A single equation relating all properties of a gas.
where R is the universal gas constant
Constant n and T Constant n and P Constant P and T
V a 1/P Boyle’s Law
V a T
Charles’ Law
V a n
Avogadro’s Law
PV = nRT
Ideal Gas Law
Ideal Gas Law
PV = nRT
P = pressure
(typical units are atm or torr or mm Hg)
V = volume (typical units are L)
n = number of moles
T = temperature (must be in K)
R = gas constant
4
The universal gas constant, R, can be calculated at STP using a temperature of 273 K, a pressure of 1.00
atm, a quantity of
1 mol of a gas, and a molar volume of 22.4 L.
P V
R = PV = (1.00 atm)(22.4 L) nT (1 mol) (273K)
n T
= 0.0821 L • atm mol • K
Summary of Units for the Universal Gas
Constant
The ideal gas law can also be written in terms of molar mass of a gas.
PV = nRT
n =mass in grams (g) molar mass (
M
)PV =
M
gRT
Ideal Gas Law Practice
A 0.210 g gas sample has a pressure of 432 torr in a 333 mL container at 23 ºC.
What is the molar mass of the gas?
Knowns
Solving For M
Calculate
P = 432 torr = 0.568 atm V = 0.333 L
T =296 K mass = 0.210 g
M = gRT
PV
= 0.210 g × 0.0821 L atm/mol K × 296 K
0.568 atm × 0.333 L
= 27.0 g/mol
PV =
M
gRT
Ideal Gas Law Practice
•
Calculate the molar mass (
M
) of an
unknown gas if 0.768 g occupies a
volume of 754 mL at 30. ºC and 342
9
Dinitrogen oxide (N2O), laughing gas, is used by dentists as an anesthetic. If a 20.0-L tank of laughing gas
contains 2.86 mol of N2O at 23 °C, what is the pressure (mmHg) in the tank?
Learning Check
10
Learning Check
A cylinder contains 5.0 L of O2 at 20 °C and 0.85 atm. How many grams of oxygen are in the cylinder?
11
What is the molar mass (g/mol) of a gas if 0.250 g of the gas occupies 215 mL at 0.813 atm and 30.0 °C?
STEP 1 Organize the data given for the gas.
R = 0.0821 L atm/mol K P = 0.813 atm
V = 0.215 L n = ? mol
T = 30.0 °C + 273 = 303 K
Ans: 35.6 g/mol
12
Kinetic Molecular Theory of Gases
Gases consist of small particles that
• move rapidly in straight paths • have no attractive forces
• are very far apart
• have very small volumes compared to
the volume of the container they occupy
• have kinetic energies that increase
with an increase in Kelvin
Real gases typically behave like ideal gases over a fairly wide range of temperatures and pressures.
Conditions where real gases deviate from ideal gases:
1) At high pressure (small volumes)
Distance between particles is small and the particles do not behave independently.
2) At low temperature
Particles experience intermolecular interactions.
Real Gases
14
Dalton’s law of partial pressures states that the total pressure
• depends on the total number of gas
particles, not on the types of particles
• exerted by a gas mixture is the sum of the
partial pressures of those gases
PT = P1 + P2 + P3 ...
The total pressure of a mixture is the sum of the partial pressures of the different gases in the mixture.
Ptotal = P1 + P2 + P3…
Each gas behaves independently in the mixture. Application of Dalton’s Law
Collecting a gas over water
Gases collected over H2O contain both the gas and H2O vapor.
Vapor pressure of H2O is constant at a given T.
Pbottle is equalized so that Pbottle = Patm thus
Patm = Pgas + PH2O
Dalton’s Law of Partial Pressures
16
Illustrating Partial Pressures
17
Learning Check
18
For some dives, scuba divers use a mixture of nitrogen and oxygen gases (Nitrox) with a pressure of 8.00 atm. If the oxygen in a tank of Nitrox has a
partial pressure of 2190 mmHg, what is the partial pressure of the nitrogen?
1) 520 mmHg 2) 2040 mmHg
3) 3890 mmHg
Learning Check
A sample of O2 gas is collected over water at 22 ºC and 662 torr. What is the partial pressure of O2 gas? The
vapor pressure of water is 19.8 torr at 22 ºC.
Knowns
Solving For PO2
Calculate
Patm = 662 torr PH2O = 19.8 torr
PO2 = Patm – PH2O
PO2 = 662 torr – 19.8 torr = 642 torr
Partial Pressures Problems
Solve for VO2 with Boyle’s Law
V2 =
P2
P1V1
(continued)
A 250. mL sample of O2 was collected over water at 23 ºC and 760 torr. What volume will the O2 occupy at
23 ºC when PO2 is 760 torr?
The vapor pressure of water at 23 ºC is 21.2 torr.
Calculate
P1V1 = P2V2
739 mm Hg 760 mm Hg
0.250 L × = 0.243 L O2
V2 =
P2 P1V1
=
Partial Pressures Problems
Calculate the density of Cl2 at STP.
molar mass Cl2 = 70.9 g/mol
d =
L 1 mol
22.4 L
d = molar mass g × g= mol
× 1 mol Cl2
22.4 L Cl2
= 3.17 g/L 70.9 g Cl2
1 mol Cl2
Sense Check: Gas densities are expected to be low.
(
)
(
)
Gas Density Practice
Gas Stoichiometry
© 2014 John Wiley & Sons, Inc. All rights reserved.
At STP: the molar volume can be used as a conversion factor to convert between moles and volume.
23
Gases in Equations
The volume or amount of a gas in a chemical reaction can be calculated from
• the ideal gas law
mol P4 = Calculate
For the following reaction:
Calculate the number of moles of phosphorus needed to react with 4.0 L of H2 gas at 273 K and 1.0 atm.
Knowns V =4.0 L T = 273 K P = 1.0 atm
= 0.0030 mol P4 4.0 L H2 ×
22.4 L H2
1 mol H2 1 mol P4
6 mol H2
×
P4 (s) + 6 H2 (g) 4 PH3 (g)
Solution Map L H2 mol H2 mol P4
Gas Stoichiometry Practice at STP
25
Example of Using the Ideal Gas Law with an
Equation
What volume, in L, of Cl2 gas at 1.20 atm and
27 °C is needed to completely react with 1.50 g of aluminum?
2Al(s) + 3Cl2(g) 2AlCl3(s)
g given mol given mol gas
L gas using ideal gas law
26 What volume (L) of O2 at24 °C and 0.950 atm is needed to react with 28.0 g of NH3?
4NH3(g) + 5O2(g) 4NO(g) + 6H2O(g)
g given mol given mol gas
L gas using ideal gas law
52.6 L
27
What mass of Fe will react with 5.50 L of O2 atSTP? 4Fe(s) + 3O2(g) 2Fe2O3(s)
L gas moles gas (using 22.4 L at STP) moles Fe g Fe
18.3 g of Fe
