Gases

Chapter 5

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 Lecture Outline

5.1 Substances That Exist as Gases

5.2 Pressure of a Gas

5.3 The Ideal Gas Equation

5.4 Gas density

5.5 Gas Stoichiometry

5.6 Dalton's Law of Partial Pressures

Elements that exist as gases (blue colored) at
250C and 1 atmosphere

5.1
5.1
 Physical Characteristics of Gases

• Gases assume the volume and shape of their

containers.
• Gases are the most compressible state of matter
– large distance between molecules
• Gases will mix evenly and completely when
confined to the same container – form
homogeneous mixtures
• Gases have much lower densities than liquids
and solids.
 Force
Pressure = Area
(force = mass x acceleration)

Units of Pressure

1 pascal (Pa) = 1 N/m2

1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
1 atm = 14.7 PSI
You should remember units of P Barometer
5.2
16 km 0.2 atm

6 km 0.5 atm

Sea level 1 atm

5.2
 Example: pressure unit conversions
1 pascal (Pa) = 1 N/m2, 1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
489 mm Hg is A) how many Pa? kPa?

B) how many torr?

C) How many atm?

A) 65.2 kPa B) 489 torr C) 0.643 atm

Manometers Used to Measure Gas Pressures

5.2
 Lecture 2: ideal gases

5.1 Substances That Exist as Gases

5.2 Pressure of a Gas

5.3 The Ideal Gas Equation

5.4 Gas density

5.5 Gas Stoichiometry

5.6 Dalton's Law of Partial Pressures

 Avogadro’s Law
• The molar amounts of any two gases with the same volume are the same at a
given T and P.
• Standard temperature and pressure:
(STP) = 0C (273.15 K) and 1 atm (760 mm Hg)
• Standard molar volume of a gas at STP = 22.4 L/mol

Each of these 22.4 L bulbs contains 1.00 mol of gas at 0 °C and 1 atm pressure.
Note that the volume occupied by 1 mol of gas is the same even though the mass of 1 mol of
each gas is different.
 Example: use of Avogadro’s law
Consider the following reaction: N2(g) + 3H2(g) → 2NH3(g)
How many L H2(g) would be needed to react with 11.4 L N2(g) if the temperature
and pressure for both are the same?
A. 17.1 L B. 11.4 L C. 7.6L D34.2 L E. 3.8L

Ans: D
 “Ideal” Gases
1
Boyle’s law: V (at constant n and T)
P
Charles’ law: V  T(at constant n and P)
Avogadro’s law: V n(at constant P and T)

nT
V
P
nT nT
V = constant x =R R is the gas constant
P P

PV = nRT
 The Ideal Gas Law
 The relationships among P, V, T, and n
 PV = nRT PV (1 atm)(22.414L)
R= =
nT (1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

(remember R value (0.0821) and units, but will
always be given for tests and quizzes)
If the values of three of the four variables in the ideal
gas law are known, the fourth can be calculated.

15
 The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.

PV = nRT
PV (1 atm)(22.414L)
R= =
nT (1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

Example: What is the volume (in liters) occupied by 49.8 g of
HCl(g) at STP?
STP, so we know: T = 0 0C = 273.15 K, P = 1 atm

PV = nRT 1 mol HCl

nRT n = 49.8 g x = 1.37 mol
V= 36.45 g HCl
P
L•atm
1.37 mol x 0.0821 mol•K
x 273.15 K
V=
1 atm

V = 30.6 L
Example: calculate the volume occupied by 637 g of SO2 (MM 64.07)
at 6.08 x 103 mmHg and –23 °C.

Ans: 25.5 L
Example: how many g of oxygen gas, O2(g), are contained in a volume
of 200 L, at a pressure of 700 mm Hg and a temperature of 27 oC?
R = 0.08206 L • atm / (mol • K)

Ans: 225 g
 Lecture 3: gas density

5.1 Substances That Exist as Gases

5.2 Pressure of a Gas

5.3 The Ideal Gas Equation

5.4 Gas density

5.5 Gas Stoichiometry

5.6 Dalton's Law of Partial Pressures

 Density (d ) Calculations

m PM m is the mass of the gas in g

d= =
V RT M is the molar mass of the gas

Molar Mass (M ) of a Gaseous Substance

dRT
M= d is the density of the gas in g/L
P

Remember these equations!

