The density of a gas mixture of chlorine, hydrogen and oxygen, in which the number of oxygen atoms is 10 times greater

The density of a gas mixture of chlorine, hydrogen and oxygen, in which the number of oxygen atoms is 10 times greater than the number of chlorine atoms, has a hydrogen density of 4.69. An electric discharge was passed through the gas mixture, the reaction products were condensed. Determine the mass fraction of the substance in the condensate

The equations of the proceeding reactions:
H2 + Cl2 = 2HCl
2H2 + O2 = 2H2O
Let the total amount of substances in the mixture be 1 mol, n (H2) = x mol, n (Cl2) = y mol and n (O2) = z mol, then:
by condition z = 10y
D (H2 + O2 + Cl2) / H2 = 4.69
2x + 71y + 32z = 9.38
We find the composition of the mixture by solving the system of equations:
x + y + z = 1
z = 10y
2x + 71y + 32z = 9.38
x = 0.78 mol
y = 0.02 mol
z = 0.20 mol
Hydrogen is in excess with respect to both substances reacting with it – according to equation (1), 0.02 mol of H2 is needed, according to equation (2) – 0.04 mol, the excess is (0.78 -0.02 – 0.04 ) = 0.36 mol.
We calculate the amount and mass of HCl formed:
n (HCl) = 2n (Cl2) = 2 ∙ 0.02 = 0.04 mol
m (HCl) = 0.04 ∙ 36.5 = 1.46 g
We calculate the amount and mass of water formed:
n (H2O) = 2n (O2) = 2 ∙ 0.2 = 0.4 mol
m (H2O) = 0.4 ∙ 18 = 7.2 g
We calculate the mass of the solution and the mass fraction of HCl in it:
m = 1.46 + 7.2 = 8.66
ω = 1.46 / 8.66 ∙ 100% = 16.86%
Answer: 16.86%