Gas Laws

Pressure—chemical, physical and conversions

Boyle’s Law

Charles’s Law

Combined Gas Law

The Propertiesof Gases

Some of the properties of gases were discovered by balloonists trying to improve their flight performance. These balloonists are using their knowledge of these properties to stay aloft.

Chemical Properties Produce Gases

• Chemists harness chemical properties to produce a desired gas through chemical reactions. Such as the reaction of zinc and hydrochloric acid.

Physical Properties of Gases

Gases are compressible and that they assume the shape and volume of any container. Gases are all infinitely soluble in one another. Each of these characteristics can be explained by the distances between the molecules (or atoms) in a gaseous sample.

Physical Properties of Gases are affected by temperature and pressure

Pressure

• Pressure is defined as force divided by the area.

A

FP

Pressure

• The mercury in the inverted tube is pushed upward by the force of atmospheric pressure pushing down on the surface of the mercury in the dish. The height of the mercury in the tube changes with changing atmospheric pressure. Under conditions of standard atmospheric pressure, the height of the mercury in the tube is 760 mm. (1 atm = 760 mm Hg = 760 torr = 1.01 kPa)

Collisions cause Pressure

• The pressure of a gas is caused by the collision of molecules against the sides of the container.

Low Pressure vs. High Pressure inside a System

The number of collisions of gas molecules against the wall of the container determines the pressure in the container.

Notice the difference in the number of collisions. Figure (a) would have a lower pressure than Figure (b).

Figure 5.3A gas can easily be compressed into a smaller volume by pushing in a piston. This property suggests that there is a lot of space between the molecules. Liquids and solids are almost incompressible, which suggests that their molecules are in contact with one another.

Robert Boyle

Robert Boyle, an Irish chemist (1627-1691), performed the first quantitative experiments on gases used a j-shaped tube to study the relationship between the pressure of the trapped gas and its volume.

Boyle’s Law

• Boyle’s Law states that at constant temperature the volume of a fixed amount of gas is inversely proportional to its pressure.

Boyle’s Law:

P1V1 = P2V2

Boyle Proves Changes in Pressure cause Changes in Volume

As the pressure in a closed system (like a piston) decreases, the volume of the gas inside the system increases. The pressure in the system decreases exponentially. Proving an indirect relationship.

Example:

• Sulfur dioxide (SO2), a gas, that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53 L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at a constant temperature, what will be the new volume of the gas?

Solution:

P1V1= P2V2

P1= 5.6 x 103 Pa P2= 1.5 x 104 Pa

V1= 1.53 L V2= ?

Rearrange the formula to isolate V2.

P1V1 = (5.6X 103 Pa)(1.53 L) = O.57 L

P2 (1.5 X 104 Pa)

Does Boyle’s law really work?

Since Boyle’s experiments (only three centuries of technological advances!) we have found that his law only holds precisely at very low pressures.

We describe a gas that strictly follows Boyle’s law an “ideal gas”.

Jacques Charles

In the century following Boyle, a French physicist, Jacques Charles (1746-1823), was the first person to fill a balloon with hydrogen gas and who made the first solo balloon flight.

Charles’s Law

• Charles’s Law states that at constant pressure the volume of a fixed amount of gas is directly proportional to its absolute temperature.

2

2

1

1

T

V

T

V

Volume vs. Temperature: Charles’ Law

• Notice the linear relationship. This relationship between temperature and volume describes a “direct relationship”. This means when temperature increases, so does the volume.

The importance of 0 Kelvin

• At temperatures below 0 K, the extrapolated volume of gases would be negative. The fact that a gas can’t have a negative volume tells us 0 K has a special significance.

• Absolute temperature is measured in Kelvins. At 0 K, all motion of any atom or bond ceases, therefore producing no energy. Temperatures of approximately 0.000001K have been produced in laboratories, but 0 K has never been reached.

Example:

• A sample of a gas at 15°C and 1 atm has a volume of 2.58 L. What volume will the gas occupy at 38°C and 1 atm?

• (NOTE: The pressure did not change. So you do not need to worry about it!)

Solution:

• V1 = V2 Don’t forget to convert °C to K

T1 T2

V1= 2.58L V2=?

T1 = 15°C=288K T2 = 38°C=311K

Rearrange to solve for V2.

V1T2 = (2.58L)(311K) = 2.79 L

T1 (288K)

The Combined Gas Law• The combined gas law was derived from

Boyle’s and Charles’s work. A direct relationship was observed. As temperature increased, volume increased. As volume increased pressure increased. This resulted in a combined formula to calculate changes observed in a gas due to changes in either temperature, pressure or volume.

Combined Gas Law Equation

• By combining the equation for Boyle’s Law and Charles’s Law. We derive the Combined Gas Law Equation where:

2

22

1

11

T

VP

T

VP

Example:

• A sample of a gas at 15°C and 2.0 atm has a volume of 2 mL. What volume will the gas occupy at 38°C and 1 atm?

Solution

P1V1 = P2 V2 Don’t forget to convert Temperatures!

T1 T2

P1= 2 atm P2= 1 atm

V1=2 mL V2=?

T1=15°C=288K T2=38°C=311K

Rearrange to solve for V2!

V2= P1V1T2 = (2 atm)(2 mL)(311K) = 4.32 mL

T1P2 (288K)(1 atm)

Summary:

• Boyle’s Law – Inverse relationship

when PV and if PV

• Charles’s Law -- Direct relationship

When VT and if VT