Question 12.29: Calculating Partial Pressures Using Mole Fractions The compo......
Calculating Partial Pressures Using Mole Fractions
The composition of a gaseous mixture is 4.23 moles of Ne, 0.93 mole of Ar, and 7.65 moles of H _2 . Calculate the partial pressure, in atmospheres, of each gas in the mixture if the total pressure is 5.00 atm at a certain temperature.
We first calculate the mole fraction of each gas.
X_{\textrm{Ne}} = \frac{4.23 \cancel{\textrm{mole}}}{(4.23 + 0.93 + 7.65) \cancel{\textrm{mole}}} = 0.33021077 (calculator answer)
= 0.330 (correct answer)
X_{\textrm{Ar}} = \frac{0.93 \cancel{\textrm{mole}}}{(4.23 + 0.93 + 7.65) \cancel{\textrm{mole}}} = 0.072599531 (calculator answer)
= 0.073 (correct answer)
X_{\textrm{H}_2} = \frac{7.65 \cancel{\textrm{mole}}}{(4.23 + 0.93 + 7.65) \cancel{\textrm{mole}}} = 0.59718969 (calculator answer)
= 0.597 (correct answer)
To calculate partial pressures, we rearrange the equation
\frac{P_{\textrm{A}}}{P_{\textrm{total}}} = X_{\textrm{A}}to isolate the partial pressure on a side by itself.
P_{\textrm{A}} = X_{\textrm{A}} \times P_{\textrm{total}}Substituting known quantities into this equation gives the partial pressures.
P_{\textrm{Ne}} = 0.330 × 5.00 atm = 1.65 atm (calculator and correct answer)
P_{\textrm{Ar}} = 0.073 × 5.00 atm = 0.365 atm (calculator answer)
= 0.36 atm (correct answer)
P_{\textrm{H}_2} = 0.597 × 5.00 atm = 2.985 atm (calculator answer)
= 2.98 atm (correct answer)
Answer Double Check: The sum of the partial pressures of the gases in the mixture should equal the total pressure of the mixture. Such is the case here.
(1.65 + 0.36 + 2.98) atm = 4.99 atm
The sum 4.99 atm is consistent with the given total pressure of 5.00 atm; rounding errors are the basis for the two pressures differing in the hundredths digit.