Gases
Chapter 5
Substances that exist as gases
Elements that exist as gases at 250C and 1 atmosphere
5.1
Our Atmosphere:
10 miles 0.2 atm
4 miles 0.5 atm
Sea level1 atm
• exerts pressure on earth
• more at sea level
• less on mountain top
• The air we breathe:
• 79% N2
• 21% O2
Pressure of Gas
Atmospheric pressure
1 atm = 760 mmHg = 760 torr
(1 torr = 1mm Hg)
1 atm = 101,325 Pa
1 atm = 101 kPa
The Gas Laws
PV = nRT
R is the gas constant
4 variables are involved:
• P = pressure
• V = volume
• n = # of moles
• T = temperature (in Kelvin)
Ideal Gas Equation
Ideal gas is a hypothetical gas
whose pressure-volumetemperature behavior can be
completely accounted for by the
ideal gas equation.
Pressure and Temperature
• Pressure = force/area
(we will use torr, mm Hg, Pa & atm)
• Always use Kelvin temperature (K)
K = ° C + 273
What is the pressure of the gas (in atm) when 5.0 moles
of CO gas are present in a container of 20.0 L at 27 oC?
n= 5.0mole, V=20.0L, T= 27 oC=(27+273.15)K=300.15K
PV=nRT
P=nRT / V
= 5.0mole*0.082 L• atm / (mol • K)*300.15K/20.0L
= 6.15 atm
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.
Molar volume of gas
1 mole of gas at STP = 22.4 Liters
2 moles of gas at STP = 44.8 L
R = 0.0821 L • atm / (mol • K)
= 8.314 J/(K·mol)
What is the volume (in liters) occupied by 49.8 g of HCl
at STP?
n = 49.8 g x
1 mol HCl
= 1.37 mol
36.45 g HCl
1 mole of gas at STP = 22.4 Liters
V = 1.37 mol x 22.4 L/mol = 30.6 L
Argon is an inert gas used in lightbulbs to retard the vaporization
of the filament. A certain lightbulb containing argon at 1.20 atm
and 18 0C is heated to 85 0C at constant volume. What is the
final pressure of argon in the lightbulb (in atm)?
PV = nRT
n, V and R are constant
nR
P
=
= constant
T
V
P1
P2
=
T1
T2
P1 = 1.20 atm
T1 = 291 K
P2 = ?
T2 = 358 K
T2
= 1.20 atm x 358 K = 1.48 atm
P2 = P1 x
291 K
T1
Density (d) Calculations
PM
m
d=
=
V
RT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRT
M=
P
d is the density of the gas in g/L
5.4
What is the density of HCl gas in grams per liter at
700 mmHg and 25 oC?
PM
m
d=
=
V
RT
P=700mmHg=700/760atm=0.92atm
T= 25 oC=25+273.15K=298.15K
d =
0.92 atm x 36.45 g/mol
0.0821
=1.37g/L
L•atm
mol•K
x 298.15 K
What is the molar mass (g/mol) of 7.10 grams of gas
whose volume is 5.40 L at 741 torr and 40 oC?
dRT
M=
P
T=313.15K
M=
7.10 g
m
=
= 1.31
d=
5.40
L
V
P= 741torr=741/760atm=0.975atm
g
1.31
L
M = 34.6 g/mol
x 0.0821
L•atm
mol•K
x 313.15 K
0.975 atm
g
L
Gas Stoichiometry
The combustion process for methane is
CH4(g) + 2 O2(g)  CO2(g) + 2 H2O(l)
If 15.0 moles of methane are reacted, what is the volume of
carbon dioxide (in L) produced at 23.0 oC and 0.985 atm?
x 1CO2/1CH4
15 mole CH4 ---------------- 15 mole CO2
V=
nRT
=
P
L•atm
x 296.15 K
mol•K
= 369.8 L
0.985 atm
15mol x 0.0821
Dalton’s Law of Partial Pressures
Partial pressure is the pressure of the individual gas in the mixture.
V and T
are
constant
P1
P2
Ptotal = P1 + P2
Consider a case in which two gases, A and B, are in a
container of volume V.
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nA
XA =
nA + nB
nB
XB =
nA + nB
PB = XB PT
Pi = Xi PT
mole fraction (Xi) =
ni
nT
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
Xpropane =
8.24 + 0.421 + 0.116
= 0.0132
Ppropane = 0.0132 x 1.37 atm = 0.0181 atm
Kinetic Molecular Theory of Gases
1. A gas is composed of molecules that are separated from
each other by distances far greater than their own
dimensions. The molecules can be considered to be points;
that is, they possess mass but have negligible volume.
2. Gas molecules are in constant motion in random directions,
and they frequently collide with one another. Collisions
among molecules are perfectly elastic.
3. Gas molecules exert neither attractive nor repulsive forces
on one another.
4. The average kinetic energy of the molecules is proportional
to the temperature of the gas in kelvins. Any two gases at
the same temperature will have the same average kinetic
energy
u2 = (u12 + u22 + …+ uN2)/N KE a T
KE = ½ mu2
Mean square speed