Gas Variables

Physical Characteristics Typical Units

Volume, V liters (L)

Pressure, Patmosphere

(1 atm=101.3 kPa=760 Torr)

Temperature, T Kelvin (K)

Number of atoms or molecules, n

mole (1 mol = 6.022x1023 atoms or molecules)

Showed that Pressure influences the volume

of a gas during a controlled experiment.

Robert Boyle

Robert BoyleIreland

January 25, 1627 – December 30, 1690

Boyle's experimentTorricelli's experiment did more than

just show that air has weight; it also provided a way of creating a vacuum because the space above the column of mercury at the top of the barometer is almost completely empty. (It is free of air or other gases except a negligible amount of mercury vapor.) Torricelli's work with a vacuum soon caught the eye of the British scientist Robert Boyle.

Boyle's ExperimentBoyle's most famous experiments with

gases dealt with what he called the "spring of air." These experiments were based on the observation that gases are elastic. (They return to their original size and shape after being stretched or squeezed.) Boyle studied the elasticity of gases in a J-tube similar to the apparatus shown in the figure below. By adding mercury to the open end of the tube, he trapped a small volume of air in the sealed end.

Trapped air

Boyle’s Law: P1V1 = P2V2

Boyle’s Law: P1V1 = P2V2

A Boyle’s law graph will always have a ½ hyperbola shape. Illustrated by

the equation PV = kPV = k Volume and pressure are inversely proportional.

If one increases the other decreases.

Boyle’s Law: P1V1 = P2V2

Boyle's Law

The pressure of a gas is inversely related to the volume when the Temperature does not change

Then the PV product remains constant

PP11VV11 = P = P22VV22

A Boyle’s Law Problem

Freon-12, (CCl2F2), is used in refrigeration systems. What is the new volume (L) of a 1.6 L sample of Freon gas initially at 50 mm Hg after its pressure is changed to 200 mm Hg at constant T? Initial conditions Final conditions

P1 = 50 mm Hg P2 = 200 mm Hg

V1 = 1.6 L V2 = ?

VV22 = = 1.6 L x 50 mm Hg 1.6 L x 50 mm Hg = = 0.4 L0.4 L

200 mm Hg200 mm Hg

Jaques CharlesJaques Charles

Charles invented the Charles invented the hydrogen-filled hydrogen-filled balloon and on balloon and on December 1, 1783, December 1, 1783, he ascended into he ascended into the air and became the air and became possibly the first possibly the first man in history to man in history to witness a double witness a double sunset sunset

Jaques CharlesJacques Charles carried out

experiments in 1786 and 1787 that showed a direct relationship

between the temperature and volume

of gases at constant pressure. You know that most matter expands as its temperature rises. Gases are no different. When Benjamin Thomson and Lord Kelvin proposed an absolute temperature scale in 1848, it was possible to set up the mathematical expression of Charles’s law.

Charles’ Law: V and T

Charles’s law states that Charles’s law states that the volume of a the volume of a sample of gas is directly proportional to sample of gas is directly proportional to the the absoluteabsolute temperature when pressure temperature when pressure

remains constant.remains constant.

Charles’ Law

Compares the V and T of Compares the V and T of Confined gases Confined gases

How does volume change with temperature?How does volume change with temperature?

V1 = 125 mL V2 = 250 mLT1 = 273 K T2 = 546 K

1 mole of gas & Pressure = 753 mmHg

D

V and T ProblemV and T Problem

A balloon has a volume of A balloon has a volume of 785 mL on a Fall day when 785 mL on a Fall day when the temperature is 21°C. In the temperature is 21°C. In the winter, the gas cools to the winter, the gas cools to 0°C. What is the new volume 0°C. What is the new volume of the balloon?of the balloon?

VT Calculation

Initial conditionsInitial conditions Final conditionsFinal conditions

V1 = 785 mL V2 = ?

T1 = 21°C = 294 K294 K T2 = 0°C = 273 K273 K

V2 = _______ mL x __ K = _______ mL

K

Check your answer: If temperature decreases,

V should decrease.

273

294

785 728.9728.9

Charles Law

A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL?

1) 443°C 2) 170°C 3) - 82°C

2) 170°C

Solution

2) 170°C

A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL?

TT22 = = VV22TT11

VV11

T2 = 640 mL x 291 K = 443 K

420 mL

T2 = 443 K - 273 K = 170°C

Gay-Lussac’s LawJoseph Louis Gay-Lussac in

1802 made reference in his

paper to unpublished work done by

Jacques Charles. Charles had found that oxygen, nitrogen, hydrogen,

carbon dioxide, and plain air

expand to the same extent over the same 80 degree interval.

Gay-Lussac

Gay-Lussac was no slouch

in the area of ballooning.

On September 16, 1804, he ascended to an altitude of 7016 meters (just over 23,000 feet - about 4.3 miles). This remained the world altitude record for almost 50 years.

Gay-Lussac’s law:

The Pressure of a sample of gas at The Pressure of a sample of gas at constant volume will vary directly constant volume will vary directly with with absoluteabsolute (Kelvin) temperature (Kelvin) temperature.

Temperature & pressure

As P then T

At constant Volume & moles

2

2

1

1

T

P

T

P