Question

An equilibrium mixture of the reaction \(2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)\) had \(0.5\) mole \(\mathrm{H}_{2} \mathrm{~S}, 0.10\) mole \(\mathrm{H}_{2}\) and \(0.4\) mole \(\mathrm{S}_{2}\) in one litre vessel. The value of equilibrium constant \((\mathrm{K})\) in \(\mathrm{mol}\) litre \(^{-1}\) is : (a) \(0.004\) (b) \(0.008\) (c) \(0.016\) (d) \(0.160\)

Short answer

0.016

Step-by-step solution

Understanding the Equilibrium Expression

The equilibrium constant, K, for the reaction can be expressed in terms of the concentrations of the gases at equilibrium. For the reaction \(2 \mathrm{H}_2\mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_2(g) + \mathrm{S}_2(g)\), the equilibrium expression is \(K = \frac{[\mathrm{H}_2]^2 [\mathrm{S}_2]}{[\mathrm{H}_2\mathrm{S}]^2}\) where [X] denotes the concentration of X in mol/L.

Calculate the Equilibrium Concentrations

Given that the equilibrium concentrations of \(\mathrm{H}_2\mathrm{S}\), \(\mathrm{H}_2\), and \(\mathrm{S}_2\) are 0.5 mol/L, 0.10 mol/L, and 0.4 mol/L respectively, we can directly substitute these into the equilibrium expression.

Substitute the Concentrations and Solve for K

Substituting the given concentrations into the equilibrium expression: \(K = \frac{(0.10)^2 \times 0.4}{(0.5)^2} = \frac{0.01 \times 0.4}{0.25} = \frac{0.004}{0.25} = 0.016\).

Choose the Correct Answer

Comparing our answer with the given options, the correct value of the equilibrium constant K is 0.016.

Key concepts

Chemical Equilibrium

Let's delve into the concept of chemical equilibrium, a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This balance means that the concentrations of the reactants and products remain constant over time, although they are not necessarily equal. When you boil water, it eventually reaches a point where it turns into steam at the same rate that steam condenses back into water. In a closed system, the amount of liquid water and steam remains steady, illustrating a state of equilibrium.

To better understand, consider the equilibrium maintained in our body's hemoglobin as it picks up oxygen in the lungs and releases it in tissues. The oxygen binding and release occur continuously, but overall levels stay relatively unchanged, a dynamic yet stable state mirroring chemical equilibrium.

Reaction Quotient

The reaction quotient, denoted as Q, is a measure that tells us how far a system is from reaching equilibrium. It is calculated using the same formula as the equilibrium constant, K, but with the initial concentrations of the reactants and products.
For example, if you start with pure reactants, Q would be equal to zero because there are no product concentrations in the expression. As the reaction progresses, Q changes until it equals the equilibrium constant, K, indicating that the system has reached equilibrium.

It's like a GPS for chemical reactions, providing real-time data on where you are versus your destination—equilibrium. If Q < K, the system will shift to the right, forming more products. If Q > K, it'll shift left, forming more reactants. Equilibrium is achieved when Q equals K, and no further shifts occur.

Equilibrium Expression

The equilibrium expression for a reaction gives us the equilibrium constant, K, outlining the ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients in the balanced chemical equation. For our given reaction, the equilibrium expression is
\(K = \frac{[\mathrm{H}_2]^2 [\mathrm{S}_2]}{[\mathrm{H}_2\mathrm{S}]^2}\)
, where [X] symbolizes the concentration of substance X at equilibrium.Consider the equilibrium expression as a recipe that always remains the same, regardless of how much you make. Just as in cooking, you scale ingredients up or down maintaining the proportions, in a reaction, changing the amounts of reactants or products doesn't alter the equilibrium expression or the value of K, if the temperature is constant. It's this consistency that allows chemists to predict how a reaction will behave under various conditions.