Pressure:

Pressure is force per unit area and can be measured in several ways. The pressure of the atmosphere at sea level when the air is at standard conditions is 1.00 atmosphere. As one observes the atmospheric pressure at higher altitudes, the pressure decreases.

In British Units the pressure due to the atmosphere is 14.7 lb/in² or simply 14.7 psi.

Demo:

News paper and stick to demonstrate pressure.

Expressing the atmospheric pressure in mks units gives 1.01325x10⁵ Pa/m². Another common units is the torr or mmHg.

Demo:

Use atmospheric pressure and vacuum pump to push mercury up a tube.

From the demonstration we can see that the pressure due to the atmosphere is enough to lift a column of mercury a distance of 760 mm and hence one atmosphere is 760 mm Hg or 760 torr. Some times the pressure is expressed as 29.95 in Hg.

Demo: Boyle's Law

Use vacuum chamber and balloon to demonstrate the volume-pressure relation

The mathematical expression of Boyle's Law is:

P₁V₁ = P₂V₂

Demo: Charles' Law

Use balloon and a 1000 ml volumetric flask to demonstrate the temperature volume relation.

The mathematical expression for Charles' Law is:

V₁/T₁ = V₂/T₂

Amedeo Avogadro was first to propose that equal volumes of different gases contained equal numbers of molecules when under like conditions. The average volume for one mole of gas at standard temperature and pressure 1.00 atm and 0°C was found to be 22.4 liters/mole. 1.00 atm and 0°C are called STP. Using these relationships it is possible to make a great number of calculation involving dual states of gasses.

Problem:

One liter of gas is heated from 25°C to 100°C. What is the new volume? Answer: 1.25

Problem:

3.00 liters of gas at 1.00 atm is compressed so that the volume is 1.00 liters. What is the new pressure? Answer: 3.00 atm

Problem:

5.00 liters of gas at 760 torr and 20.0°C is heated to 100°C and the pressure is changed to 800 torr. What is the new volume?

Answer: 6.05 liters

Problem:

How many moles of gas are contained in 1.00 liters of gas at 100^oC and 700 torr pressure? Answer: .0301 moles

Note how the above gas laws always deal with two states. The ideal gas law describes the state of an ideal gas. It is called a state equation.

PV = nRT

Where P is pressure, V is volume, n is moles R is a constant and T is the temperature in kelvin. This equation is a single state equation. The selection of the units is dependent upon the units of R. R can have any of the following units.

R = .08206 literxatm/(Kxmole)

R = 62.37 literxtorr/(Kxmole)

R = 8.314 m³xPa/(Kxmole)

R = 8.314 J/(Kxmole)

In each case the units that must be used in the equation are contained in the gas constant.

What is an ideal gas? An Ideal gas in made up of point masses that have no interactions with one another. Most of the time, real gases behave nearly ideally, and difference between real and ideal gases can be ignored.

Problem:

How many moles of gas are contained in 1.00 liters of gas at 100^oC and 700 torr pressure? Answer: .0301 moles

Problem:

What volume of gas is produced at 750 torr and 20^oC when 5.00 g of aluminum react with excess HCl?

We can make a general dual state equation that embodies all of the other gas laws. If we assume that the number of moles of gas remain constant when changing from one state to another, then solving for all the variables on one side and all the variables on the other we get:

PV/T = nR

For any state this statement is true, therefore:

P₁V₁/T₁ = P₂V₂/T₂

This is a general dual state equation.

Problem:

5.00 liters of gas at 760 torr and 20.0^oC is heated to 100^oC and the pressure is changed to 800 torr. What is the new volume?

Answer: 6.05 liters

Dalton's Law of partial pressure states that the total pressure is the sum of all the individual pressures of each gas in a mixture:

P = P₁ + P₂ + P₃ +...

or

P = RT/V (n₁ + n₂ + n₃ +...)

