Question

A gas mixture is made by combining 6.6 g each of Ar, Ne, and an unknown diatomic gas. At STP, the mixture occupies a volume of 15.65 L. What is the molar mass of the unknown gas?

Answer 1

1st find the total number of moles of gas
Given:
P = 1.0 atm
V = 15.65 L
T = 273.0 K

find number of moles using:
P * V = n*R*T
1 atm * 15.65 L = n * 0.08206 atm.L/mol.K * 273 K
n = 0.6986 mol

Now find moles of Ar and Ne

Molar mass of Ar = 39.95 g/mol


mass(Ar)= 6.6 g

use:
number of mol of Ar,
n = mass of Ar/molar mass of Ar
=(6.6 g)/(39.95 g/mol)
= 0.1652 mol

Molar mass of Ne = 20.18 g/mol


mass(Ne)= 6.6 g

use:
number of mol of Ne,
n = mass of Ne/molar mass of Ne
=(6.6 g)/(20.18 g/mol)
= 0.3271 mol

so,
moles of unknown = total moles - moles of Ar - moles of Ne
= 0.6986 mol - 0.1652 mol - 0.3271 mol
= 0.2063 mol

now use:
moles of unknown = mass / molar mass
0.2063 = 6.6/MM
MM = 32 g/mol

Answer: 32 g/mol