Gases
Measurements on Gases
• Volume- amount of space the gas occupies:
1 L = 1000 mL = 1000 cm3 = 1 x10-3 m3
• Amount – most commonly expressed in terms of
moles (n):
m = MM x n
• Temperature – measured in degrees Celsius but
commonly must convert to Kelvin:
TK = t*C
+
273.15
• Pressure – gas molecules are constantly
colliding & because of this they exert a force
over an area:
1.013 bar = 1 atm = 760 mmHg (or torr) = 1 x 105 Pa = 14.7 psi
Barometer
Manometer
Example 1
• A balloon with a volume of 2.06 L contains
0.368 g of helium at 22 degrees Celsius
and 1.08 atm. Express the volume of the
balloon in m3, the temperature in K, and
the pressure in mmHg.
– V = 2.06 x 10-3 m3
– nHe = 0.0919 mole
– T = 22 + 273.15 = 295 K
– P = 821 mmHg
Gas Laws
• Boyle’s Law:
P1V1 = P2V2
• Charles’ Law:
V1 = V2
T1
T2
• Gay-Lusaac’s Law: P1 = P2
T1 T2
• Combined Gas Law:
P1V1 = P2V2
T1
T2
Example 2
• A tank is filled with a gas to a pressure of
977 mmHg at 25*C. When the tank is
heated, the pressure increases to 1.50
atm. To what temperature was the gas
heated?
– 75oC
The Ideal Gas Law
– The Ideal Gas Law Constant (R):
0.0821 L atm/mol K
- ideal gas law problems
8.31 J/ mol K
- equations involving energy
8.31 Kg m2/s2 mol k
- molecular speed problems
Molar Volume
Gas Law Calculations
Initial & Final State Problems:
• Starting with a sample of gas at 25*C and 1.00
atm you might be asked to calculate the
pressure developed when the sample is heated
to 95*C at a constant volume. Determine a twopoint equation and solve for the final pressure.
– Initial State: P1V = nRT1
– Final State: P2V = nRT2
– Divide the 2 equations to derive a “two-point” equation:
• P1 = T1
P2 = T2
– Rearrange to solve for the variable you want: P2 = P1 T2
T1
Ans: 1.23 atm
Example 3
• A 250.0 mL flask, open to the atmosphere,
contains 0.0110 mol of air at 0 *C. On
heating, part of the air escapes: how much
remains in the flask at 100 *C?
– 0.00805 mol of air
Example 4
• If 2.50 g of sulfur hexafluoride is
introduced into an evacuated 500.0 mL
container at 83*C, what pressure (atm) is
developed?
– Ans: 1.00 atm
Density & The Ideal Gas Law
The ideal gas law offers a simple approach to the
experimental determination of the molar mass of a gas.
– Remember that m = MM x n and
n = PV and d = m
RT
V
– So you can substitute these equations
into the ideal gas law to solve fro
density (d) or molar mass (M)
–Gas Density and Human Disasters: Many gases that are
denser than air have been involved in natural and humancaused disasters. The dense gases in smog that blanket urban
centers, such as Mexico City (see photo), contribute greatly to
respiratory illness. In World War I, poisonous phosgene gas
(COCl2) was used against ground troops as they lay in
trenches. In 1984, the unintentional release of
methylisocyanate from a Union Carbide India Ltd. chemical
plant in Bhopal, India, killed thousands of people as vapors
spread from the outskirts into the city. In 1986 in Cameroon,
CO2 released naturally from Lake Nyos suffocated thousands
as it flowed down valleys into villages. Some paleontologists
suggest that a similar process in volcanic lakes may have
contributed to dinosaur kills.
Example 5
Acetone is widely used in nail polish remover. A
sample of liquid acetone is placed in a 3.00 L flask
and vaporized by heating to 95*C at 1.02 atm. The
vapor filling the flask at this temperature and
pressure weighs 5.87 g:
(a) What is the density of acetone vapor under
these conditions?
Ans: 1.96 g/L
(b) Calculate the molar mass of acetone.
Ans: 58.1 g/mol
(c) Acetone contains three elements C, H, and O.
