SME
General Chemistry I · Problem type
A gas collected over water
Use this for “Hydrogen is collected over water: 0.250 L at 25 °C and 755 torr in all. Water’s vapor pressure is 23.8 torr. How many moles of hydrogen were collected?”
Diagram
Dalton’s law: P = 731.2 + 23.8 = 755 torr.
Each gas’s share of the particles is its share of the pressure: 24 drawn, 23 H₂, 1 H₂O (rounded).
This is an example. Type your own values to start a new problem.
Pₜₒₜₐₗ
Total pressure
example · torr
Pwater
Water’s vapor pressure
example · torr
Pgas
Pressure of the dry gas
calculated · torr
Pₐₜₘ
Pressure of the dry gas in atm
calculated · atm
V
Volume collected
example · L
t
Temperature in °C
example · °C
T
Temperature
calculated · K
n
Amount of the gas
calculated · mol
Formulas
Pgas = Pₜₒₜₐₗ − Pwater
731.2 = 755 − 23.8
Pₐₜₘ
=
Pgas
760
0.9621
=
731.2
760
T
=
t
+
273.15
298.15 = 25 + 273.15
Pₐₜₘ
×
V
=
n
×
0.08206
×
T
0.9621 × 0.25 = 0.009831 × 0.08206 × 298.15
Assumptions
•
The bottle holds the gas and water vapor together. By Dalton’s law their partial pressures add to the total, which matches the room’s pressure when the water levels are even.
•
Read water’s vapor pressure at the water’s temperature from a table: 23.8 torr at 25 °C, 17.5 torr at 20 °C, 31.8 torr at 30 °C.
•
The gas is ideal. R = 0.08206 L·atm/(mol·K), so the pressure goes in atm (760 torr = 1 atm), the volume in liters and the temperature in kelvins.
Step-by-step
WE KNOW
Pₜₒₜₐₗ = 755 torr, Pwater = 23.8 torr, V = 0.25 L, t = 25 °C
FIND
pressure of the dry gas (Pgas), pressure of the dry gas in atm (Pₐₜₘ), temperature (T), amount of the gas (n)
Step 1 · Find pressure of the dry gas (Pgas)
Use Pgas = Pₜₒₜₐₗ − Pwater
Dalton’s law: the total is the gas plus the water vapor, so take the vapor off.
Pgas = 755 − 23.8
Pgas = 731.2 torr
Step 2 · Find pressure of the dry gas in atm (Pₐₜₘ)
Use Pₐₜₘ = Pgas ÷ 760
R is in L·atm/(mol·K), so change torr to atm: 760 torr make 1 atm.
Pₐₜₘ
=
731.2
760
Pₐₜₘ = 0.9621 atm
Step 3 · Find temperature (T)
Use T = t + 273.15
The gas laws use kelvins, which start 273.15 degrees below 0 °C.
T
=
25
+
273.15
T
=
298.15
K
Step 4 · Find amount of the gas (n)
Use Pₐₜₘ × V = n × 0.08206 × T
Only the dry gas’s own pressure counts its moles: divide PV by RT.
n
=
Pₐₜₘ
×
V
0.08206 ×
T
n
=
0.9621
×
0.25
0.08206 × 298.15
n
=
0.9621
×
0.25
24.466
n
=
0.24052
24.466
n
=
0.009831
mol
Check
Put the numbers back in. Both sides should match.
731.2 = 755 − 23.8 ✓
0.9621
=
731.2
760
✓
298.15 = 25 + 273.15 ✓
0.9621 × 0.25 = 0.009831 × 0.08206 × 298.15 ✓
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