Question 12.29: Calculating Partial Pressures Using Mole Fractions The compo......

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

to isolate the partial pressure on a side by itself.

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.