Gas Laws

Boyle’s Law

Charles’s Law

Gay-Lussac

Combined Gas Law

Properties of Gases

V = volume of the gas (liters, L)

T = temperature (Kelvin, K)

P = pressure (atmospheres, atm)

n = amount (moles, mol)

Gas properties can be modeled using math.Model depends on:

Pressure - Temperature - Volume Relationship

P T V P T V

Gay-Lussac’s P T

Charles V T

P T

V

P T

V P T V P T V

Boyle’s P 1V

Pressure and Balloons

A

B = pressure exerted ON balloonA = pressure exerted BY balloon

BWhen balloon is being filled:

PA > PB

When balloon is filled and tied:PA = PB

When balloon deflates:PA < PB

When the balloons are untied,will the large balloon (A) inflatethe small balloon (B); will they end up the same size or will the small balloon inflate the large balloon?

Why?

Balloon Riddle

A

B

C

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.

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 (and constant number of gas molecules) 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 kPa. If the pressure is changed to 15 kPa at a constant temperature, what will be the new volume of the gas?

Solution:

P1V1= P2V2

P1= 5.6 kPa P2= 15 kPa

V1= 1.53 L V2= ?

Rearrange the formula to isolate V2.

P1V1 = (5.6 kPa)(1.53 L) = O.571 L

P2 (15 kPa)

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 (and constant number of gas molecules) the volume of a fixed amount of gas is directly proportional to its absolute temperature.

2

2

1

1

T

V

T

V

*All gas laws must be calculated with Kelvin temperature!

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)

Gay-Lussac

Joseph Louis Gay-Lussac was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries.

1778 – 1850

Charles's law, describing how gases tend to expand when heated, was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.

Gay-Lussac’s Gas Law• The pressure of a fixed mass and fixed

volume of a gas is directly proportional to the gas's temperature.

1 2

1 2

P P

T T

*All gas laws must be calculated with Kelvin temperature!

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• Gay-Lussac Law -- Direct relationship

When PT and if PT