# 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%