Chapter 10 Gas Laws

Well what can we do with all this you ask: with this simple equation

PV = nRT

Essentially, use of this equation boils down to 2 types of problems.

Single Value
Change of Condition

I. Single Value

In this type of problem three of the four variables are given and you must solve for the fourth.

P, V, and t solve for n
P, V, and n solve for T
P, n, and T solve for V
n, T, and V solve for P

Here are three sample problems of this type. The first is trival, the second more interesting and the third even more interesting.

II. Change of Condition

The characteristic feature of the change of condition problem, which involves 2 or 3 of the variable n,P, V and T, is the identification two values for one of P, V or T variables.

Here are three sample problems of this type. .

The approach is to establish which variables in the equation are constant and which are changing. Separate the variable from the constants, note the constants are equal, therefore so are the variables and then solve for the unknown.

Following this approach we can obtain relationships such as;

and many more.

Our knowledge of gas laws can be extended to stoichiometry problems involving gases.

Sample Problem #1

Partial Pressure

If we begin with the ideal gas law,

PV = nRT

we can rearrange the equation to show a relationship between pressure and the number of moles of gas,

So pressure is directly related to the number of moles of gas. But suppose the gas is actually a mixture rather than a pure substance? For ideal gases the total pressure of a mixture is simply the sum of the pressures of the component gases if they were alone in the container.

The pressures of the individual component gases, P₁, P₂, and P₃ are called the partial pressures of the component gases. So

and if we factor out the we have,

Sample Problem #1

Dalton, who is credited with the above relationship for partial pressures, was a meteorologist and performed many experiments working on determining the amount of water vapor absorbed by dry air at different temperatures. So we can look at a problem dealing with water vapor.

When a gas is generated the easiest way to collect the gas is by displacing water from a container. The gas is produced in a reaction vessel which is vented via a tube to a container of water. As the reaction proceeds the gas produced displaces the water in the container. In this way the volume of gas produced in the reaction can be measured. However, one problem associated with this experiment involves Dalton's law of partial pressures. The problem is the gas collected is not pure. It also contains water vapor. It turns out, and we will study this in more detail in the next chapter (in CHEM 1515), that at a specific temperature the amount of water in the vapor phase above a liquid is known. This is called the vapor pressure of water. At around 25 deg. C the vapor pressure of water is approximately 24 mmHg. So the total pressure of the gas sample collected is the pressure due to the pure gas generated in the reaction and the pressure due to water in the vapor phase.

P_Total(P_atm) = P_sample + P_water

Sample Problem #2

The ideal gas equation is an empirical relationship which describes how an ideal gas behaves under a given set of conditions, but it does not explain why gases behave as they do. To try to explain the behavior of an ideal gas a model which will enable us to image how gases behave at the atomic level is needed. Such a model has been developed and is known at the Kinetic-molecular theory for ideal gases. The model evolved over a period of 100 years and is the product of the work of many early scientists. The kinetic molecular model is based on the following postulates;

Gases consist of tiny (submicroscopic) molecules which are in continuous, random motion.
The distance between molecules is large compared with the size of the molecules themselves. The volume occupied by a gas consists mostly of empty space.
Gas molecules have no attraction for one another.
Gas molecules move in straight lines in all directions, colliding frequently with one another and with the walls of the container.
No energy is lost by the collision of a gas molecule with another gas molecule or with the walls of the container. All collisions are perfectly elastic.
The average kinetic energy for molecules is the same for all gases at the same temperature, and its value is directly proportional to the absolute temperature.

I have prepared a computer generated model to represent these postulates. So lets study the computer generated model and see how it behaves.

Well what can we do with all this you ask: with this simple equation

PV = nRT

Essentially, use of this equation boils down to 2 types of problems.

Single Value

Change of Condition

I. Single Value

In this type of problem three of the four variables are given and you must solve for the fourth.

P, V, and t solve for n

P, V, and n solve for T

P, n, and T solve for V

n, T, and V solve for P

Here are three sample problems of this type. The first is trival, the second more interesting and the third even more interesting.

II. Change of Condition

The characteristic feature of the change of condition problem, which involves 2 or 3 of the variable n,P, V and T, is the identification two values for one of P, V or T variables.

Here are three sample problems of this type. .

The approach is to establish which variables in the equation are constant and which are changing. Separate the variable from the constants, note the constants are equal, therefore so are the variables and then solve for the unknown.

Following this approach we can obtain relationships such as;

and many more.

Our knowledge of gas laws can be extended to stoichiometry problems involving gases.

Partial Pressure

If we begin with the ideal gas law,

PV = nRT

we can rearrange the equation to show a relationship between pressure and the number of moles of gas,

So pressure is directly related to the number of moles of gas. But suppose the gas is actually a mixture rather than a pure substance? For ideal gases the total pressure of a mixture is simply the sum of the pressures of the component gases if they were alone in the container.

The pressures of the individual component gases, P1, P2, and P3 are called the partial pressures of the component gases. So

and if we factor out the we have,

Dalton, who is credited with the above relationship for partial pressures, was a meteorologist and performed many experiments working on determining the amount of water vapor absorbed by dry air at different temperatures. So we can look at a problem dealing with water vapor.

PTotal(Patm) = Psample + Pwater

Gases consist of tiny (submicroscopic) molecules which are in continuous, random motion.

The distance between molecules is large compared with the size of the molecules themselves. The volume occupied by a gas consists mostly of empty space.

Gas molecules have no attraction for one another.

Gas molecules move in straight lines in all directions, colliding frequently with one another and with the walls of the container.

No energy is lost by the collision of a gas molecule with another gas molecule or with the walls of the container. All collisions are perfectly elastic.

The average kinetic energy for molecules is the same for all gases at the same temperature, and its value is directly proportional to the absolute temperature.

I have prepared a computer generated model to represent these postulates. So lets study the computer generated model and see how it behaves.

The pressures of the individual component gases, P₁, P₂, and P₃ are called the partial pressures of the component gases. So

P_Total(P_atm) = P_sample + P_water