For a gas, temperature and pressure are directly
proportional. When you keep everything else constant, as the temperature of a gas goes
up, its pressure goes up. As the temperature of a gas goes down, its pressure goes down. If you heat up a gas, the gas particles move
faster. If the gas is in a solid container, with fixed volume, this means that the faster
the gas particles move, the more times per second they collide with the sides of the
container. That registers as increased pressure. The converse is also true – if you cool down
this container of gas, that means the gas particles are moving more slowly. So there
will be fewer collisions with the sides of the container per second, which means lower
pressure. Joseph Louis Gay-Lussac shares credit with
Guillaume Amontons for establishing a Gas Law describing the relationship between temperature
and pressure. Gay-Lussac’s Law says that when the volume and amount of gas is constant,
pressure and temperature are directly proportional. P ∝ T You can write this mathematically
as P=kT where P=pressure,
T=temperature in Kelvin, and k=is a proportionality constant.
We can rearrange this equation so it reads P/T=k, or the ratio of pressure to temperature
is a constant, k. Very often, Gay-Lussac’s law is used to
compare two situations, a “before” and an “after.” In that case, you can say
P1 / T1=k, and P2 / T2=k, so you can write Gay-Lussac’s law as
P1 / T1=P2 / T2. Let’s see an example. Example 1: A canister of nitrogen gas has
a pressure of 2000 psi (pounds per square inch) at 20 C°. What will the pressure be
if you increase the temperature to 25 C° ? Let’s write down Gay-Lussac’s Law: P1/ T1=P2 / T2, because we have a “before”
and “after.” Convert temperatures to Kelvin: Kelvin=C°+ 273.15. T1=293.15 K, T2=298.15 K
Substitute in what we know: 2000 psi / 293.15K=P2/ 298.15 K Solve for P2 (multiply both sides
by 298.15 K) P2=(2000 psi )(298.15 K)/293.15 K P2=2034 psi Example 2. Here’s another example: At 10
C°, a gas exerts 0.95 atm of pressure. At what temperature (in Celsius) will it exert
a pressure of 0.75 atm? P1 /T1=P2/T2.
Convert temperatures to Kelvin: Kelvin=C°+ 273.15.
T1=283.15 K 0.95 atm/ 283.15 K=0.75 atm/T2
Solve for T2 T2=(283.15 K)(0.75 atm)/0.95 atm
T2=223.54 K Convert to Celsius: 223.54K – 273.15= – 49.6 C° Gay-Lussac’s Law relates temperature and
pressure for a gas, but there are other gas laws which relate the other essential variables
associated with a gas. Charles’s Law is the relationship between temperature and volume.
Boyle’s Law is the relationship between pressure and volume. And the combined gas
law puts all 3 together: Temperature, Pressure, and Volume. Notice that to use any of these
laws, the amount of gas must be constant. Avogadro’s Law describes the relationship
between volume and the amount of a gas (usually in terms of n, the number of moles). When
we combine all 4 laws, we get the Ideal Gas Law. To decide which of these gas laws to
use when solving a problem, make a list of what information you have, and what information
you need. If a variable doesn’t come up, or is held constant in the problem, you don’t
need it in your equation.