Britney Kuhn
Dec 14, 2024
A gas mixture contains each of the following gases at the indicated partial pressures: N2, 315 torr; O2, 134 torr; and He, 219 torr?
A gas mixture contains the following gases at their respective partial pressures: nitrogen (N2) at 315 torr, oxygen (O2) at 134 torr, and helium (He) at 219 torr. What is the total pressure of this gas mixture? Additionally, what is the mass of each gas present in a 2.15 L sample of this mixture at a temperature of 25.0 °C?
2 Answers
total pressure = partial pressure due to N2 + partial pressure due to O2 + partial pressure due to He = 315 + 134 + 219 = 668 torr or 668/760 = 0.879 atm ( as 1 atm = 760 torr)
now PV = nRT in order to calculate total mole of gas
P = 0.879 atm
V = 2.15 L
n = total no.of moles of all three gases = ?
R = 0.0821 L atm/K/mole
T = 25 + 273 = 298 K
0.879 X 2.15 = n X 0.0821 X 298
1.889 = n X 24.466
n = 1.889/24.466 = 0.077
now partial pressure = mole fraction X total pressure
partial pressure of N2 = mole fraction of N2 X total pressure
315 = no.of moles of N2/total no.of moles X 668
315 = no.of moles of N2/ 0.077 X 668
no.of moles of N2 = 315 X 0.077 / 668 = 0.036
molar mass of N2 = 28 g/mole
so amount of N2 = 28 X 0036 = 1.008 g
similalrly ...partial pressure of O2 = mole fraction of O2 X total pressure
134 = no.of moles of O2/0.077 X 668
no.of moles of O2 = 134 X 0.077 / 668 = 0.015
molar mass of O2 = 32 g/mole
so amount of O2 = 32 X 0.015 = 0.48 g
and finally....partial pressure of He = mole fracion of He X total pressure
219 = no.of moles of He/0.077 X 668
no.of moles of He = 219 X 0.077/668 = 0.025
molar mass of He = 4 g/mole
amount of He = 0.025 X 4 = 0.1 g
(315 torr) + (134 torr) + (219 torr) = 668 torr total
n = PV / RT = (668 torr) x (2.15 L) / ((62.36367 L torr/K mol) x (25.0 + 273.15) K) = 0.07724 mol total
(0.07724 mol) x (315 torr N2 / 668 torr total) x (28.01344 g N2/mol) = 1.02 g N2
(0.07724 mol) x (134 torr O2 / 668 torr total) x (31.99886 g O2/mol) = 0.496 g O2
(0.07724 mol) x (219 torr He) / 668 torr total) x (4.002602 g He/mol) = 0.101 g He
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