CO2 = 86.8%
Ne = 13.2%
First, let's determine the molar mass of CO2 and Ne. Start by looking up the atomic weights of the involved elements.
Atomic weight carbon = 12.0107
Atomic weight oxygen =15.999
Atomic weight neon =20.1797
Molar mass CO2 = 12.0107 + 2 * 15.999 = 44.0087 g/mol
And the molar mass of neon is the same as the atomic weight since it's a noble gas.
Since we know the total number of moles of gas particles is 1.25, let's set up an equation to solve. I'll use X as the number of moles of CO2 and (1.25-X) for the number of moles of neon. So
44.0087X + (1.25-X)*20.1797 = 47.6
And solve for X
44.0087X + (1.25-X)*20.1797 = 47.6
44.0087X + (1.25*20.1797 - 20.1797X = 47.6
44.0087X + 25.224625 - 20.1797X = 47.6
44.0087X - 20.1797X = 47.6 - 25.224625
23.829X = 22.375375
X = 22.375375/23.829
X = 0.93899765
So we now know that there's 0.93899765 moles of CO2 in the gas mixture. So the mass of CO2 is
0.93899765 mol * 44.0087 g/mol = 41.32406588 g
And we now have 2 ways to calculate the mass of neon. We can determine the number of moles of neon, then multiple by the atomic weight. Or we can take the total mass of the gas and subtract the mass of CO2. Let's use both methods as a cross check.
(1.25 - 0.93899765) * 20.1797
= 0.31100235 * 20.1797
= 6.275934124 g
and
47.6 g - 41.32406588 g
= 6.275934124 g
And both methods match, so we have confidence that the math was done correctly. To get the percentages of each gas, just divide their masses by the total mass. So
% CO2 = 41.32406588 / 47.6 = 0.868152644 = 86.8152644%
% Ne = 6.275934124 / 47.6 = 0.131847356 = 13.1847356%
And the percentages to 3 significant figures are
CO2 = 86.8%
Ne = 13.2%
