1. Problem Solving: Using Either
The Gas Laws
Problem Solving:
Using Either
P1V1 T1
P2V2 T2 or =
PV = nRT

2. Example Problems
A 2.00 L bottle containing only air is sealed at a temperature of 22°C and a pressure of atm. The bottle is placed in a freezer and allowed to cool to 3.0°C. What is the pressure in the bottle?
Step 1:
Decide which formula to use.
P1V1 T1
P2V2 T2 =
Step 2:
Identify variables given & variable that is unknown.
V is constant because bottle does not change.
T1 = 22oC
P1 = atm
T2 = 3.0oC
P2 = ? atm

3. Step 3:
Convert all temperatures to KELVIN & make sure pressure units are consistent .
T1 = = 295 K
T2 = = 276 K
Step 4:
Plug in all known values into equation.
.982
295 P2
276 =
Step 5:
Solve for the Unknown (do the math!).
(.982)(276) = 295 P2
P2 = atm

4. 2) Hydrogen gas is collected by water displacement. Total volume
collected is L at a temperature of 17°C and a pressure of mmHg.
What volume of dry hydrogen gas is collected?
Step 1:
Decide which formula to use.
P1V1 T1
P2V2 T2 =
Step 2:
Identify variables given & variable that is unknown.
Total Volume = V1
V1 = L
Temperature is constant.
P2 = must subtract water vapor
17oC from P1
P1 = mmHg
V2 = volume of dry hydrogen = ??

5. T (oC) P (mmHg) P (mmHg) Step 3:
Convert all temperatures to KELVIN & make sure pressure units are consistent .
Not needed since temperature is constant.
Step 4:
Determine the water vapor pressure in atmospheres at 17oC and subtract this value from P1.
P2 = – = mmHg
T (oC) P
(mmHg)
P (mmHg) 10
9.2 17
14.5 11
9.8 18
15.5 12
10.5 19
16.5 13
11.2 20
17.5 14 21
18.7 15
12.8 22
19.8 16
13.6 23
21.1
Step 5:
Plug in all known values into equation.
(751.64)(.461) = (737.14) V2
Step 6:
Solve for the Unknown (do the math!).
( x .461)
737.14 =
0.470 L

6. 3) What pressure in atmospheres will 1
3) What pressure in atmospheres will 1.36 kg of N2O gas exert when it is
compressed in a 25.0 L cylinder and is stored in an outdoor shed where the
temperature can reach 59°C during the summer?
Step 1:
Decide which formula to use.
PV = nRT
Step 2:
Identify variables given & variable that is unknown.
Mass = kg
V = L
T = 59oC
P = ?? atm
R = L-atm/K-mol

7. Make sure answer has unit of pressure required!!
Step 3:
Convert all temperatures to KELVIN & make sure pressure units are consistent .
T = = K
Step 4:
Convert mass to moles.
1.36 kg N2O must be converted to moles using the molar mass of N2O
Molar mass N2O: (2 x 14.01) = g/mol
1.36 kg
1000 g
1 mol =
30.9 mol g
1 kg
Step 5:
Plug in all known values into equation.
Make sure answer has unit of pressure required!!
P (25.0) = (30.9)(.0821)(332)
Step 6:
Solve for the Unknown (do the math!).
P = (30.9 x x 332)
25.0
P = atm