Prompt Title: Equilibrium Constant Calculation

To calculate the equilibrium constant (Kc) for the reaction, first, we need to identify the balanced chemical equation for the reaction. The reaction between sulfur dioxide (SO₂) and nitrogen dioxide (NO₂) forms sulfur trioxide (SO₃) and nitrogen monoxide (NO):

SO₂ (g) + NO₂ (g) ⇌ SO₃ (g) + NO (g)

Next, we need to calculate the number of moles for each of the substances. To do this, divide the mass of each substance by its molar mass:

Moles of SO₂ = 7.68 g / 64.07 g/mol ≈ 0.120 mol Moles of NO₂ = 4.6 g / 46.01 g/mol ≈ 0.100 mol Moles of SO₃ = 4.8 g / 80.06 g/mol ≈ 0.060 mol

Now, let's determine the changes in the moles of each substance. Since we know that 4.8 g of SO₃ is formed at equilibrium, and the stoichiometry of the reaction is 1:1, it means that 0.060 mol of SO₂ reacted with 0.060 mol of NO₂ to form 0.060 mol of SO₃ and 0.060 mol of NO:

Initial moles: SO₂: 0.120 mol NO₂: 0.100 mol SO₃: 0 mol NO: 0 mol

Changes in moles: SO₂: -0.060 mol NO₂: -0.060 mol SO₃: +0.060 mol NO: +0.060 mol

Equilibrium moles: SO₂: 0.060 mol NO₂: 0.040 mol SO₃: 0.060 mol NO: 0.060 mol

Since the reaction takes place in a 1-liter vessel, the equilibrium concentrations of each substance are equal to their equilibrium moles:

[SO₂] = 0.060 M [NO₂] = 0.040 M [SO₃] = 0.060 M [NO] = 0.060 M

Now, we can calculate the equilibrium constant (Kc) using the equilibrium concentrations:

Kc = ([SO₃][NO]) / ([SO₂][NO₂])

Kc = (0.060 M * 0.060 M) / (0.060 M * 0.040 M) = 0.0036 / 0.0024 = 1.5

So, the equilibrium constant Kc for the reaction is 1.5.