Ideal Gas Law
Volume is inversely proportional to pressure.
Volume is directly proportional to temperature.
Temperature is directly proportional to pressure.
What is the variable “n” stand for? moles
P V α n T
- α means “is proportional to” so these variables are related by a
constant called the “gas constant,” R
Ideal Gas Law:
PV = nRT
R = 0.08206 L · atm
mol · K
R = 8.314

L · kPa
mol · K
(← SI units)
You MUST change P, V, n and T into the same units of R!
STP: 1.00 atm = 101.325 kPa = 760. mm Hg = 760. torr = 14.7 psi
273 K = 0 ˚C
1.
What will be the volume of 2.006 x 1020 molecules of nitrogen at 27.0 ˚C and a pressure of
100. cm Hg?
P = 100.0 cm Hg 10 mm
1.00 atm
= 1.32 atm
1 cm
760. mm Hg
V=?L
n = 2.006 E 20 molecules
R = 0.08206 L atm/ mol K
T = 27.0 + 273 = 300 K
1 mol
6.022 E 23 molecules
= 3.331 mol
PV=nRT
(1.32) V = (3.331) (0.8206) (300)
V = 62.1 L
2. 0.980 grams of chloroform in the vapor state occupies 200. mL at a pressure of 752 mm Hg
and at 21.0 ˚C. Calculate the molar mass (g/mol) of chloroform.
P = 752 mm Hg
1.00 atm
= 0.989 atm
760. mm Hg
V = 200. mL
1L
1000 mL
= .200 L
n = ? mol
R = 0.08206 L atm/ mol K
T = 21.0 + 273 = 294 K
PV=nRT
(.989) (.200) = n (0.08206) (294)
n = 0.00820 mol
molar mass = 0.980/0.00820 = 120. g/mol
according to google =
119.38 g/mol
3. An engineer pumps 5.00 mol of carbon monoxide gas into a cylinder that has a capacity of
20.0 L. What is the pressure in kPa of CO inside the cylinder at 25.0 ºC?
Use other value of R, or convert once you’re done
P = ? kPa
V = 20.0 L
n = 5.00 mol
R = 8.314 L kPa/mol K
T = 298 K
PV=nRT
(P) (20.0) = (5.00) (8.314) (298)
n = 619 kPa
Dalton's Law of partial pressures:
all the partial pressures of the individual gases in a mixture will equal the total pressure of the
mixture
PTOTAL = pgas 1 + pgas 2 + pgas 3....
PTOTAL = pgas + pwater vapor
However, there is an unavoidable problem. The gas saturates with water vapor and now the total
pressure inside the bottle is the sum of two pressures - the gas itself and the added water vapor.
WE DO NOT WANT THE WATER VAPOR PRESSURE.
So we get rid of it by subtraction.
Pdry gas = Ptotal - Pwater vapor
This means we must get the water vapor pressure from somewhere.
We get it from a table because the water vapor pressure depends only on the temperature, NOT
how big the container is or the pressure of the other gas.
4. A mixture of neon and argon gases exerts a total pressure of 2.39 atm. The partial
pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon?
PTOTAL = pNe + pAr
2.39 = 1.84 + pAr
pAr = 0.55 atm
5. A 450 cm3 sample of hydrogen is collect over water at 12 oC. The pressure of the
hydrogen and water vapor mixture is 78.5 kPa. What is the partial pressure of the dry
hydrogen gas?
PTOTAL = pH2 + pwater vapor
78.5 = pH2 + 1.4
PH2 = 0.55 atm
6. 888 cm3 of oxygen are collected over water with a temperature of 25 oC. The total
pressure of the gases is 55.8 kPa. What is the partial pressure of the dry gas?
PTOTAL = pO2 + pwater vapor
55.8 = pH2 + 3.2
PO2 = 52.6 atm
Graham’s Law:
7.
What is the relative rate of diffusion between hydrogen and nitrogen?
𝑟𝑎𝑡𝑒𝐻2
𝑟𝑎𝑡𝑒𝑁2
=√
28.02
= 3.72
2.02
H2 travels 3.72 times faster than N2
8.
At a certain temperature the velocity of chlorine molecules is 0.0410 m/s. What is the
velocity of sulfur dioxide at the same temperature and pressure?
Let x = rate of SO2
𝑥
0.0410
=√
70.90
64.07
X = 0.0431 m/s
9.
