Problem 88 - Chemistry The Molecular Nature of Matter

Question

Consider the equilibrium \(2 \mathrm{NaHSO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g)\) How will the position of equilibrium be affected by the following changes? (a) Adding \(\mathrm{NaHSO}_{3}\) to the reaction vessel (b) Removing \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) from the reaction vessel (c) Adding \(\mathrm{H}_{2} \mathrm{O}\) to the reaction vessel (d) Increasing the volume of the reaction vessel at con- stant temperature

Step-by-Step Solution

Answer

Adding NaHSO3 or removing Na2SO3 will shift the equilibrium to the right. Adding H2O shifts it to the left. Increasing the volume shifts it to the Right.

Step 1: Identify the Direction of Shift for Adding NaHSO3

When NaHSO3 (sodium bisulfite) is added to the reaction vessel, it increases the concentration of a reactant. According to Le Chatelier's Principle, the system will counteract this change by consuming the added reactant and shifting the equilibrium to the right, toward the products.

Step 2: Identify the Direction of Shift for Removing Na2SO3

When Na2SO3 (sodium sulfite) is removed from the reaction vessel, it decreases the concentration of a product. Le Chatelier's Principle states that the equilibrium will shift in the direction that opposes this decrease, thus the system will shift to the right to produce more Na2SO3.

Step 3: Identify the Direction of Shift for Adding H2O

The addition of H2O (water) increases the concentration of a product. According to Le Chatelier's Principle, the equilibrium will tend to shift to the left, toward the reactants, to reduce the concentration of water.

Step 4: Identify the Direction of Shift for Increasing Volume

Increasing the volume of the reaction vessel at constant temperature effectively reduces the partial pressure of the gases involved. Since there are more moles of gas on the right side of the equation (H2O (g) + SO2 (g)) than on the left side, the system will shift to the right to increase the pressure, offsetting the volume increase.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentration of reactants and products over time. It's a dynamic balance, not a static one, with the reaction continuing to occur in both directions at equal rates. A simple representation of equilibrium is given by the equation \( A + B \rightleftharpoons C + D \), where the double arrows indicate that both the forward (reactants to products) and reverse (products to reactants) reactions are occurring simultaneously.

In an equilibrium expression for a reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant (K) is expressed as \( K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \) where the square brackets denote the concentration of each species. The equilibrium constant is a measure of the extent of the reaction; if K is much greater than 1, the equilibrium lies towards the products, while if K is much less than 1, it lies towards the reactants. Understanding this principle is essential as it gives insight into how different factors will influence the position of equilibrium and therefore the concentrations of reactants and products at equilibrium.

Reaction Shift

A reaction shift in the context of chemical equilibrium refers to the change in the position of equilibrium when a system at equilibrium is subjected to an external change. This change can be in the form of a concentration alteration, a temperature adjustment, or a pressure or volume change when dealing with gases.

When an external change is applied, the system reacts by shifting the position of equilibrium to minimize the disturbance, in accordance with Le Chatelier's Principle. The direction of this shift is crucial for predicting the outcome of such a disturbance. For example, adding more reactants or removing products typically causes the equilibrium to shift to the right, favoring product formation. Conversely, adding more products or removing reactants typically shifts the equilibrium to the left, favoring reactant formation.

This concept is particularly important in industrial processes, where maximizing product yield is essential. By understanding how the reaction shift operates, chemists can strategically manipulate conditions to steer the equilibrium in the desired direction.

Equilibrium Disturbances

Equilibrium disturbances occur when an external stress, such as changes in concentration, pressure, volume, or temperature, is applied to a chemical system at equilibrium. Le Chatelier's Principle helps us predict how the system will respond to restore a new equilibrium state.

• Concentration Changes: Increasing the concentration of reactants or decreasing the concentration of products will shift the equilibrium towards the products (right shift). Conversely, increasing the concentration of products or decreasing the concentration of reactants will shift the equilibrium towards the reactants (left shift).
• Pressure and Volume Changes: For reactions involving gases, changing the pressure by changing the volume can affect the equilibrium position. Reducing the volume (increasing pressure) will shift the equilibrium towards the side with fewer moles of gas, while increasing the volume (decreasing pressure) will favor the side with more moles of gas.
• Temperature Changes: For exothermic reactions, an increase in temperature will shift the equilibrium to the left (favoring reactants), and a decrease will shift it to the right (favoring products). For endothermic reactions, the opposite applies.

In the context of the textbook problem, these principles explain why adding reactants or removing products shifts the equilibrium towards products, and adding products or decreasing the volume shifts it towards reactants. Such insights are pivotal in the control and optimization of chemical processes.