Avogadro’s Principle
• Equal volumes of gases at the same temperature
and pressure contain equal number of molecules.
Volume-Volume Problem
• In one method of manufacturing nitric acid,
ammonia is oxidized to nitrogen monoxide
and water:
4NH3(g) + 5O2(g)  4NO(g) + 6H2O(l)
• What volume of oxygen will be used in a
reaction of 2800L of NH3? What volume of NO
will be produced? All volumes are measured
under the same conditions.
Volume- Volume Problem
You Try!
• Fluorine reacts violently with water to produce
hydrogen fluoride and ozone according to the
following equation:
•
3F2(g) + 3H2O(l)  6HF(g) + O3(g)
• What volume of O3 and HF gas would be produced
by the complete reaction of 3.60 X 104 mL of fluorine
gas? All gases are measured under the same
condition.
Molar Volume = 22.4 L
• Molar Volume Defined - the volume occupied by one
mole of a gas at S.T.P.
• Recall:
• 1 mole = 6.022 X 1023 molecules= molar mass = 22.4 L
Molar Volume Problems
• What is the volume, in liters, of 3.50 mol of F2 at STP?
• How many moles are contained in 5.60L of Cl2 at STP?
• Find the mass, in grams, of 2.80 L of CO2 at STP.
• Find the volume in liters of 3.50 g CO at STP.
Molar Volume Problems
You Try!
• What is the volume, in liters, of 0.0400 mol of CO2 at STP?
• How many moles are contained in 0.125 L of Ne at STP?
• Find the mass, in grams, of 15.0 mL of SO2 at STP.
• Find the volume in liters of 0.0170 g H2S at STP.
Determining the Density of a Gas at STP
22.4L/mol
Density of 1 mole of a gas at STP = Molar Mass/Molar Volume
Density at STP Problem
Calculate the density a gas will have at
STP if its molar mass is 39.9 g/mol.
Density = 39.9g x 1 mol
1 mol 22.4L
Density at STP Problem
You Try!
What is the molar mass of a
sample of gas that has a
density of 1.09 g/L at STP?
Molar Mass = 1.09g x 22.4L
1L
1mol
Ideal Gas Equation
• Recall: Boyle’s Law states Pressure and Volume are
inversely proportional if temp. is held constant.
(V = k times 1/P)
• Recall: Charles’ Law states volume and temperature are
directly proportional if pressure is held constant.
(V = kT)
• Avogadro’s Principle states at equal temperatures and
equal pressures, equal volumes of gases contain the
same number of molecules.
( V = kn)
• Therefore.... V = nkT/P or PV = nRT (Ideal Gas Equation)
Value of the ideal gas law constant
• R = PV/nT or at STP,
• R =(1atm)(22.4L)/(1 mol)(273K) = .0821atm.L/molK
Ideal Gas Law Problem #1
What is the pressure in atmospheres
exerted by a 0.500 mol sample of nitrogen
gas in a 10.0L container at 298 K?
Ideal Gas Law Problem #2
How many moles of helium gas would it
take to fill a balloon with a volume of
1000.0 cm3 (1 cm3 = 1mL) when the
temperature is 320C and the
atmospheric pressure is 752 mm of Hg?
• A tank with a volume of 658 mL contains 1.50 grams
of neon gas. The maximum safe pressure that the
tank can withstand is 4.50 X 102 kPa. At what
temperature will the tank have that pressure?
Ideal Gas Law Problems:
You Try!
A large balloon contains 11.7 g of helium. What volume will the helium
occupy at an altitude of 10 000 m where the atmospheric pressure is
0.262 atm and temperature is a -50o C.
A paper label has been lost from an old tank of compressed gas. To
help identify the unknown gas, you must calculate its molar mass. It is
known that the tank has a capacity of 90.0 L and weighs 39.2 kg when
empty. You find its current mass to be 50.5 kg. The gauge shows a
pressure of 1780 kPa. When the temperature is 18oC . What is the
molar mass of the gas in the cylinder?
Mass-Volume Stoichiometry at STP
• Steps in Solving Mass-Volume Stoichiometry Problems
– 1. Write a balanced equation.
– 2. Find the number of moles of a given substance.
– 3. Use the ratio of moles of a given substance to
moles of a required substance to find the moles of a gas.
--4. Express moles of a gas in terms of volume of a gas.
Sample Mass- Volume Problem
• Sodium reacts vigorously with water to produce
hydrogen and sodium hydroxide according to the
following equation:
2Na(s) + 2H2O(l)  2 NaOH(aq) + H2(g)
If 0.027 g of sodium reacts with excess water, what
volume of hydrogen at STP is formed?
Mass-Volume Problem- You Try!
Urea, (NH2)2CO is an important fertilizer that is
manufactured by the following reaction:
