Gas Laws

Chemistry is “Real” gas

Pressure

Pressure is force per unit area Standard atmospheric pressure

1 atmosphere760 mm Hg = 760 torr29.92 inches Hg101.325 kPa14.7 psi

Barometers

Mercury barometer

Manometers

Open arm manometer

Manometers

Open arm manometer

Manometers

Closed arm manometer

Pressure

Converting units Convert 728 torr into atmospheres. 728 torr x 1 atmosphere

760 torr

= 0.958 atm Convert 86 kPa into torr. 86 kPa x 760 torr

101.325 kPa

= 645 torr

Pressure and volume: Boyle’s Law

As pressure is increased, volume decreases by the same fraction (constant temperature)

P1V1 = P2V2

Find the new volume if the gas in a 4.5 mL syringe is compressed from 1.05 atm to 2.31 atm.

Boyle’s Law

Make a list of variables P1 = 1.05 atm V1 = 4.5 mL P2 = 2.31 atm V2 = V2

Plug variables into equation and solve for V2

1.05 atm x 4.5 mL = 2.31 atm x V2

2.31 atm 2.31 atm

1.05 x 4.5 mL = V2

2.31 = 2.05 mL

Boyle’s Law

Freddie Krueger compresses air in a syringe from 5.1 mL to 1.9 mL. If the gas was initially at 101 kPa, what is the new pressure?

101 kPa x 5.1 mL = P2 x 1.9 mL

101 x 5.1kPa = P2

1.9 = 271 kPa

Boyle’s Law

Kinetic explanation of Boyle’s Law – when volume is decreased, particles of a gas have less room and strike the walls of the container more often.

Temperature and volume: Charles’ Law As the temperature increases, the volume

increases (constant pressure) V1/T1 = V2/T2

(T must be in kelvins) George of the Jungle has a syringe of

nitrogen gas with volume 4.9 mL. The temperature of the jungle is 40ºC (313K). He places the syringe in a pot of boiling water (100ºC, 373K). What is the new volume?

Charles’ Law

List variables:

V1 = 4.9mL T1 = 313K

V2 = V2 T2 = 373K Plug variables into Charles’ Law

equation and solve for V2

4.9mL V2

313K 373K

=

Charles’ Law

Solve for V2

4.9mL V2

313K 373K

4.9mLx373K = V2

313K

= 5.84 mL

=

Charles’ Law

Jim Jones has a syringe full of hydrogen cyanide gas (9.4 mL) at 33ºC. He submerges it in dry ice/carbon tetrachloride and the volume goes down to 7.6 mL. What is the temperature of the dry ice/carbon tetrachloride?

Charles’ Law

V1/T1 = V2/T2

9.4 mL 7.6 mL

306K T2

9.4 1

(306Kx7.6) T2

(306Kx7.6)/9.4 = T2

= 247K (-26ºC)

=

=

Charles’ Law

Kinetic explanation of Charles’ Law – as temperature increases, the particles move faster and hit the walls of the container harder, increasing the volume.

In a rigid container the pressure increases. (Gay-Lussac’s Law)

Combined Gas law

Combination of Boyle’s and Charles’ Laws

P1V1 = P2V2

T1 T2

The amount of gas remains constant.

Combined Gas Law

Jane compresses a sample of fluorine gas at standard pressure in a syringe from 6.2 mL to 2.3 mL. As she does this the temperature of the gas increases from 296K to 310K. What is the new pressure of the gas in atmospheres?

Combined Gas Law

1atm x 6.2 mL P2 x 2.3 mL

296K 310K

1 x 6.2 x 310 P2

296 x 2.3

= 2.8 atm

=

=

Combined Gas Law

JJ leaves his basketball on the hot pavement on a summer afternoon. The pressure in the ball increases from 20.7 psi to 21.3 psi. The internal temperature of the ball went from 22ºC to 41ºC. If the original volume was 5.2 liters, what is the final volume?

Combined Gas Law

P1V1 = P2V2

T1 T2

20.7psi x 5.2 L = 21.3psi x V2

295K 314K

20.7psi x 5.2 L x 314K = V2

295K x 21.3psi

= 5.4 L

Law of combining gas volumes Under the same conditions, equal

volumes of any gas contain the same number of particles (Avogadro’s principle)

Standard conditions – 0ºC (273K) and 1 atm

Under standard conditions, one mole of a gas occupies 22.4 liters (molar volume)

Law of combining gas volumes

In a reaction where all the reactants and products are gases, the mole ratios are also volume ratios

2H2 + O2 2H2O