In a mixture of sulfur dioxide and sulfuric gas, there are 11 oxygen atoms per 5 sulfur atoms.

In a mixture of sulfur dioxide and sulfuric gas, there are 11 oxygen atoms per 5 sulfur atoms. calculate the average molar mass of the mixture.

1. Let’s write down the schemes of decomposition of gases into atoms:

SO2 → S + 2O;

SO3 → S + 3O;

2. let n (SO2) = x mol; and n (SO3) = y mol;

3.we express the number of atoms:

n1 (S) = n (SO2) = x mol;

n2 (S) = n (SO3) = y mol;

ntotal (S) = n1 (S) + n2 (S) = x + y = 5;

n1 (O) = n (SO2) * 2 = 2x mol;

n2 (O) = n (SO3) * 3 = 3y mol;

ntotal (O) = n1 (O) + n2 (O) = 2x + 3y = 11 mol;

4. Let’s compose a system of equations and find the number of atoms in the mixture:

x + y = 5;

2x + 3y = 11;

y = 5 – x;

2x + 3 * (5 – x) = 11;

2x + 15 – 3x = 11;

x = 4;

y = 1;

5.Calculate the volume fractions of gases in the mixture:

n (mixtures) = n (SO2) + n (SO3) = 4 + 1 = 5 mol;

ϕ (SO2) = n (SO2): n (mixtures) = 4: 5 = 0.8;

ϕ (SO3) = n (SO3): n (mixtures) = 1: 5 = 0.2;

6.Calculate the molar mass of the mixture:

M (mixture) = ϕ (SO2) * M (SO2) + ϕ (SO3) * M (SO3);

M (mixture) = 0.8 * 64 + 0.2 * 80 = 67.2 g / mol.

Answer: 67.2 g / mol.