Problem 109 - General Chemistry: Principles and Modern Applications

Question

For the reaction \(\mathrm{SO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{aq}), K=1.25 \mathrm{at}\) \(25^{\circ} \mathrm{C} .\) Will the amount of \(\mathrm{SO}_{2}(\mathrm{g})\) be greater than or less than the amount of \(\mathrm{SO}_{2}(\mathrm{aq}) ?\)

Step-by-Step Solution

Answer

The amount of \(\mathrm{SO}_{2}(\mathrm{aq})\) will be greater than the amount of \(\mathrm{SO}_{2}(\mathrm{g})\) at equilibrium at \(25^{\circ} \mathrm{C}\).

Step 1: Understanding equilibrium constant

The equilibrium constant \(K\) for a reaction is the ratio of the concentrations of the products to the reactants when the system has reached equilibrium. The magnitude of \(K\) gives us information about the composition of the equilibrium state. If \(K > 1\), the system contains more products than reactants at equilibrium; if \(K < 1\), the system contains more reactants.

Step 2: Applying equilibrium constant to the given reaction

For the reaction \(\mathrm{SO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{aq})\), since we are not given any particular concentrations or amount, we can simply regard \(\mathrm{SO}_{2}(\mathrm{g})\) as reactant and \(\mathrm{SO}_{2}(\mathrm{aq})\) as product. Therefore, as given \(K=1.25\) and with our understanding from the last step, we can conclude that at equilibrium, the system contains more of \(\mathrm{SO}_{2}(\mathrm{aq})\) which is the product than \(\mathrm{SO}_{2}(\mathrm{g})\) which we regarded as reactant.

Key Concepts

Chemical Equilibrium

When a chemical reaction occurs, the reactants transform into products, but under certain conditions, this conversion is reversible. A state of chemical equilibrium is reached when the rate at which reactants are converted into products is equal to the rate at which products revert back into reactants. This dynamic state doesn't mean that the chemical processes have stopped, but rather that they continue with no net change in the amounts of substances involved.

To understand chemical equilibrium more practically, imagine a room where two doors are being used equally for entering and leaving. The number of people in the room remains constant, not because no one is moving, but because the in-and-out traffic is balanced. Similarly, in a chemical equilibrium, the amount of reactants and products remains consistent over time.

Reaction Quotient

While chemical equilibrium provides a snapshot of a system's state once it's settled, the reaction quotient, designated as Q, helps assess the system's status at any moment during the reaction—before it reaches equilibrium. Q is calculated using the same formula as the equilibrium constant K, but with the initial concentrations or partial pressures of the reactants and products.

Comparing Q to K helps predict the direction in which a reaction must proceed to reach equilibrium. If Q is less than K, the reaction will move forward, turning reactants into products. Conversely, if Q is greater than K, the reaction will shift backward, favoring reactant formation. When Q = K, the system is at equilibrium, and no net reaction occurs.

Equilibrium State

An equilibrium state represents a condition where the forward and reverse reactions occur at the same rate, resulting in no observable changes in the amounts of reactants and products. It's important to note that being in an equilibrium state does not necessarily mean that the concentrations of reactants and products are equal. The ratio of product to reactant concentrations at equilibrium is represented by the equilibrium constant, K.

In the case of the gas-to-aqueous reaction for sulfur dioxide (SO₂(g) ⇌ SO₂(aq)), the K value of 1.25 tells us that the final product, SO₂(aq), will be favored over the reactant, SO₂(g), at equilibrium at 25°C. Therefore, the amount of SO₂(aq) will indeed be greater at equilibrium, reflecting a system where the product is preferred, though both forms will indeed be present.