When 1.00 g of acetone is burned 2.27 g of CO2
and 0.932 g of H2O are formed. What is the
molecular formula of acetone?
Ans: C3H6O
Stoichiometry of Gaseous Reactions
• A molar ratio from a balanced chemical
reaction is also used in reactions involving
gases however, the ideal gas law can now be
applied.
• Example 6: A nickel smelter in Sudbury, Ontario
produces 1% of the world’s supply of sulfur
dioxide by the reaction of nickel II sulfide with
oxygen another product of the reaction is nickel
II oxide:
What volume of sulfur dioxide at 25oC and a
pressure of one bar is produced from a metric
ton of nickel II sulfide?
Ans: 2.73 x 105 L
Gas A to Gas B
Example 7
• Octane, C8H18, is one of the hydrocarbons
in gasoline. On combustion octane
produces carbon dioxide and water. How
many liters of oxygen, measured at 0.974
atm and 24*C, are required to burn 1.00 g
of octane?
– Ans: 2.73 L
Law of Combining Volumes
• The volume of any 2 gases in a reaction at
constant temperature and pressure is the
same as the reacting molar ratio:
2 H2O (l)  2H2 (g) + O2 (g)
4 L H2 x 1 L O2 = 2 L O2
2 L H2
Example 8
• Consider the reaction for the formation of water
from its elemental units.
– (a) What volume of hydrogen gas at room
temperature and 1.00 atm is required to react with
1.00 L of oxygen at the same temperature and
pressure?
• Ans: 2.00 L hydrogen gas
– (b) What volume of water at 25*C and 1.00 atm
(d=0.997 /mL) is formed from the reaction in (a)?
• Ans: 1.48 mL of water
– (c) What mass of water is formed from the reaction
assuming a yield of 85.2%?
• Ans: 1.26 g of water
Example 9
The alkali metals react with the halogens to form
ionic metal halides. What mass of potassium
chloride forms when 5.25 L of chlorine gas at
0.950 atm and 293 K reacts with 17.0 g of
potassium?
Ans: 30.9 g KCl
Dalton’s Law of Partial Pressures
• The total pressure of a gas mixture is the
sum of the partial pressures of the
components of the mixture.
Ptot = PA + PB
+…..
PH2 = 2.46 atm
PHe = 3.69 atm
then Ptot = 6.15 atm
Wet Gases
• When a gas is collected by bubbling through
water then it picks up water vapor. Then the
total pressure is the sum of the pressure of the
water vapor and the gas collected. So Dalton’s
Law can be applied by:
Ptot = PH2O
+
PA
*The partial pressure of water is equal to the vapor
pressure of water. This has a fixed value at a given
temperature (PH2O @ 25*C = 23.76 mmHg)
Gas collection by water displacement.
Example 10
• A student prepares a sample of hydrogen
gas by electrolyzing water at 25oC. She
collects 152 mL of hydrogen gas at a total
pressure of 758 mmHg. Calculate:
– (a) the partial pressure of hydrogen gas.
• Ans: 734 mmHg
– (b) the number of moles of hydrogen gas
collected.
• Ans: 0.00600 mol of hydrogen gas
Partial Pressures & Mole Fraction
• The partial pressure of a gas (PA) divided
by the total pressure (Ptot) is equal to the
number of moles of that gas divided by the
total moles of gases:
• PA = nA
Ptot ntot
• Mole fraction: XA = nA
ntot
• Partial Pressures: PA = XA Ptot
Example 11
• Methane burns in air. When one mole of
methane and four moles of oxygen are heated:
(a) What are the mole fractions of oxygen,
carbon dioxide, and water vapor in the resulting
mixture (assume all the methane is converted)?
XCH4 = 0, XCO2 = 0.200, XH2O =0.400, XO2 = 0.400
(b) If the total pressure of the mixture is 1.26
atm, what are the partial pressures of each gas?
PCO2 = 0.252 atm, PH2O =0.504 atm, PO2 = 0.504 atm
Kinetic Theory of Gases
The Molecular Model of Gases:
• Gases are mostly empty space (assumes that
gases do not have their own volume).
