Gases
Chapter 14
14.1 The Gas Laws
• Kinetic Theory helps us understand the
behavior of gases:
1st – All gases are made of tiny particles.
2nd – Gas particles are in constant, random
motion.
3rd – All collisions between
gas particles are
perfectly elastic.
In order to study Gases; one must keep track
the types of units used in each problem.
• Temperature: oC or K.
• Pressure: kPa, mm Hg, Torr. or Atm.
• Volume: mm3, cm3, m3, L, mL.
• In this chapter we are dealing with Ideal
Gases. Ideal Gas particles do not have a
volume and no mutual attraction.
STP - Standard Temperature & Pressure.
• Standard Temperature is 0 oC (273 K)
• Standard Pressure is 1 atm (760 mmHg)
Boyle’s Law
• Boyle’s Law states that at constant
temperature, the pressure of a gas varies
inversely with the volume of a gas.
P1 V1 = P2 V2
• EX1: A gas has a volume 2.0 L and a
pressure of 1.0 atm, what volume
will the gas have at 4.0 atm? At
constant temperature.
• EX2: A gas has a volume 3 L and a
pressure of 2.0 atm, what pressure
will the gas have at 24 L? At
constant temperature.
• Practice Problem 1: A gas has a
volume 50.0 L and a pressure of 8.0
atm, what volume will the gas have at
10.0 atm?
• Practice Problem 2: A gas has a
volume 20.0 L and a pressure of 5.0
atm, what pressure will the gas have at
25.0 L?
Charles’ Law
• At constant pressure, the volume of a gas
varies directly with the temperature of a
gas.
V1 = V 2
T1 T 2
• All temperatures must be in Kelvin (K)
K = oC + 273
• EX1: A gas has a volume 24 L and a
temp of 27.0 °C, what volume will the
gas have at 127.0 °C ?
• EX2: A gas has a volume 30 L and a
temp of 77.0 °C, what temp will the gas
have at 120 L?
• Practice Problem 1: A gas has a volume
50 L and a temp of 227 °C, what volume
will the gas have at 127 °C?
• Practice Problem 2: A gas has a volume
900 cm3 and a temp of 100.0 K, what
temp will the gas have at 450 cm3?
Gases
Chapter 14
14.2 The Combined Gas Law &
Avogadro’s Principle
• The Combined Gas Law joins Boyle’s Law
with Charles’s Law:
P1 V1 = P2 V2
T1
T2
• All calculation must be in Kelvin!!!
K = oC + 273.
• EX1: A gas at 2.0 atm
and 27.0 °C fills a
flexible container with
an initial volume of 3.0
L. If the temperature is
raised to 127.0 °C and
the pressure is increased
to 4.0 atm, what is the
new volume?
• EX2: A helium-filled
balloon at sea level has a
volume of 2.0 L at 1.0
atm and 280 °C. If it is
released and rises to an
elevation at which the
pressure is 1.5 atm and
the temperature is 27 °C,
what will be the new
volume of the balloon?
• Practice Problem 1: At 200 K
and 1.00 atm pressure, a
sample of gas occupies 30.0mL. If the temperature is
increased to 300.0 K and the
entire gas sample is
transferred to a 20.0-mL
container, what will be the
gas pressure inside the
container?
• Practice Problem 2: A sample of air in a
syringe exerts a pressure of 100 kPa at a
temperature of 27.0 °C. The syringe is
placed in a warm water bath at 87.0 °C.
The pressure of the air is
increased to 120 kPa by
pushing the plunger in,
which reduces the
volume to 0.20 -mL.
What was the original
volume of the air?
• Practice Problem 3: An
unopened, cold 2.00-L bottle of
soda contains 46.0-mL of gas
confined at a pressure of 1.30
atm at a temperature of 5.0 °C.
If the bottle is dropped into a
lake and sinks to a depth at
which the pressure is 1.52 atom
and the temperature is 2.09 °C,
what will be the volume of the
gas in the bottle?
