Question

Consider the following reactions: \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) \quad\) and \(\quad \mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \rightleftharpoons 2 \mathrm{HI}(g)\) List two property differences between these two reactions that relate to equilibrium.

Short answer

In summary, the two property differences between these reactions related to equilibrium are: 1. Differences in their equilibrium constant expressions due to the state of iodine (gaseous in the first reaction and solid in the second reaction). Specifically, \(K_1 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\) for the first reaction, and \(K_2 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2]}\) for the second reaction. 2. Differences in the effect of pressure or volume changes due to the different participation of gaseous and solid species in the reactions, according to Le Chatelier's principle. The first reaction will be more sensitive to pressure and volume changes since all species involved are gases, while the second reaction will be less affected by these changes due to the presence of solid iodine.

Step-by-step solution

1. Reaction Quotient (Q) & Equilibrium Constant (K)

The reaction quotient (Q) is defined as the ratio of the concentrations of the products raised to their stoichiometric coefficients to the concentrations of the reactants raised to their stoichiometric coefficients. For the first reaction, the reaction quotient is given by: \[Q_1 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\] At equilibrium, the reaction quotient (Q) becomes the equilibrium constant (K). Therefore, the equilibrium constant for the first reaction is: \[K_1 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\] For the second reaction, the equilibrium expression is: \[Q_2 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2]}\] Since the concentration of solid iodine (I2) does not affect the equilibrium, it is omitted from the equation. At equilibrium, the reaction quotient becomes the equilibrium constant: \[K_2 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2]}\] Notice that the equilibrium constant expressions for the two reactions are different.

2. Le Chatelier's Principle

Le Chatelier's principle states that if a change in conditions is imposed on a system at equilibrium, the system will adjust itself in a way to counteract the change and restore equilibrium. For the first reaction, changes in pressure or volume will affect the equilibrium since all species involved are gases: \[\mathrm{H}_2(g) + \mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g)\] If the pressure increases or the volume decreases, the system will shift towards the side with fewer moles of gas, which is the side with the products (HI). Conversely, if the pressure decreases or the volume increases, the system will shift towards the side with more moles of gas, which is the side with the reactants (H2 and I2). For the second reaction, changes in pressure or volume will have no effect on the position of solid iodine in the equilibrium: \[\mathrm{H}_2(g) + \mathrm{I}_2(s) \rightleftharpoons 2 \mathrm{HI}(g)\] Since the concentration of solid iodine (I2) does not change with pressure or volume, only the gaseous reactant and product will be affected. Therefore, Le Chatelier's principle will have a different impact on the second reaction compared to the first one. In summary, the two property differences between these reactions related to equilibrium are: 1. Differences in their equilibrium constant expressions due to the state of iodine (gaseous in the first reaction and solid in the second reaction). 2. Differences in the effect of pressure or volume changes due to the different participation of gaseous and solid species in the reactions, according to Le Chatelier's principle.

Key concepts

Reaction Quotient

The reaction quotient, often represented by the letter \( Q \), is a valuable tool for assessing the progress of a chemical reaction. It is calculated by taking the ratio of the concentrations of products to reactants, each raised to the power of their respective coefficients. For example, in the reaction \( \mathrm{H}_2(g) + \mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g) \), the reaction quotient \( Q_1 \) is expressed as:

• \( Q_1 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]} \)

At any given moment in time during the reaction, this expression tells us the current state of the reaction. By comparing \( Q \) with the equilibrium constant \( K \), one can determine the direction in which the reaction will proceed to achieve equilibrium.
Notice, in the second reaction, iodine is solid, so it does not appear in \( Q_2 \). Solids have a constant concentration that does not change as the reaction progresses, so:

• \( Q_2 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2]} \)

This omission leads to a different interpretation for reactions involving solids, highlighting the importance of understanding the physical state of reactants and products in equilibrium calculations.

Equilibrium Constant

The equilibrium constant \( K \) is a fundamental aspect of chemical equilibrium, representing the state of balance in a chemical reaction where the forward and backward reactions occur at the same rate. It is defined based on the concentration of products and reactants at equilibrium similar to the reaction quotient but is unique to a reaction's temperature. For our reactions:

• First Reaction: \( K_1 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]} \)
• Second Reaction: \( K_2 = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2]} \)

The difference between \( K_1 \) and \( K_2 \) lies in the presence of solid iodine in the second reaction, which does not influence the equilibrium expression. This reflects the critical rule in equilibrium calculations: only the concentrations of species in the gaseous or aqueous state are included.
Knowing \( K \) helps to predict the extent of a reaction; a large \( K \) means a reaction heavily favors products, while a small \( K \) signifies a reaction favoring reactants. It's key to remember \( K \) can change with temperature, but is constant for a given reaction at a given temperature.

Le Chatelier's Principle

Le Chatelier's Principle provides a system for predicting the effect of changes in concentration, pressure, or temperature on a chemical equilibrium. This principle states that if a system at equilibrium experiences a disturbance, it will adjust in a way that tends to counteract that change.
For the reaction \( \mathrm{H}_2(g) + \mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g) \), adding pressure by decreasing volume shifts the equilibrium toward fewer moles of gas—toward the products. Conversely, reducing pressure shifts it toward the reactants.
However, the second reaction, \( \mathrm{H}_2(g) + \mathrm{I}_2(s) \rightleftharpoons 2 \mathrm{HI}(g) \), behaves differently because solid iodine does not participate in pressure changes. This is crucial when predicting the behavior of reactions involving solids versus gases under changing conditions. Each type of reactant reacts differently to increases or decreases in pressure, reflecting the nuanced applications of Le Chatelier’s Principle.

Gaseous vs Solid Reactants

Understanding the distinction between gaseous and solid reactants in equilibrium is essential. Gases and solutions are dynamic participants in chemical reactions because their concentrations can change, influencing the equilibrium state. For gases, every molecule can potentially affect the equilibrium expression, as seen in:

• \( \mathrm{H}_2(g) + \mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g) \)

Solids, however, like iodine in the reaction \( \mathrm{H}_2(g) + \mathrm{I}_2(s) \rightleftharpoons 2 \mathrm{HI}(g) \), maintain a constant state under set conditions and do not appear in the equilibrium expression. This means changes to the system such as pressure shifts will impact the equilibrium involving gases but leave solid phases largely unaffected.
This characteristic is critical for formulating forecasts about how reactions proceed in different states, leading to more accurate predictions for chemical systems in real-world scenarios.