#### Answer

Boyle's law: P % 1/V at constant n and T
In the kinetic molecular theory (KMT), P is proportional to the collision frequency which is
proportional to 1/V. As the volume increases there will be fewer collisions per unit area with
the walls of the container and pressure will decrease (Boyle's law).
Charles's law: V % T at constant n and P
When a gas is heated to a higher temperature, the velocities of the gas molecules increase and
thus hit the walls of the container more often and with more force. In order to keep the
pressure constant, the volume of the container must increase (this increases surface area
which decreases the number of collisions per unit area which decreases the pressure).
Therefore, volume and temperature are directly related at constant n and P (Charles’s law).
Avogadro’s law: V % n at constant P and T
CHAPTER 5 GASES 3
As gas is added to a container (n increases), there will be an immediate increase in the
number of gas particle collisions with the walls of the container. This results in an increase in
pressure in the container. However, the container is such that it wants to keep the pressure
constant. In order to keep pressure constant, the volume of the container increases in order to
reduce the collision frequency which reduces the pressure. V is directly related to n at
constant P and T.
Dalton’s law of partial pressure: Ptot = P1 + P2 + P3 + …
The KMT assumes that gas particles are volumeless and that they exert no interparticle forces
on each other. Gas molecules all behave the same way. Therefore, a mixture of gases behaves
as one big gas sample. You can concentrate on the partial pressures of the individual
components of the mixture or you can collectively group all of the gases together to
determine the total pressure. One mole of an ideal gas behaves the same whether it is a pure
gas or a mixture of gases.
P vs. n relationship at constant V and T. From question 3, this is a direct relationship. As gas
is added to a container, there will be an increase in the collision frequency, resulting in an
increase in pressure. P and n are directly related at constant V and T.
P vs. T relationship at constant V and n. From question 3, this is a direct relationship. As the
temperature of the gas sample increases, the gas molecules move with a faster average
velocity. This increases the gas collision frequency as well as increases the force of each gas
particle collision. Both of these result in an increase in pressure. Pressure and temperature are
directly related at constant V and n.

#### Work Step by Step

See above.