Gas Laws
Gas Law chemistry is very straightforward provided one is clear on definitions of terms and
parameter units when performing calculations. On a conceptual level, familiarity with the
principles of collision theory is essential.
Ideal Collision Theory of Gases
(1) All molecules of gas are assumed to be point-like particles with no size. This means they are
said to possess zero volume.
(2) All energy contained by molecules of gas is assumed to be kinetic energy. This means that all
energy is involved in the motion of these molecules throughout the container; gas molecules
never stop moving. Temperature is a direct measure of kinetic energy.
(3) Due to the zero volume assumption (point 1), molecules of gas are assumed to never collide
with each other. This means pressure, which is defined as the number of collisions per unit time
per unit surface area of the container, always refers to collisions between molecules of gas and
the walls of the container.
Note: All three of these assumptions are actually false. When used, the molecules of gas are
said to behave like "ideal gases." When the gases are said to be "real," these assumptions are
eliminated. This differentiation will be shown to impact mathematical formulas used.
The main parameters in Gas Law chemistry are volume (V), temperature (T), pressure (P), and
the number of moles of gas (n).
Gas Law Units
The standard unit for Volume is Liters (L). Occasionally, milliliters (mL) or cubic centimeters
(cm3) are used. The relations are: 1 L = 1000 mL; 1 mL = 1 cm3
The standard unit for Temperature is Kelvin (K). Kelvin is an absolute temperature scale; it is
impossible to have T < 0 Kelvin. The relations are: K = oC + 273.15; oC = 5/9 (oF - 32)
Also, because temperature relates to kinetic energy, Ek = 3/2 kT, where Ek is kinetic energy and k
is Boltzmann's constant = 1.38 x 10-23 J/K
There are several standard units for Pressure, and unfortunately all of them are used at different
times. The most important for Gas Law chemistry is atmospheres (atm). Others in use are Torr,
mm Hg (millimeters of Mercury), and KPa (kilopascals). The relations are: 1 atm = 760 Torr;
1 atm = 760 mm Hg; 1 atm = 101.3 KPa
As always, moles = mass/ Molar Mass, or n = m/MM
Simple Gas Laws
(1) Boyle's Law: states that pressure and volume are inversely proportional; as one increases, the
other decreases. From Ideal Collision Theory, if the volume of a container decreases, molecules
of gas moving at a constant rate of speed (constant temperature) will collide more often with the
container walls, meaning the pressure increases. Obviously, the opposite is also true: if the
volume increases, collisions are fewer and pressure decreases. Mathematically, Boyle's Law takes
the form:
Pi Vi = Pf Vf or Pi / Vf = Pf /Vi
subscripts i and f refer to initial and final conditions
(2) Charles' Law: states that temperature and volume are directly proportional; as one increases,
the other increases. From Ideal Collision Theory, if the volume of a container increases, the
molecules of gas must move faster (temperature increases) to travel the distance necessary to
maintain a constant rate of collisions with container walls (constant pressure). Obviously, the
opposite is also true: if the volume decreases, molecules need to move slower, have lower
temperature, to maintain same number of collisions. Charles' Law takes the form:
Tf Vi = Ti Vf or Vi / Ti = Vf /Tf
subscripts i and f refer to initial and final conditions
(3) Gay-Lussac's Law: states that pressure and temperature are directly proportional; as one
increases, the other increases. From Ideal Collision Theory, at a constant volume of container, if
the temperature increases, molecules of gas are moving faster and there are more collisions of gas
molecules with container walls per unit time, so pressure increases. Obviously, the opposite is
also true: pressure, based upon collisions, decreases if molecules are moving slower (have lower
temperature). Gay-Lussac's Law takes the form:
Tf Pi = Ti Pf or Pi / Ti = Pf /Tf
subscripts i and f refer to initial and final conditions
These three laws, taken together, form the Combined Gas Law:
Pi V i = Pf V f
Ti
Tf
Holding any of the parameters fixed gives the three bi-functional laws
(4) Avogadro's Law: at standard conditions of temperature and pressure (STP, taken as 273K
and 1 atm), one mole of any ideal gas occupies exactly 22.4 L.
(5) Ideal Gas Law: relates T, V, P if have only one set of conditions rather than the two sets
indicated above. Use is made of Avogadro's Law. At STP:
P V = (1 atm)(22.4L) = 0.08205 L-atm/K for one mole of ideal gas
Ti
(273K)
or PV = nRT for n moles of ideal gas, where R = universal gas constant = 0.08205 L-atm/K-mole
(6) Van der Waal's Equation: it was stated that the assumptions of the Ideal Collision Theory
are actually false. When these assumptions are eliminated, the Ideal Gas Law transforms into the
Van der Waal's Equation:
(P + a/V2) (V - b) = nRT, where a and b are empirical constants and differ for every gas
a refers to the fact that gas molecules collide with each other; this slows them down due to heat
loss, and also alters their trajectories of movement. In combination, these factors effect the rate of
collisions with container walls, thus affecting pressure.
b refers to the fact that gas molecules are not point-like particles; they take up space, so the
effective volume of the container is less than theoretical maximum volume.
Manipulations of Ideal Gas Law
PV = nRT can be transformed into other forms to calculate other parameters
(1) To calculate molar mass of a gas, use the fact that n = m/MM
PV = nRT, PV = (m/MM)RT, MM = mRT/PV
(2) To calculate density of a gas, use the fact that Density = mass/ volume, or D = m/V
PV = nRT, PV = (m/MM)RT, P(MM)/RT = m/V,
P(MM)/RT = D
Supplemental Gas Laws
(1) Dalton's Law of Partial Pressures: according to Ideal Collision Theory, all gases are
independent of each other since they do not collide. Therefore, the rate of collisions of each gas
with the container walls depends only upon the kinetic energy of that gas. This means the
contribution made by each gas to the total pressure is independent of each other and can be
added together. In simple language, the whole (pressure) is equal to the sum of its parts.
Ptotal = P1 + P2 + P3 + . . .
The partial pressures of each gas (P1, P2, P3) are found by applying the Ideal Gas Law to each
one separately. However, since V, R, and T are the same for all the gases in the system, calculate
this ratio once and then apply the fact that P is proportional to n:
PV = nRT,
P1 = n1C,
P = nRT/V,
P2 = n2C,
RT/V = C constant for all gases in system
P3 = n3C
Ptotal = C (n1 + n2 + n3 etc)
(2) Graham's Law of Diffusion: states that the ability of a gas to move across a container (to
diffuse, or spread out) is inversely proportional to its mass and size: bigger molecules move more
slowly. (Think of a comparison between an 18-wheel truck and a sports car on the freeway. The
sports car can zip in and out of lanes at a high rate of speed, while the truck lumbers along and
turns slowly.)
r1/r2 = √MM2/MM1 r1 and r2 are speeds of different types of gas molecules
MM2 and MM1 are molar masses of different types of gas molecules
In words, Graham's Law says that the speed of diffusion is inversely proportional to the square
root of the ratio of the molar masses.