Which simply states that the pressure is dependent upon the total number of moles of gas contained in the volume.

Problem:

What is the partial pressure of oxygen and nitrogen in air at STP. The weight percent is 21% Oxygen and 79% nitrogen. Assume 100 g of air you have .6562 moles of oxygen and 2.821 moles of nitrogen. Since moles and pressure are proportional :

P_O2 = (.6562 x 760)/(.6562 + 2.821) = 143.4 torr

P_N2 = (2.821 x 760)/(.6562 + 2.821) = 616.6 torr

We can also use Dalton's Law of partial pressure to determine the effect of water vapor on the volume of a gas. Consider a gas collected by the displacement of water. The pressure in the container is due to the pressure exerted by the gas and the pressure exerted by the water vapor. The vapor pressure of water is due to the equilibrium pressure of water vapor and is dependent only upon the temperature of the water. See page 976 in books.

Demo: Definition of boiling point.

Use vacuum chamber to boil water.

Demo: Boil water with hands

Use thick walled spherical glass container, fill with water and boil. Cork after boiling occurs and let cool. Lay hands upon container. It boils. Why?

Problem:

5.00 g of zinc is reacted with excess HCl. At a pressure of 700 torr and an ambient temperature of 20.0^oC, what volume of hydrogen gas is collected over water.

The basic assumptions of the theory are:

1 Gases consist of molecules or atoms which are in constant motion.

2 Volume of molecules is small compared to total volume.

3 Attractive forces between molecules is negligible.

4 Energy is transferred during collisions, but not lost.

5 The average kinetic energy of the molecules in a gas is proportional to the absolute temperature.

Since kinetic energy is given by:

KE = 1/2 mv²

we can write:

KE = 1/2 mu²

Where u is the root mean square (rms) velocity. For a given temperature the distribution of molecular velocities is:

% |

m | * u_rms1

o | * *

l | + + u_rms2

e | * + *

c | + +

u | * +

l | * + * +

e | *

s | *+ * +

+-----------------------------------------------

Velocity--->

Since the average kinetic energy of a gas molecule is dependent only upon the temperature, the heavier a gas molecule, the slower the average velocity of the molecules.

The average kinetic energy of a gas molecule is given by:

KE = 3RT/(2N)

where R is 8.314 J/(Kxmole), T is the absolute temperature and N is the Avogadro's number.

Problem:

Calculate the rms velocity of He gas at 300K.

KE = 1/2 mu² = 3RT/(2N)

Another interesting consequence of the kinetic theory of gases is that the average kinetic energy of any two gases is the same at the same temperature, that is:

KE = 1/2 m₁u₁² = 1/2 m₂u₂² = 3RT/(2N)

1 = 1/2 m₁u₁²/=(1/2 m₂u₂²)

rearranging:

u₂²/u₁² = m₁/m₂

u₂/u₁ = (m₁/m₂)^1/2

Since rate of diffusion or effusion is dependent upon the rms velocity of the molecules, we can say:

rate₂/rate₁ = (m₁/m₂)^1/2

Problem:

If oxygen effuses through a hole at a rate of 1.00 liters every 3.00 minute, how long will it take for 1.00 liters of hydrogen at the same temperature and pressure to effuse through the same hole?

Demo:

Effusion of HCl and NH₃ in a tube.

Real gas molecules have volume and attractive forces for each other. How will this effect the PV term in the ideal gas equation?

PV = nRT

Since there are attractive forces the pressure will be a little smaller since the collisions with the container will be a little less effective. The volume of gas will be a little larger since the gas molecules do take up some space. So in order for the equation to still be valid, we need to account for the attractive forces and the volume of the molecules. The result is the van der Waals equation.

(P + an²/V²)(V - nb) = nRT

The constants a and b are unique to each gas.

Use the Ideal gas equation and the van der Waals equation to calculate the molar volume for carbon dioxide at STP.

a = 3.59 b = .0427