Gases
Chapter 14
Molar Volume
• Avogadro’s Principle: at equal
temperatures and equal pressures, equal
volumes of gases contain the same
number of molecules.
• 1 mole of any gas equals 22.4 liters at STP.
Ideal Gas Equation
PV = nRT
• P = pressure measured in atmospheres (atm)
• V = volume measured in liters (L)
• n = moles measured in moles (mol)
• R = gas constant (0.08 L-atm/mol-K)
• T = temperature measured in Kelvin (K)
• EX1: What pressure is exerted by a gas in
a propane container with a volume of 2.0
L at 200 K and 5.0 mol?
• Practice Problem 1: Find the volume of a
gas with 10.0 moles at 500 K and 4.0 atm.
• PP2: A typical float at the
Macy’s Thanksgiving
Parade has a volume of
1,800,000-L at 1.0 atm and
27 °C. Find the number of
moles of gas in the float.
• PP3: Find the temperature in Celsius for a
gas held in a 2,000 mL balloon with 5.0
moles at 1520 torr.
Molecular Mass Determination
M = mRT
PV
• M = molecular mass in grams/mole
(g/mol)
• m = mass of sample in grams (g)
• R = gas constant (0.08 L-atm/mol-K)
• T = temperature in Kelvin (K)
• P = pressure in atmospheres (atm)
• V = volume in liters (L)
• EX1: What is the
molecular mass of
a gas if 1.00 L has
a mass of 2.0
grams at 200 K
and 4.0 atm.
• PP2: What is the molecular mass of a gas if
100 grams of it occupies 20.0 L at 5.0 atm
at 500 K.
•
• PP2: What is the molecular mass of a gas if
100.0 centigrams of it occupy 200.0 mL at
380 mmHg and 500 K?
Gases
Chapter 14
Mass-Volume
• Gas stoichiometry can be used to predict
the products of a reaction.
1 mole = 22.4 L at STP
Stoichiometry Solving Process
• Find the balanced equation for the
reaction.
• Convert given amount to moles.
• Use mole ratio to find moles of desired
particle.
• Convert moles of desired particle to
correct unit.
Mass-Volume Stoichiometry
EX1: How many liters of ammonia are
produced by the reaction of 56.0-grams of
nitrogen gas (N2) with excess hydrogen
gas (H2)?
N2(g) + 3 H2(g)  2 NH3(g)
• Practice Problem 1: How many liters of
water vapor (H2O) are created by the
decomposition of 400-grams of
ammonium nitrate (NH4NO3)?
NH4NO3(s)  N2O(g) + 2 H2O (g)
• Practice Problem 2: How many liters of
chlorine gas (Cl2) are needed to
completely react with 276 grams of solid
sodium (Na)?
2 Na (s) + Cl2 (g)  2 NaCl (s)
Volume-Mass Stoichiometry
• EX2: Find the mass of water that is
produced by the reaction of 67.2-L of
oxygen gas (O2) with excess hydrogen gas
(H2) at STP.
H2 (g) + O2 (g)  H2O (l)
• Practice Problem 3: Calculate the mass of
hydrogen gas (H2)needed to react with
224-L of nitrogen gas (N2) at STP.
N2 (g) + 3 H2 (g)  2 NH3 (g)
• Practice Problem 4: Calculate the mass of
carbon dioxide (CO2) produced by the
reaction of 1120-L of propane (C3H8) at
STP.
C3H8 + 5 O2 (g)  3 CO2 (g) + 4 H2O (l)
Volume-Volume Problems
• EX3: How many liters of carbon dioxide
(CO2) are produced by the reaction of
11.2-L of propane (C3H8)?
C3H8 (g) + 5O2 (g) 
3CO2 (g) + 4H2O (l)
• Practice Problem 5: How many liters of
carbon dioxide (CO2) are produced by the
reaction of 448-L of oxygen gas (O2)?
C3H8 (g) + 5 O2 (g)  3 CO2 (g) + 4 H2O (l)