Chemical Equilibrium: Calculating the Amount of Reactant Needed

How can we calculate the amount of reactant needed to reach equilibrium in a chemical reaction?

Given Data:

Equilibrium constant (Kc) for the reaction SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g) is 15.6 at 1000 K.

Amount of SO₂: 2.5 mol

Amount of SO₃ needed at equilibrium: 1.5 mol

Calculating the Amount of Reactant Needed at Equilibrium:

To find the amount of reactant needed to reach equilibrium in a chemical reaction, we can utilize the equilibrium constant expression and stoichiometry of the reaction.

When dealing with a chemical equilibrium problem, it's essential to understand how the equilibrium constant relates to the concentrations of reactants and products at equilibrium. In this case, the equilibrium constant (Kc) provided is 15.6 at 1000 K.

The equilibrium constant expression for the given reaction is:

Kc = [SO₃][NO] / [SO₂][NO₂]

Let's assume x mol of NO₂ is added to 2.5 mol of SO₂. At equilibrium, the amount of SO₃ formed should be 1.5 mol.

Following the stoichiometry of the reaction, we can express the concentrations as:

[SO₂] = 2.5 - x

[NO₂] = x

[SO₃] = 1.5

[NO] = 1.5

By substituting these values into the equilibrium constant expression, we derive the equation:

15.6 = (1.5)(1.5) / (2.5 - x)(x)

After simplifying and solving the equation, we find that approximately 2.18 mol of NO₂ must be added to 2.5 mol of SO₂ to form 1.5 mol of SO₃ at equilibrium.

Understanding how to calculate the amount of reactants needed to achieve equilibrium is crucial in predicting the outcome of chemical reactions. It involves utilizing equilibrium constants and stoichiometry to determine the optimal conditions for a reaction to reach equilibrium.