Gases
Chapter 10
BLB 12th
Expectations
Convert between different pressure units.
Gas Laws: solve for any gas quantity from
other given quantities.
Include gases in stoichiometric calculations.
Work with mole fractions and partial pressures.
Calculate and compare the average velocities
of gases.
10.1 Characteristics of Gases
Earth’s Atmosphere dry air near sea level
(from 18.1, p. 751)
Gas
Other common gases
(Table 10.1, p. 384)
% (by mole)
N2
78.084
O2
20.948
Ar
0.934
CO2
0.0382
Ne
0.001818
He
0.000524
Characteristics of Gases, cont.
3 states of matter: solid, liquid, gas
Properties of gases:
1.
2.
3.
4.
Gases expand to fill a container.
Gases are highly compressible.
Gases mix readily and completely mix with
other gases.
Gases exert pressure on their surroundings.
All gases behave similarly regardless of
identity.
Characteristics of Gases, cont.
In order to fully describe a gas, four quantities
are needed:
1. Pressure (P) – in Pa (SI unit), atm, mm Hg,
torr
2. Volume (V) – in L
3. Temperature (T) – in K
4. Quantity of gas (n) – in moles
10.2 Pressure
P = F/A
Measuring pressure:


Atmospheric pressure – measured with a
barometer. (p. 386)
Gas pressure in a container – measured with
a manometer. (p. 387)
Standard atmospheric pressure = 1 atm
1 atm = 760 torr = 760 mm Hg = 29.92 in Hg
= 101,325 Pa = 14.70 psi = 1013.25 mBar
Barometer
Manometer
Pressure Conversions
10.4 The Ideal-Gas Equation
PV = nRT
P – pressure in atm (additive)
V – volume in L
n – mol (additive)
R – gas constant (Table 10.2, p. 402)
= 0.08206 L·atm/mol·K
= 8.314 J/mol·K (101.3 J = 1 L·atm)
T – temperature in K
A gas which obeys this equation is said to
behave ideally.
Ideal-Gas Equation, cont.
There are no ideal gases.
A real gas approaches ideal behavior at
low pressures and high temperatures,
where molecules can behave (almost)
independently. (section 10.9)
Standard temperature & pressure (STP)
T = 0°C (273.15 K)
P = 1 atm
Molar Volume
Of an ideal gas at STP?
Of a real gas?
Molar Volumes of Gases
25
Ideal
22.41
Cl2
22.06
CO2
22.31
NH3
22.40
Molar volume (L)
20
15
10
5
0
Gas
N2
22.40
He
22.41
H2
22.42
Calculate the following for a sample of Cl2 gas
with a volume of 9.22 L at 1124 torr and 24°C.
a. Mass of Cl2?
b. Volume (in L) at STP?
Cont. Cl2 gas with a volume of 9.22 L at 1124
torr and 24°C.
c. At what temperature will V = 15.00 L if P = 876 torr?
d. At what pressure will V = 6.00 L if T = 58°C
10.3 The [Other] Gas Laws
Name
Variables
Constant Rel’n
Law
Boyle
P
V
T, n
1
V
P
Charles
T
V
P, n
V∝T
V1 V2

T1 T2
Avogadro
n
V
P, T
V∝n
V1 V2

n1 n 2
V
n
1
VT
P
P1V1 P2 V2

T1
T2
Combined P, T
P1V1 = P2V2
Boyle’s Law
Boyle’s Law for Real Gases
Charles’s Law & Absolute Zero
Charles’s Law for Real Gases
Avogadro’s Law: Equal volumes of gases at the
same T and P contain equal numbers of molecules.
A sample of gas occupies a volume of 1248 ft3
at 0.988 atm and 28.0°C.
a. Calculate the pressure if volume is decreased to
978 ft3 at constant T.
b. At what temperature in °C is the volume 1435 ft3
at constant P?
10.30 Nitrogen and hydrogen gases react to form
ammonia gas: N2(g) + 3 H2(g) → 2 NH3(g). At a certain
temperature and pressure, 1.2 L of N2 reacts with 3.6 L
of H2. If all the N2 and H2 are consumed, what volume
NH3 will be produced?
10.5 Further Applications of PV=nRT
Gas Densities and Molar Mass (M)
m
PV    RT
M 
density (g/L)
m PM
density  
RT
V
molar mass (g/mol)
mRT
molar mass  M 
PV
Calculate the density of SF6 at 455 torr and 32°C.
Calculate the molar mass of a vapor that has a density
of 6.345 g/L at 22°C and 743 torr.
Gas Stoichiometry


Use gas information to obtain moles.
Otherwise, standard stoichiometry guidelines
apply.
10.58 Calcium hydride, CaH2, reacts with water to form
hydrogen gas. How many grams of CaH2 are needed
to generate 64.5 L of H2 gas if the pressure of H2 is 814
torr at 32°C?
CaH2(s) + 2 H2O(l) → Ca(OH)2(aq) + 2 H2(g)
10.6 Gas Mixtures and Partial Pressures
For a fixed-volume container:
pressures and moles are additive;
volume is fixed.
Dalton’s Law of Partial Pressure
 RT 
Ptotal  P1  P2  ...  ntotal 

 V 
Collecting gases over water:
Ptotal  Pgas  Pwater
Collection of a gas over water
Total gas collected = product gas + water vapor
Ptotal = Pgas+ Pwater
Acetylene gas, C2H2(g), can be prepared by the reaction of
calcium carbide with water. Calculate the volume of C2H2 that is
collected over water at 21°C by reaction of 3.26 g of CaC2 if the
total pressure of the gas is 748 torr? The vapor pressure of
water at 21°C is 18.65 torr.
CaC2(s) + 2 H2O(l) → Ca(OH)2(aq) + C2H2(g)
Gas Mixtures, cont.
Mole fraction (X) – ratio of moles of one substance
to the total number of moles in mixture.
n1
P1
X1 

ntotal Ptotal
A mixture of gases contains 0.75 mol N2, 0.30 mol O2,
and 0.15 mol CO2. If the total pressure of the mixture
is 1.56 atm, what is the partial pressure of each
component?
5.25 g of SO2(g) and 2.35 g of N2(g) are placed into a
13.6-L container at 25°C.
(a) What is the PSO2?
(b) What is the PN2?
(c) What is the Ptotal?
10.7 Kinetic-Molecular Theory of Gases
Postulates: (pp. 403)
1. Particles are in constant, random motion.
2. Particles are so small … that the volume of
each is negligible relative to the total volume.
3. Attractive and repulsive forces between
particles are negligible.
4. Energy can be transferred between particles;
average kinetic energy is constant.
5. Average kinetic energy is directly proportional
to the absolute temperature. At a given T all
gas particles have same average kinetic
energy.
Molecular Speeds for N2
Root-mean-square speed
Molecular Speeds of Different Gases at 25°C
Molecular Speed
Average kinetic energy is the same for any
gas at a given T.
► But the mass of each gas is different.◄
Root-mean-square speed depends on mass
and T.


Lighter molecules move faster.
Heavier molecules move more slowly.
urms
3RT

M
R  8.314 molJK
M  molar mass in kg / mol
10.77 (a) Order the following based on average
molecular speed at 25°C: Ne, HBr, SO2, NF3, CO
(b) Calculate the rms speed of NF3 at 25°C.