Module 8
Gases
Substances that Exist as Gases
• At 25oC and 760 torr (1 atm), the following substances
exist as gases:
Elements
Elements
H2
N2
O2
O3(Ozone)
F2
Cl2
He
Ne
Ar
Kr
Xe
Rn
Compounds Compounds
HF
HCl
HBr
HI
CO
CO2
NH3
NO2
SO2
H2S
HCN
CH4
(methane)
Properties of Gases
• Compressibility-Gases can be compresses into smaller volumes.
Their densities can be increased by applying pressure. If too much
pressure is applied they will become liquids or solids.
• Indefinite shape and volume-A gas can be made to fit the vessel in
which it is placed.
• Expansion-Gases expand without limits so that gas samples
completely and uniformly occupy the volume of a container.
• Miscibility or diffusion-Gases diffuse into each other completely.
• Low density-Because the density of a gas is small, it is usually
measured in g/L.
• The average kinetic energy (KE) of gaseous molecules is directly
proportional to their absolute temperature (KE a T (K)). Provided
that T is the same, KE of different gas molecules is equal.
• The amounts and properties of gases are described in terms of T
(Temperature in K), P (pressure), V (Volume they occupy),
and n (number of moles present).
Characteristics of Ideal Gases
• The equations that will be used apply only to ideal gases
or those behaving very closely as ideal gases. An ideal
gas is considered to have the following characteristics:
a. each particle (atom or molecule) has a negligible
volume
b. has no attractive forces
c. undergoes elastic collisions (they rebound after
colliding and bounce back in the opposite direction with
the same speed).
• Real gases can behave as ideal gases by avoiding:
a. extremely low temperatures
b. very small volumes
c. very high pressures
Pressure
• Pressure is defined as force per unit area.
• The common units of pressure are:
a. atmosphere (atm)
b. torr c. mm of mercury (mm Hg)
d. Pascal e. bar
• 1.00 atm = 760 torr = 760 mm Hg =
1.01 x 105 Pa = 1.01 bar.
• At sea level the pressure is 760 torr.
Above sea level it is less than 760 torr.
Below sea level it is greater than 760 torr.
Barometer
• The barometer is a device used to
measure pressure:
Patm = h
h (mm Hg)
Patm
mercury surface
Schematic of a barometer
Manometer
•
A manometer is a partially filled glass tube of mercurey with one arm open
to the atmosphere (side P1) and the other arm (side P2 ) attached to a gas
tank. It can be used to measure the pressure of gas inside of a container.
The difference in the height of mercury from one arm of a manometer to the other is
58 mm. If the atmospheric pressure is 1.02 atm, then what is the pressure (in torr)
of the gas in the tank that is attached to the manometer?
Pgas = Patm + Dh
Pgas = 1.02 atm x (760 mm Hg/1 atm) + 63 mm = 839 mm Hg = 839 torr
Standard Temperature and
Pressure (STP) and Standard
Molar Volume
• STP = 0.00oC (273.15K) and 1 atm (760
torr)
• At STP 1 mol of an ideal gas occupies
22.4 L.
180
160
140
120
100
80
60
40
20
0
0
10
20
30
40
50
30
40
50
P (atm)
0.25
0.2
1/V (1/L)
• Boyle’s Law: V a 1/P
(at constant T and n)
Therefore, Volume is
inversely related
(inversely proportional) to
pressure. If the pressure
of a gas at constant
temperature and number
of moles is doubled, the
volume will be cut in half.
Volume (L)
Gas Laws
0.15
0.1
0.05
0
0
10
20
P (atm)
Gas Laws
250
200
V (L)
• Charles’ Law: V a T(K)
(at constant P and n)
For example, if the
temperature (in K) of a
gas at constant pressure
and composition is
tripled, the volume will
triple.
150
100
50
0
0
100
200
300
T (K)
400
500
Gas Laws
• Avogadro’s Law- V a n (constant T and P)
Example:
If the number of moles of a gas at constant
temperature and pressure is quadrupled,
its volume will quadruple.
