A 0.500-L reaction vessel at \(700 \mathrm{~K}\) contains \(1.20 \times 10^{-3} \mathrm{~mol} \mathrm{SO}_{2}(\mathrm{~g}), 5.0 \times 10^{-4} \mathrm{~mol} \mathrm{O}_{2}(\mathrm{~g})\), and \(1.0 \times 10^{-4} \mathrm{~mol} \mathrm{SO}_{3}(\mathrm{~g}) .\) At \(700 \mathrm{~K}, K_{c}=1.7 \times 10^{6}\) for the cquilibrium \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{SO}_{3}(\mathrm{~g}) .\) (a) Calculate the reaction quotient \(Q_{e}\) (b) Will more \(\mathrm{SO}_{3}(\mathrm{~g})\) tend to form?

When studying chemical reactions, especially reversible reactions, it's crucial to determine how far the reaction has proceeded at any given moment. The reaction quotient (\( Q_c \)) serves this purpose by providing a snapshot of a reaction's progress. It is calculated using the molar concentrations of the reactants and products at a particular instance, which are not necessarily in equilibrium.

To calculate the reaction quotient, you use an expression that is similar to the equilibrium constant but without the requirement that the system is at equilibrium. For the provided exercise, the reaction quotient is given as \[\begin{equation}Q_c = \frac{[SO_3]^2}{[SO_2]^2 \times [O_2]}\end{equation}\]
Here, the brackets represent the molar concentration of the gases. By plugging in these concentrations, you obtain a value that you can compare with the equilibrium constant (\( K_c \)) to predict the direction in which the reaction will shift to attain equilibrium.

The equilibrium constant (\( K_c \)) is a fundamental concept in chemical equilibrium that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective stoichiometric coefficients in the balanced chemical equation. It is only affected by changes in temperature. In our exercise, \( K_c = 1.7 \times 10^{6} \) for the reaction at \( 700 \mathrm{K} \).

Once the reaction quotient (\( Q_c \)) has been calculated, comparing \( Q_c \) to \( K_c \) can tell you if the system is at equilibrium (\( Q_c = K_c \)), or if the reaction will proceed to form more products (\( Q_c < K_c \)), or more reactants (\( Q_c > K_c \)). It's a cornerstone for understanding how reactions adjust under different conditions and for optimizing the yields of desired products.

Molar concentration, commonly referred to as molarity, is measured in moles per liter (\( \frac{mol}{L} \)) and reflects the amount of a substance within a given volume of solution. To calculate molar concentration, divide the number of moles of the substance by the volume of the solution in liters. In the context of the exercise, this step is essential when determining the initial concentrations needed to calculate \( Q_c \).

Understanding molar concentration is critical because changes in concentration directly influence the direction and extent of chemical reactions. Knowing how to calculate and manipulate concentrations allows for control over the reaction's progress, which is essential to fields such as industrial chemistry and pharmacology.

Le Chatelier's principle is a qualitative tool in chemistry that describes how a system at equilibrium responds to disturbances or changes in conditions, such as concentration, pressure, or temperature. It states that if an equilibrium system is subjected to a change, the system will adjust to partially oppose the effect of the change and re-establish equilibrium.

For example, increasing the concentration of the reactants will shift the equilibrium to favor the formation of products, and vice versa. In the provided exercise, if \( Q_c \) is found to be less than \( K_c \), then according to Le Chatelier's principle, the reaction will shift to the right, forming more \( SO_3 \) until equilibrium is reestablished. This principle helps to predict the outcome of a reaction under variable conditions, making it a powerful tool for chemists to control the synthesis and yield of chemical substances.