For the chemical equation SO2 (g) + NO2 (g) SO3 (g) + NO (g) SO2 (g) the equilibrium constant at a certain temperature is 3.00. At this temperature, calculate the number of moles of NO2 (g) that must be added to 2.30 mol SO2 (g) in order to form 1.00 mol SO3 (g) at equilibrium.

The number of initial moles of NO2 are 1.256 moles

Explanation:

Step 1: Data given

K = 3.00

Moles of SO2 = 2.30 moles

Moles SO3 formed = 1.00 moles

Step 2: The balanced equation

SO2 (g) + NO2 (g) → SO3 (g) + NO (g)

Step 3: The initial number of moles

SO2 = 2.30 moles

NO2 = Y moles

SO3 = 0 moles

NO = 0 moles

Step 4: The number of moles at equilibrium

For 1 mol SO2 we need 1 mol NO2 to produce 1 mol SO3 and 1 mol NO

SO2 = 2.30 - X moles

NO2 = Y - X moles

SO3 = X moles

NO = X moles

At the equilibrium we have 1.00 mol SO3

SO3 = X moles = 1.00

X = 1.00

Moles SO2 = 2.30 - 1.00 = 1.30

Moles NO2 = Y-1.00

SO3 = 1.00 moles

NO = 1.00 moles

Step 5: Calculat Kc

Kc = [NO][SO3] / [NO2][SO2]

3.00 = (1.00 * 1.00) / (1.30 * (Y-1.00))

3.00 = 1 / (1.30Y - 1.30)

1 = 3 * (1.30Y - 1.30)

1 = 3.90Y - 3.90

4.90 = 3.90Y

Y = 1.256

The number of initial moles of NO2 are 1.256 moles