• Gas molecules are in constant and chaotic
motion. Their velocities are constantly changing
because of this.
• Collisions of gases are elastic (assumes no
attractive forces).
• Gas pressure is caused by collisions of
molecules with the walls of the container. As a
result, pressure increases with the energy and
frequency of these collisions. Also, average
kinetic energy of a collection of gases is
assumed to be directly proportional to the Kelvin
temperature of the gas sample.
Average Speed
(Root Mean Square Velocity)
• The equation below is derived from the average
translational kinetic energy of a gas molecule:
• It follows that at a given temperature, molecules of
different gases have the same average kinetic energy of
translational motion
and
• the average translational kinetic energy of a gas
molecule is directly proportional to the Kelvin
temperature so that:
u = _(3RT) ½
(M)
* An R value of 8.31 x 103 g m2/(s2 mol K) is used for average speed
calculations.
Example 12
• Calculate the average velocity for the
atoms in a one mole sample of helium gas
at 25oC.
– urms = 1.36 x 103 m/s
Graham’s Law of Effusion
• The average speed is inversely
proportional to the square root of the molar
mass (MM). So for two different gases A
and B at the same temperature then we
can write:
rate of effusion B = (MMA) 1/2
rate of effusion A
(MMB)
Example: Using Graham’s Law
A mixture of helium (He) and methane (CH4) is
placed in an effusion apparatus. Calculate the ratio of
their effusion rates:
Ans: He effuses 2.002 times faster than
methane
Example 13
In an effusion experiment, argon gas is
allowed to expand through a tiny opening into an
evacuated flask of volume 120.0 mL for 32.0 s, at
which point the pressure in the flask is found to be
12.5 mmHg. This experiment is repeated with a gas X
of unknown molar mass at the same T and P. It is
found that the pressure in the flask builds up to 12.5
mmHg after 48.0 s. Calculate the molar mass of X.
Ans: 89.9 g/mol
Real Gases
• The ideal gas law has been used with the
assumption that it applies exactly. However, all
real gases deviate at least slightly from the ideal
gas law.
• These deviations arise because the ideal gas
law neglects two factors:
– 1. attractive forces between gas particles
– 2. the finite volume of gas particles
*In general, the closer a gas is to the liquid state, the
more it will deviate from the ideal gas law.
Correction for Real Gas Behavior
Chemistry in the Atmosphere
• Principal components of the Earth’s atmosphere
are nitrogen and oxygen. The lowest layer of the
atmosphere is called the troposphere.
• Other gases in smaller amounts are water vapor,
carbon dioxide, argon, neon, helium, methane,
krypton, hydrogen, nitrogen monoxide and
xenon.
• Chemistry in higher levels of the atmosphere is
mostly determined by the effects of high energy
radiation (coming from the sun and other
sources in space).
Air Pollution
• The combustion of petroleum in vehicles
produces CO, CO2, NO, and NO2.
• In the troposphere, the NO2 formed assist
in the formation of ozone. The ozone
formed then leads to the formation of OH
(the hydroxyl radical) and other pollutants.
This process is often referred to as
photochemical smog.
Acid Rain
• Another major source of pollution results from
the burning of coal to produce electricity.
• Some coal (especially in the Midwest) contains
significant amounts of sulfur, which when burns
produces SO2.
• The SO2 then becomes oxidized by oxygen in
the air to produce SO3.
• The SO3 then reacts with water to produce
H2SO4. This acid results in acid rain that is
harmful to the environment and living organisms.
MC #1
• When a sample of oxygen gas in a closed
container of constant volume is heated until its
absolute temperature is doubled, which of the
following is also doubled?
(A) The density of the gas
(B) The pressure of the gas
(C) The average velocity of the gas molecules
(D) The number of molecules per cm3
(E) The potential energy of the molecules
MC #2
• At 25 °C, a sample of NH3 (molar mass 17
grams) effuses at the rate of 0.050 mole per
minute. Under the same conditions, which of the
following Gas effuses at approximately one-half
that rate?