• At the same T & P equal volumes of gases
contain the same number of moles and
molecules (at STP 1 mol of gas occupies a
volume of 22.4 L).
Combined Gas Law
• Taking into account Boyle’s, Charles’, and Avogadro’s
law we arrive at the combined Gas Law:
P1V1 = P2V2
n1T1
n2T2
If n is constant: P1V1
T1
= P2V2
T2
Any unit of P and V as long as they are the same on both
sides of the equation. T1 and T2 must be in K.
Ideal Gas Equation
• The ideal gas equation is as follows:
PV = nRT R is the ideal gas constant.
It can have the units:
.0821 L x atm or 62.4 L x torr
K x mol
K x mol
Molar Mass and Density of Gases
• Since PV = nRT and n = g/MM and
d = g/V, then:
PV = g R T and V = g x R x T
MM
P x MM
And: d = g = g x P x MM
V
gxRxT
d = P x MM
RxT
Dalton’s Law of Partial Pressures
• At constant volume and temperature, the
total pressure extended by a mixture of
ideal gases is the sum of the partial
pressures of those gases.
PA=200 torr
PB=150 torr
PT = PA + PB = 350 torr
Place A and B in
same container
Gas A
Gas B
At constant T and V
conditions.
Gas A & B
Dalton’s Law of Partial Pressures
• PT = PA + PB + PC + …= Since PV = nRT then P= nRT/V
PT =
nART + nBRT + nCRT + … = (nA + nB + nC +…)(RT)
V
V
V
V
There is a simple relation that exists between total pressure and individual
pressures. Consider a sample containing gases A and B. Dividing PA by PT
we obtain:
nA RT
PA =
V
PT (nA + nB)RT
V
=
nA
= XA Where XA is
nA + n B
the mole
fraction of A.
Mole fraction is a dimensionless quantity that expresses the ratio of moles of
one component to the number of total moles. The mole fraction can be any
number between 0 and 1. Note that the sum of all mole fractions must equal
to one. If two components are present, then:
XA + XB = 1
Rearranging the above equation (PA/PT = XA), we can express the partial
pressure of A and B as:
PA = XAPT
PB = XBPT
Therefore, in a sample containing two gases (A & B), the total pressure of the
sample is given by:
PT = PA + PB = XAPT + XBPT
Vapor Pressure of Water
• Gases that are insoluble and don’t react with water can be collected over
water. The partial pressure exerted by the water vapor above the liquid is
called its vapor pressure.
• Every liquid shows characteristic vapor pressures that vary with
temperature.
• If a gas is collected over water it is saturated with water vapor, and at
atmospheric pressure (PT = atmospheric pressure):
PT = Pgas + Pwater or Pgas = PT – Pwater
gas
gas + water vapor
Vapor pressure of water (Pwater) in torr near room
temperature:
Temp (oC) Pwater Temp (oC) Pwater
Temp (oC) Pwater
20
17.5
23
21.1
26
25.2
21
18.7
24
22.4
27
26.7
22
19.8
25
23.8
28
28.4
Graham’s Law: Diffusion and Effusion
of Gases
• Diffusion is the intermingling of gases.
• Effusion is the leaking out of gases
through a small hole or orifice.
• RateA/RateB = (MB/MA)1/2
The rate is the rate of effusion:
V/t
mL / s or L / min, etc..
Gay-Lussac’s Law (Law of
Combining Volumes)
• At constant temperature and pressure, the
volumes of reacting gases can be expressed as
the simple whole number ratio of the moles of
gases that are reacting (V a M at constant T and
P).
• If the reaction is carried out at STP, then
1 mol gas = 22.4 L
H2(g) + Cl(2)
2HCl(g
1 mol
1 mol
1 volume 1 volume
22.4 L
22.4 L
2 mol
2 volumes
44.8 L
At STP