Ideal Gas Law
Describing a sample of a gas
• 4 variables are needed to completely describe
a sample of a gas:
•
•
•
•
Temperature
Pressure
Volume
Amount (number of moles) of gas
Equation of State
• An equation relating the macroscopic
variables that describe some type of matter.
• The ideal gas law is an equation of state for
gases.
Boyle’s Law Graphs
PV
=
k
Pressure vs. Volume
Volume vs. 1/Pressure
P = kV-1
V = kP-1
Charles’ Law Graph
V = mT (in Kelvins)
Gay-Lussac’s Law Graph
P = m’T
Avogadro’s Law
V = nK
Recall
Boyle’s Law
Charles’ Law
V  1/P
V  T (Kelvin)
Avogadro’s
Law
Vn
Constant T, n Constant P, n Constant T, P
So V  1/P X n X T or V  nT/P
Ideal Gas Law
• To turn a proportionality into an equation,
insert a constant: V = RnT/P
• Or multiply both sides by P:
• PV = nRT where R is the ideal gas law
constant. If three of the variables are known,
the 4th can be determined.
• The units of R depend on the units used for P,
T, and V.
Units of R
• Two common values of R:
• 0.08206 LiterAtm
MoleK
• 8.314 Joules or 8.314 LiterKPa
MoleK
MoleK
Problem-Solving
• Most commonly used value of R in the US:
• 0.08206 LiterAtm
MoleK
•
•
•
•
Note:
Pressure must be in atm
Volume must be in liters
Temperature must be in Kelvins
Ideal Gas Law Problems
• What pressure is exerted by 0.75 moles of a
gas at 25C in a container with a volume of 1.5
L?
• Find the volume of 0.85 moles of gas at a
pressure of 520 torr and a temperature of
15C.
• How many moles of gas are present in a
sample at 700 torr, 333C, and occupying a
volume of 452 mL?
Extensions of Ideal Gas Law Problems
• PV = nRT
• n = mass
formula mass
• Density = mass
volume
Memorize the three fundamental
equations.
• Substitute and rearrange as problem
demands.
• PV = nRT or PV = massRT
formula mass
• Rearrange to solve for mass or density
volume
• (Pformula mass) = mass/volume = density
RT
Formula mass (Identity) of gas
• Formula mass = massRT
PV
• Or formula mass = densityRT
P
Density of a gas
• At STP, density of a gas = molar mass/22.4 L
• This is an easy relationship but it is only true
at STP!!!
Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressures
• For a mixture of gases:
• Ptot = P1 + P2 + P3 + …
• The total pressure of a gas mixture is the sum
of the partial pressures of the component
gases. The pressure exerted by each gas in an
unreactive mixture is independent of the
other gases in the mixture.
Addition or Subtraction Problems
• Three gases, He, N2, and Ar are present in a
gas mixture. The partial pressure of He is 360
torr, of N2 is 400 torr, and of Ar is 250 torr.
Find the total pressure.
• Ar is added to the above mixture until the
total pressure is 1200 torr. Find the new
pressure of the Argon.
Collecting Gas by Water Displacement
When the water
levels inside and
outside the inverted
container are the
same, the total
pressure inside the
container above the
water is equal to the
atomspheric
pressure.
Sometimes gases are collected by
water displacement C H (g) + H O(g)
2
2
2
Line up the water levels!
Ptot = Pgas + Pwater
• The volume of gas collects above the water,
but some of the water molecules evaporate
and go into the gas phase as well.
• The vapor pressure of water depends only on
the temperature. Look it up in a reference
table and then subtract it from the total
pressure.
Extension of Dalton’s Law
• Since PV = nRT then
• Ptot = ntotRT & for each component, Pi = niRT
V
V
Pi = niRT/V
Ptot
ntotRT/V
Which reduces to Pi / Ptot = ni / ntot
Mole Fraction
• ni / ntot is called the mole fraction = i
• Pi = (ni / ntot)Ptot
Effusion
gas
vacuum
Effusion
• Process where molecules of a gas confined in
a container randomly pass through a tiny
opening in the container.
• Rates of effusion can be used to determine
the molar mass of a gas.
• Kinetic energy of molecules in a gas depends
only on temperature and equals ½ mv2.
Effusion
Two gases at the same T have the
same average KE:
½ M1V12 = ½ M2V22
V12 = M2
V22
M1
Note: This
V is the
velocity of
the
molecules,
NOT the
volume of
the
container.
Effusion
Two gases at the same T have the
same average KE:
½ M1V12 = ½ M2V22
Graham’s Law of Effusion
• The rates of effusion of gases at the same
pressure and temperature are inversely
proportional to the square roots of their molar
masses.
• The heavier gases move more slowly.
Effusion
• Recall: the faster you are going, the less time
it takes you to get somewhere.
Diffusion
• Gradual mixing of two or more molecules due
to their spontaneous, random motion.
Gases are in constant, random
motion and tend to move from
regions of higher concentration to
regions of lower concentration.
Diffusion
Molecular speed and Temperature
Molecular speed and mass