Answer:
About 0.054 moles.
Explanation:
Apply the ideal gas law. Recall that:
[tex]\displaystyle PV = n RT[/tex]
Solve for n, the number of moles:
[tex]\displaystyle n = \frac{PV}{RT}[/tex]
Determine the pressure of the hydrogen gas. Recall that by Dalton's Law of Partial Pressures, the total pressure is equal to the sum of the partial pressures of each individual gas:
[tex]\displaystyle P_T = P_\ell + P_\text{H$_2$}[/tex]
Convert the vapor pressure of the liquid to atm (1.00 atm = 760. torr):
[tex]\displaystyle 18\text{ torr} \cdot \frac{1.00\text{ atm}}{760.\text{ torr}} = 0.024\text{ atm}[/tex]
Therefore, the partial pressure of the hydrogen gas is:
[tex]\displaystyle \begin{aligned} P_T & = P_\ell + P_\text{H$_2$} \\ \\ (0.788\text{ atm}) & = (0.024\text{ atm}) + P_\text{H$_2$} \\ \\ P_\text{H$_2$} & = 0.764\text{ atm}\end{aligned}[/tex]
Therefore, the number of moles of hydrogen gas present is (the temperature in kelvins is 273.15 + 20.0 = 293.2 K):
[tex]\displaystyle \begin{aligned} n & = \frac{PV}{RT} \\ \\ & = \frac{(0.764\text{ atm})(1.7\text{ L})}{\left(0.08206 \text{ }\dfrac{\text{L-atm}}{\text{mol-K}}\right)(293.2\text{ K})}\\ \\ & = 0.054\text{ mol H$_2$} \end{aligned}[/tex]
