves forward, producing more products. If Q is greater, the reaction moves in reverse, producing more reactants. The condition Q = K_eq indicates that the system is at equilibrium. Understanding Q is key in predicting how changes in conditions, such as concentration, pressure, or temperature, will affect the direction of a reaction.

Le Chatelier's principle provides a qualitative way to understand how a system at equilibrium responds to external changes. It states that if a stress is applied to a system at equilibrium, the system will adjust in a way that opposes the stress. Stresses can include changes in concentration, pressure, or temperature.

For instance, adding more reactants into the system will shift the equilibrium to produce more products, while removing a product will result in more reactant being converted to make up for the loss. This principle helps us predict the effects of such changes and is a vital tool when trying to manipulate industrial chemical reactions or predict the behavior of natural systems.

The equilibrium position of a reaction is a term used to describe the relative concentrations of reactants and products at equilibrium. It tells us where the balance between the forward and reverse reactions lies. This doesn't necessarily mean that the reactants and products are present in equal concentrations; rather, it's where their rates of formation are equal.

In this problem, because K_eq is significantly greater than 1, the equilibrium position is far to the right, meaning the concentration of the product (HI) is much higher than that of the reactants ((H₂) and I₂). This demonstrates how K_eq helps us to understand the extent of the reaction and the equilibrium position within the reaction vessel.