The balanced chemical equation for the given reaction is:
SO₂(g) + NO₂(g) ⇌ SO₂(g) + NO(g)
The equilibrium constant for the reaction at a certain temperature is given as Kc = 2.60.
Now, let's assume that x moles of NO₂(g) react with 2.60 mol of SO₂(g) to form 1.20 mol of SO(g) at equilibrium. Then, the equilibrium concentrations of the species involved in the reaction can be expressed as:
[SO₂] = (2.60 - x) mol/L
[NO₂] = (x) mol/L
[SO] = (1.20) mol/L
[NO] = (x) mol/L
Using the equilibrium constant expression for the given reaction:
Kc = ([SO][NO]) / ([SO₂][NO₂])
Substituting the values of the concentrations at equilibrium and the given value of Kc, we get:
2.60 = [(1.20)(x)] / [(2.60 - x)(x)]
Simplifying the above equation, we get:
3.12 - 2.60x = x²
Rearranging and solving the quadratic equation, we get:
x² + 2.60x - 3.12 = 0
Using the quadratic formula, we get:
x = (-2.60 ± √(2.60² - 4(1)(-3.12))) / (2(1))
x = (-2.60 ± 2.81) / 2
x = -0.105 or x = 2.96
Since the value of x represents the number of moles of NO₂(g) that react with 2.60 mol of SO₂(g), the negative value of x is not meaningful in this context. Therefore, we can conclude that 2.96 mol of NO₂(g) must be added to 2.60 mol of SO₂(g) to form 1.20 mol of SO(g) at equilibrium.