Sulfur dioxide and oxygen gases react at high

temperature (400 o C) in the presence of a catalyst(like Pt) to form sulfur trioxide gas. The reaction is
started from a gas mixture at 400oC with the partial pressures PSO2
= 15 atm and PO2= 10. atm. What
will be the final partial pressures of SO2(g), O2(g),and SO3(g), when the reaction is completed at400oC in a constant volume?

..........2SO2 + O2 ==> 2SO3

I.........15.....10.......0
You don't give a Kp; I assume the reaction is to go to completion.
SO2 can give 15 x 2 mols SO3/2 mols SO2 = 15 atm SO3.
O2 can give 10 x 2 mols SO3/1 mol O2 = 20 mols SO3; therefore,
SO2 is the limiting reagent
15 atm SO3 formed
pSO2 = 15-15 = 0
pO2 used = 15 atm SO2 x (1 mol O2/2 mol SO2) = 7.5 mols O2 used.
pO2 unused = 10-7.5 = 2.5 atm.

To determine the final partial pressures of SO2(g), O2(g), and SO3(g), we need to consider the stoichiometry of the reaction and the ideal gas law.

The balanced chemical equation for the reaction is:

2SO2(g) + O2(g) ⇄ 2SO3(g)

From the equation, we can see that two moles of SO2 react with one mole of O2 to produce two moles of SO3.

First, we need to determine the initial moles of SO2, O2, and SO3 using the partial pressures given:

nSO2_initial = PSO2 * V / (R * T)
nO2_initial = PO2 * V / (R * T)

Where:
PSO2 = Partial pressure of SO2 = 15 atm
PO2 = Partial pressure of O2 = 10 atm
V = Volume of the gas mixture
R = Ideal gas constant = 0.0821 L.atm/mol.K
T = Temperature in Kelvin (400 °C = 400 + 273.15 K)

Assuming the volume of the gas mixture is constant, we can cancel out V in the equations.

nSO2_initial = (15 atm) / (0.0821 L.atm/mol.K * 673.15 K)
nO2_initial = (10 atm) / (0.0821 L.atm/mol.K * 673.15 K)

Next, we use the stoichiometry of the reaction to determine the number of moles of SO3 formed when the reaction is completed:

nSO3_final = 2 * nSO2_initial

Now we can calculate the final partial pressures of SO2(g), O2(g), and SO3(g) using the ideal gas law:

PSO2_final = nSO2_final * R * T / V
PO2_final = nO2_final * R * T / V
PSO3_final = nSO3_final * R * T / V

Substituting the values and solving for the partial pressures will give us the final values.