Question 12.28: Calculating the Mole Fraction for a Gas in a Gaseous Mixture......
Calculating the Mole Fraction for a Gas in a Gaseous Mixture
A gaseous mixture contains 10.0 g each of the gases N _2 , O _2 , and Ar. What is the mole fraction of each gas in the mixture?
We first calculate the number of moles of each gas present.
N _2: \quad \quad 10.0 \cancel{\textrm{g N}_2} \times \frac{1 \textrm{mole N}_2}{28.02 \cancel{\textrm{g N}_2}} = 0.35688793 mole N _2 (calculator answer)
= 0.357 mole N _2 (correct answer)
O _2 : \quad \quad 10.0 \cancel{\textrm{g O}_2} \times \frac{1 \textrm{mole O}_2}{32.00 \cancel{\textrm{g O}_2}} = 0.3125 mole O _2 (calculator answer)
= 0.312 mole O _2 (correct answer)
Ar : \quad \quad 10.0 \cancel{\textrm{g Ar}} \times \frac{1 \textrm{mole Ar}}{39.95 \cancel{\textrm{g Ar}}} = 0.25031289 mole Ar (calculator answer)
= 0.250 mole Ar (correct answer)
The total number of moles of gas present is
n_{\textrm{total}} = n_{\textrm{N}_2} + n_{\textrm{O}_2} + n_{\textrm{Ar}}= (0.357 + 0.312 + 0.250) mole
= 0.919 mole (calculator and correct answer)
Mole fractions are calculated as ratios of individual component moles to total moles.
X_{\textrm{N}_2} = \frac{0.357 \cancel{\textrm{mole}}}{0.919 \cancel{\textrm{mole}}} = 0.38846572 (calculator answer)
= 0.388 (correct answer)
X_{\textrm{O}_2} = \frac{0.312 \cancel{\textrm{mole}}}{0.919 \cancel{\textrm{mole}}} = 0.33949945 (calculator answer)
= 0.339 (correct answer)
X_{\textrm{Ar}} = \frac{0.250 \cancel{\textrm{mole}}}{0.919 \cancel{\textrm{mole}}} = 0.27203482 (calculator answer)
= 0.272 (correct answer)
Answer Double Check: The sum of all mole fractions should always add to one. Such is the case here.
0.388 + 0.339 + 0.272 = 0.999
Rounding errors cause the sum to be 0.999 rather than 1.000.