Consider the equilibrium \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons\) \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\). (a) If the partial pressure of \(\mathrm{CO}_{2}\) is increased, what happens to the partial pressure of \(\mathrm{H}_{2}\) ? (b) If the partial pressure of \(\mathrm{CO}\) is decreased, what happens to the partial pressure of \(\mathrm{CO}_{2}\) ? (c) If the concentration of \(\mathrm{CO}\) is increased, what happens to the concentration of \(\mathrm{H}_{2}\) ? (d) If the concentration of \(\mathrm{H}_{2} \mathrm{O}\) is decreased, what happens to the equilibrium constant for the reaction?

Le Chatelier's principle is a central concept in chemical equilibrium that predicts how a system at equilibrium reacts to disturbances or changes in conditions such as concentration, pressure, or temperature.

When a chemical system is at equilibrium and experiences a change in one of these conditions, the system will adjust to partially counteract the imposed change. For students to understand this concept better, imagine a balanced seesaw; if more weight is added on one side, the seesaw tilts until a new balance is achieved. Similarly, in a chemical reaction such as \( \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \), increasing the partial pressure of \( \text{CO}_2 \) (adding weight on the product side), will cause the system to shift towards the reactants side (tilts back) to reduce \( \text{CO}_2 \) pressure and restore equilibrium.

This principle helps to explain various phenomena in chemistry and is widely used in industrial processes to optimize the yield of chemical reactions.

The equilibrium constant, represented as \( K_c \) for molarity or \( K_p \) for partial pressures, is a value that expresses the ratio of the concentrations of products to reactants at equilibrium for a particular reaction at a constant temperature.

It's calculated using the concentrations or partial pressures of the reactants and products, raised to the power of their coefficients in the balanced chemical equation. For our reaction \( \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \), the equilibrium constant would be expressed as: \[ K_c = \frac{{[\text{CO}_2][\text{H}_2]}}{{[\text{CO}][\text{H}_2\text{O}]}}, \]
where the square brackets denote concentrations. The value of \( K_c \) or \( K_p \) does not change unless the temperature changes. If the system is at equilibrium and we alter the concentration of one or more components, the reaction will shift in a direction that brings \( K_c \) back to its original value, without the \( K_c \) itself changing.

Partial pressure is a concept that refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume on its own at the same temperature. In the context of our chemical reaction, each gas \( \text{CO}, \text{H}_2\text{O}, \text{CO}_2, \text{H}_2 \) has its own partial pressure.

When we discuss changes in the system, such as increasing or decreasing the partial pressure of a certain gas, we are dealing with how those changes affect the reaction's equilibrium. For instance, if we decrease the partial pressure of \( \text{CO} \), it's like reducing the 'presence' of \( \text{CO} \) in the gas mixture, which according to Le Chatelier's principle, will prompt the reaction to shift right, produce more \( \text{CO} \), hence increasing its partial pressure again. This adaptive behavior allows the reaction to maintain its equilibrium constant.

The reaction quotient, \( Q \), is a measure that is similar to the equilibrium constant, but for a reaction mixture that is not at equilibrium. It's calculated in the same way as \( K_c \) or \( K_p \), using the current concentrations or partial pressures.

The reaction quotient is particularly useful for determining the direction in which a reaction will shift to reach equilibrium. If \( Q < K_c \), the reaction will proceed in the forward direction until equilibrium is reached. If \( Q > K_c \), the reaction will proceed in the reverse direction. When the system is at equilibrium, \( Q = K_c \). By understanding \( Q \), students can predict how changes like an increase in \( \text{CO} \) concentration will cause the reaction to shift right, as the system works to restore \( Q \) to the equilibrium constant, \( K_c \), and in doing so increases \( \text{H}_2 \) concentration.