2NH3(g) + CO2(g)  (NH2)2CO(s) + H2O(g)
What volume of NH3 at STP will be needed to
produce 8.50 X 104 kg of urea?
Volume- Mass Problems
Steps in Solving Volume-Mass
Stoichiometry Problems at STP
1. Write a balanced equation.
2. Change volume of gas to moles of gas.
3. Determine the ratio of moles of a given
substance to moles of required substance.
4. Express moles of required substance as grams
of required substance.
Sample Volume Mass Problem
Dinitrogen monoxide can be prepared by heating
ammonium nitrate, which decomposes according to the
following equation:
NH4NO3(s)  N2O (g) + 2H2O(l)
What mass of ammonium nitrate should be decomposed
in order to produce 250. mL of N2O measured at STP?
Volume- Mass Problem- You Try!
Oxygen can be generated in the laboratory by heating
potassium chlorate. The reaction is represented by the
following equation:
2KClO3(s)  2KCl(s) + 3O2(g)
What mass of KClO3 must be used in order to generate
5.00 L of O2, measured at STP
Using Stoichiometry Under
Nonstandard Conditions
When given a volume under nonstandard conditions and
asked to find grams of a reactant or product.
1. Use PV = nRT to convert volume of known to moles of known.
2. Compute grams of unknown by stoichiometry.
Practice Problem on Using Stoichiometry
Under Nonstandard Conditions
The principal source of sulfur is in the form of deposits of free sulfur occurring in
volcanically active regions. The sulfur was initially formed by the reaction
between the two volcanic vapors SO2 and H2S to form H2O(l) and S (s). What
volume of each gas, at 730 mm of Hg and 22oC, was needed to form a sulfur
deposit of 4.50 X 105 kg on the slopes of a volcano in Hawaii?
SO2 + H2S  H2O(l) + S (s).
What volume of each gas, at 730 mm of Hg and 22oC, was
needed to form a sulfur deposit of 4.50 X 105 kg on the slopes
of a volcano in Hawaii?
P = 730 mm Hg X
ATM
= 0.96 ATM
760 mm Hg
PV = nRT 
V = nRT
P
n = 4.50 X 105 kg X 1000g = 4.50 X 108 g S X 1 mol S = 1.41 X 107 mol S
1 kg
32g S
T = 22oC + 273 k = 295 K
R = 0.0821
V= ?
V = 1.41 X 107 mol S * 0.0821 * 295 K = 3.54 X 108 L of each gas
0.96 ATM
Practice Problem on Using Stoichiometry
Under Nonstandard Conditions- You Try!
• A 3.25-g sample of solid calcium carbide (CaC2)
reacts with water to produce acetylene gas (C2H2)
and aqueous calcium hydroxide. If the acetlylene
is at 17oC and 740 mm of Hg, how many mL of
acetylene were produced?
CaC2 + H2O  C2H2 + Ca(OH)2
Using Stoichiometry Under
Nonstandard Conditions
When given a mass of a reactant or product and
asked to find the volume of another reactant or
product under nonstandard conditions....
1.
Compute moles of unknown by using stoichiometry.
2.
Use PV = nRT to find volume of unknown.
Practice Problem on Using Stoichiometry
Under Nonstandard Conditions
• What volume of oxygen gas in liters can be
collected at 0.987 atm pressure and 25oC when
30.6 g of KClO3 decompose by heating
according to the following equation?
2KClO3(s)  2KCl(s) + 3O2(g)
Practice Problem on Using Stoichiometry
Under Nonstandard Conditions- You Try!
How many liters of gaseous carbon monoxide at
27oC and 0.247 atm can be produced from the
burning of 65.5 g of carbon according to the
following equation:
2C(s) + O2(g)  2CO(g)
Diffusion & Effusion:
i.e. How farts spread!
The constant and
random motion of gases
causes them to spread
out a fill any container
in which they are
placed.
Diffusion: The gradual mixing of
two gases.
Effusion: Can be used to estimate
The molar mass of a gas.
Effusion: gases molecules
passing through tiny opening
Graham’s Law of Gaseous Effusion
The rate of effusion of gases at the
same temperature and pressure are
inversely proportional to the square
root of their molar masses.
Rate of effusion of A
Mb

Rate of Effusion of B
Ma
Practice Problem: Graham’s
Law of Gaseous Effusion
• Compare the rates of effusion of hydrogen and
oxygen at the same temperature and pressure.
Rate of effusion of H 2
M O2

Rate of Effusion of O 2
M H2
32 g / mol
Rate of effusion of H 2

Rate of Effusion of O 2
2.02 g / mol
Graham’s Law: You Try!
Compare the rate of effusion of carbon dioxide with
that of hydrogen chloride at the same temperature
and pressure.
Rate of effusion of CO2
M HCl

Rate of Effusion of HCl
M CO2