22
Example: a 2.10-L vessel contains 4.65 g of a gas at 1.00 atm
and 27.0 0C. What is the molar mass of the gas?

dRT m 4.65 g g
M= d= = = 2.21
P V 2.10 L L

g L•atm
2.21 L x 0.0821 mol•K
x 300.15 K
M=
1 atm

M = 54.5 g/mol

23
Example: determine the molar mass of “Freon” gas if a sample weighing
0.597 g occupies 100. cm3 at 95°C, and 1,000. mmHg.

dRT
M= R = 0.082057 L • atm / (mol • K)
P

Ans: 137 g/mol

 Example: problem from practice final exam
A gas has the % mass composition 80 % C, 20 %H.
Its density is 1.77 g/L when p = 735.0 mm Hg and T = 27 oC.
a) Find its empirical formula.
b) Find its Molar Mass (g/mol) – do in same way as on previous slide
c) What is the molecular formula of the gas? dRT
R = 0.082057 L • atm / (mol • K) M=
P

a) CH3 b) 45 g/mol c) C3H9

Lecture 4: gas stoichiometry; Dalton’s Law of
partial pressure

5.1 Substances That Exist as Gases

5.2 Pressure of a Gas

5.3 The Ideal Gas Equation

5.4 Gas Density

5.5 Gas Stoichiometry

5.6 Dalton's Law of Partial Pressures

 Gas Stoichiometry

What is the volume of CO2 produced at 37 0C and 1.00

atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)
g C6H12O6 mol C6H12O6 mol CO2 V CO2

1 mol C6H12O6 6 mol CO2

5.60 g C6H12O6 x x = 0.187 mol CO2
180 g C6H12O6 1 mol C6H12O6

L•atm
0.187 mol x 0.0821 x 310.15 K
nRT mol•K
V= = = 4.76 L
P 1.00 atm
5.5
Example: what volume of CO2 gas at 645 torr and 800 K could be produced
by the reaction of 45 g of CaCO3 according to this equation?
CaCO3(s) CaO(s) + CO2(g)
Molar Mass of CaCO3 = 100 g.mol-1

34.8 L
Consider a case in which two gases, A and B, are in a
container of volume V.

nART
PA = nA is the number of moles of A
V
nBRT nB is the number of moles of B
PB =
V
nA nB
PT = PA + PB XA = XB =
nA + nB nA + nB
ni
mole fraction (Xi) =
nT
PA = XA PT PB = XB PT

Pi = Xi PT
5.6
 Dalton’s Law of Partial Pressures

V and T
are
constant

P1 P2 Ptotal = P1 + P2
P1 and P2 are partial pressures of gases 1 and 2
Example: a sample of natural gas contains 8.24 moles of CH4,
0.421 moles of C2H6, and 0.116 moles of C3H8. If the total
pressure of the gases is 1.37 atm, what is the partial pressure of
propane (C3H8)?

Pi = Xi PT PT = 1.37 atm

0.116
XC3H8 = = 0.0132
8.24 + 0.421 + 0.116

PC3H8 = 0.0132 x 1.37 atm = 0.0181 atm

 Bottle full of oxygen
gas and water vapor

2KClO3 (s) 2KCl (s) + 3O2 (g)

PT = PO2 + PH 2O
5.6
5.6
 Chemistry in Action:
Scuba Diving and the Gas Laws
Depth (ft) Pressure
(atm)
0 1

33 2

66 3

P V

5.6
Lecture 5: problems
 Show your work! 5.1
How many molecules of N2 gas can be present in a 2.5 L flask at
50°C and 650 mmHg?

Ans: 4.9 x 1022 molecules

 Show your work! 5.2
What is the pressure (in atmospheres) that will be exerted by 2,500 g of
oxygen gas (O2) when stored at 22°C in a 40.0 L cylinder?

Ans: 47.3 atm

 Show your work! 5.3
Determine the molar mass of chloroform gas if a sample weighing 0.389 g is collected
in a flask with a volume of 102 cm3 at 97°C. The pressure of the chloroform is 728
mmHg.

Ans: 121 g/mol

 Show your work! 5.4
A 0.271 g sample of an unknown vapor occupies 294 mL at 140°C and 847 mmHg.
The empirical formula of the compound is CH2. What is the molecular formula of
the compound?

Ans: C2H4
 Show your work! 5.5
Ammonium nitrite undergoes decomposition to produce only gases as shown below.
NH4NO2(s)  N2(g) + 2H2O(g)
How many liters of gas will be produced by the decomposition of 32.0 g of NH 4NO2
at 525°C and 1.5 atm? MM of NH4NO2 is 64.04 g/mol.

Ans: 65 L
 Show your work! 5.6
A mixture of three gases has a total pressure of 1,380 mmHg at 298 K. The mixture
is analyzed and is found to contain 1.27 mol N2, 3.04 mol He, and 1.50 mol Ar.
What is the partial pressure (mm Hg) of Ar?

Ans: 356 mmHg