What is the relative rate of diffusion between oxygen and carbon dioxide?
𝑟𝑎𝑡𝑒𝑂2
𝑟𝑎𝑡𝑒𝐶𝑂2
=√
44.01
32.00
= 1.17
O2 travels 1.17 times faster than CO2
Name:________________________
Date:____________________
Gas Law Problem Packet #2
Ideal Gas Law
PV = nRT
R = 0.08206
𝑳 ∙𝒂𝒕𝒎
𝒎𝒐𝒍 ∙𝑲
*** Change all temperatures to K, pressures to atm and volumes to L.
1.
A student collects 425 mL of oxygen at a temperature of 24.0 ºC and a pressure of 0.899
atm. How many moles of oxygen did the student collect?
P=
V=
n=
R=
T=
2. What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a
10.0 L container at 298 K?
3. What is the volume in liters, of 70.0 g of oxygen gas at 20.0 ºC and 0.974 atm pressure?
4. What mass of chlorine gas, Cl2, in grams, is contained in a 10.0 L tank at 27 ºC and 3.50 atm
of pressure?
5. How many grams are of carbon dioxide gas are there in a 45.1 L container at 34.0 ºC and
7.22 atm?
Dalton’s Law of Partial Pressures
6. If I place 3.00 moles of N2 and 4.00 moles of O2 in a 35.0 L container at a temperature of
25.0 ºC, what will the pressure of the resulting mixture of gases be?
7. Two flasks are connected with a stopcock. The first flask has a volume of 5.00 liters and
contains nitrogen gas at a pressure of 0.750 atm. The second flask has a volume of 8.00 L
and contains oxygen gas at a pressure of 1.25 atm. When the stopcock between the flasks
is opened and the gases are free to mix, what will the pressure be in the resulting mixture?
8. 495 cm3 of oxygen gas and 877 cm3 of nitrogen gas, both at 25.0 ºC and 114.7 kPa, are
injected into an evacuated 536 cm3 flask. Find the total pressure in the flask, assuming the
temperature remains constant.
9. 20 L of oxygen gas is collected over water at 22.0 ºC. What is the partial pressure of the
oxygen gas if the total pressure of the sample is 170 torr?
10. If a mixture gases contains argon with a partial pressure of 750 torr, neon with a partial
pressure of 900 torr, xenon with partial pressure of 125 torr, and helium with a partial
pressure of 450 mm of Hg, what is the total pressure of this mixture of gases in
ATMOSPHERES !!
11. A mixture of oxygen, hydrogen and nitrogen exerts a total pressure of 278 kPa. If the the
partial pressure of the oxygen and hydrogen are 112 kPa and 101 kPa respectively, what
would be the partial pressure exerted by nitrogen?
Chemical Demonstration Videos
Graham's Law
12. Calculate the relative rates of diffusion of H2(g) and Br2(g) at the same temperatures.
13. At a certain temperature, molecules of methane gas, CH 4 have an average velocity of
0.098 m/s. What is the average velocity of carbon dioxide molecules at this same
temperature?
14. Find the relative rate of diffusion for the gases ethane C2H6 and chlorine, Cl2.
Following section is all EXTRA CREDIT:
Finding Formula Mass (Molar Mass) and Density From Ideal Gas Law)
How do you convert moles (n) to grams (mass = m) where M= molar mass?
n = m/M
PV = mRT/M or M = mRT/PV
What is the formula for density (g/L)?
D = m/V
M = mRT/PV or M = DRT/P
15. At 28 ºC and 0.974 atm, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of the
gas?
16. What is the density of a sample of ammonia gas, NH 3, if the pressure is 0.928 atm and the
temperature is 63.0 ºC?
17. The density of a gas was found to be 2.0 g/L at 1.50 atm and 27 ºC. What is the molar
mass of the gas?
18. Agent 86 opens a vial of knockout gas at the end of a hallway 5 m from a guard. But
Agent 99 is 4 m away and is wearing a powerful perfume, which, if the guard notices will
mean immediate capture. The knockout gas has a molar mass of 255 g/mol and takes 1.5
seconds to work. The perfume odor has a molecule mass of 400 g/mol and will reach the
guard in 12 seconds. Will Agents 86 and 99 be caught? (Hint: this is a Graham’s Law
problem)