(A) O2
(B) He
(C) CO2
(D) Cl2
(E) CH4
MC #3
• Equal masses of three different ideal Gas, X, Y, and Z,
are mixed in a sealed rigid container. If the temperature
of the system remains constant, which of the following
statements about the partial pressure of gas X is
correct?
(A) It is equal to 1/3 the total pressure
(B) It depends on the intermolecular forces of attraction
between molecules of X, Y, and Z.
(C) It depends on the relative molecular masses of X, Y,
and Z.
(D) It depends on the average distance traveled between
molecular collisions.
(E) It can be calculated with knowledge only of the
volume of the container.
MC #4
• When the actual gas volume is greater then the
volume predicted by the ideal gas law, the
explanation lies in the fact that the ideal gas law
does NOT include a factor for molecular.
(A) volume
(B) mass
(C) velocity
(D) attractions
(E) shape
MC #5
• A sample of 9.00 grams of aluminum metal is
added to an excess of hydrochloric acid. The
volume of hydrogen gas produced at standard
temperature and pressure is
(A) 22.4 liters
(B) 11.2 liters
(C) 7.46 liters
(D) 5.60 liters
(E) 3.74 liters
MC #6
• A gaseous mixture containing 7.0 moles of
nitrogen, 2.5 moles of oxygen, and 0.50 mole of
helium exerts a total pressure of 0.90
atmosphere. What is the partial pressure of the
nitrogen?
(A) 0.13 atm
(B) 0.27 atm
(C) 0.63 atm
(D) 0.90 atm
(E) 6.3 atm
MC #7
• A sample of an ideal gas is cooled from 50.0
°C to 25.0 °C in a sealed container of
constant volume. Which of the following values
for the gas will decrease?
I. The average molecular mass of the gas
II. The average distance between the molecules
III. The average speed of the molecules
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
MC #8
NH4NO3(s) --> N2O(g) + 2H2O(g)
A 0.03 mol sample of NH4NO3(s) decomposes
completely according to the balanced equation
above. The total pressure in the flask measured
at 400 K is closest to which of the following?
(A) 3 atm
(B) 1 atm
(C) 0.5 atm
(D) 0.1 atm
(E) 0.03 atm
MC #9
• As the temperature is raised from 20 ° C
to 40 ° C, the average kinetic energy of
neon atoms changes by a factor of
(A) 1/2
(B) [square root of](313/293)
(C) 313/293
(D) 2
(E) 4
MC #10
• A hydrocarbon gas with an empirical
formula CH2 has a density of 1.88 grams
per liter at 0 °C and 1.00 atmosphere. A
possible formula for the hydrocarbon is
(A) CH2
(B) C2H4
(C) C3H6
(D) C4H8
(E) C5H10
FRQ #1
2 H2O2(aq) → 2 H2O(l) + O2(g)
• The mass of an aqueous solution of H2O2 is 6.951 g. The H2O2 in the
solution decomposes completely according to the reaction
represented above. The O2(g) produced is collected in an inverted
graduated tube over water at 23.4°C and has a volume of 182.4
mL when the water levels inside and outside of the tube are the
same. The atmospheric pressure in the lab is 762.6 torr, and the
equilibrium vapor pressure of water at 23.4°C is 21.6 torr.
(a) Calculate the partial pressure, in torr, of O2(g) in the gascollection tube.
(b) Calculate the number of moles of O2(g) produced in the reaction.
(c) Calculate the mass, in grams, of H2O2 that decomposed.
(d) Calculate the percent of H2O2 , by mass, in the original 6.951 g
aqueous sample.
(e) What is the oxidation number of the oxygen atoms in H2O2 and
the oxidation number of the oxygen atoms in O2.
(f) Write the balanced oxidation half-reaction for the reaction.
FRQ #2
Answer the following questions about carbon monoxide, CO(g), and carbon dioxide,
CO2(g). Assume that both gases exhibit ideal behavior.
(a)
Draw the complete Lewis structure (electron dot diagram) for the CO molecule
and for the CO2 molecule.
(b)
Identify the shape of the CO2 molecule.
(c)
One of the two gases dissolves readily in water to form a solution with a pH
below 7. Identify the gas and account for this observation by writing a chemical
equation.
(d)
A 1.0 mol sample of CO(g) is heated at constant pressure. Sketch a graph to
show the expected plot of volume verses temperature as the gas is heated.
(e)
Samples of CO(g) and CO2(g) are placed in 1 L containers at the conditions in
the diagram below.
(i) Indicate whether the average kinetic energy of the CO2 is greater than,
equal to, or less than the average kinetic energy of the CO molecules. Justify your
answer.
(ii) Indicate whether the root-mean-square speed of the CO2 molecules is
greater than, equal to or less than the root-mean-square speed of the CO molecules.
Justify your answer.
(iii) Indicate whether the number of CO2 molecules is greater than, equal, or
less than the number of CO molecules. Justify your answer.
FRQ #3 (slide 1)
• A rigid 5.00 L cylinder contains 24.5 g of N2(g) and 28.0 g
of O2(g)
(a) Calculate the total pressure, in atm, of the gas
mixture in the cylinder at 298 K.
(b) The temperature of the gas mixture in the cylinder is
decreased to 280 K. Calculate each of the following.
(i) The mole fraction of N2(g) in the cylinder.
(ii) The partial pressure, in atm, of N2(g) in the
cylinder.
(c) If the cylinder develops a pinhole-sized leak and
some of the gaseous mixture escapes, would the ratio,
N2:O2, in the cylinder increase,decrease, or remain the
same? Justify your answer.
FRQ #3 (slide 2)
• A different rigid 5.00 L cylinder contains 0.176
mol of NO(g) at 298 K. A 0.176 mol sample of
O2(g) is added to the cylinder, where a reaction
occurs to produce NO2(g).
(d) Write the balanced equation for the reaction.
(e) What reactant is the limiting reactant? Justify
with a calculation.
(f) Calculate the total pressure, in atm, in the
cylinder at 298 K after the reaction is complete.
FRQ #4
• Represented above are five identical balloons, each
filled to the same volume at 25°C and 1.0 atmosphere
pressure with the pure gases indicated.
(a) Which balloon contains the greatest mass of gas?
Explain.
(b) Compare the average kinetic energies of the gas
molecules in the balloons. Explain.
(c) Which balloon contains the gas that would be
expected to deviate most from the behavior of an ideal
gas? Explain.
(d) Twelve hours after being filled, all the balloons have
decreased in size. Predict which balloon will be the
smallest. Explain your reasoning.
FRQ #5
• A mixture of H2(g), O2(g), and 2 millilitres of H2O(l) is present in a
0.500 litre rigid container at 25°C. The number of moles of H2 and
the number of moles of O2 are equal. The total pressure is 1,146
millimetres mercury. (The equilibrium vapor pressure of pure water
at 25°C is 24 millimetres mercury.)
The mixture is sparked, and H2 and O2 react until one reactant is
completely consumed.
(a) Identify the reactant remaining and calculate the number of
moles of the reactant remaining.
(b) Calculate the total pressure in the container at the conclusion
of the reaction if the final temperature is 90°C. (The equilibrium
vapor pressure of water at 90°C is 526 millimetres mercury.)
(c) Calculate the number of moles of water present as vapor in the
container at 90°C.
FRQ #6
(a) From the standpoint of the kinetic-molecular
theory, discuss briefly the properties of gas
molecules that cause deviations from ideal
behavior.
(b) At 25°C and 1 atmosphere pressure, which
of the gases below shows the greatest deviation
from ideal behavior? Give two reasons for your
choice.
CH4
SO2
O2
H2
(c) Real gases approach ideality at low
pressure, high temperature, or both. Explain
these observations.
FRQ #7
2 HCOONa + H2SO4  2CO + 2H2O + Na2SO4
A 0.964 gram sample of a mixture of sodium
formate and sodium chloride is analyzed by
adding sulfuric acid. The equation for the
reaction for sodium formate with sulfuric acid is
shown above. The carbon monoxide formed
measures 242 milliliters when collected over
water at 752 torr and 22.0°C. Calculate the
percentage of sodium formate in the original
mixture.