Gas Laws Honors chemistry – Semester 2

Objectives

Understand and use four gas laws

Boyle’s law

Charles’s law

Gay-Lussac’s law

Avogadro’s law

Measurable properties of gas

Pressure = P

Temperature = T (in kelvins!)

Volume = V

Number of moles = n

Memory Aid!

Write the letters below in the order shown

“On Pressure TV, you can’t buy goats!” - Angie Nguyen

P T V C B G

Boyle’s law

At constant temperature,

pressure times volume is constant

PV = k

If the amount of gas remains the same

PiVi = PfVf = k

In other words, ½ the volume = 2x the pressure!

Boyle’s Law

• Constant temp (pinch “T”), note “B” underneath

• Move “P” up - down (inc. – dec. pressure)

• What happens to “V”?

As P gets bigger, V gets smaller

As P gets smaller, V gets bigger

P T V C B G

Example

A sample of gas fills 523 mL at 1.00 atm. If pressure increases to 1.97 atm, what is the new volume?

P1 = 1.00 atm V1 = 523 mL

P2 = 1.97 atm V2 = ?

P1V1 = P2V2

V2 = P1V1 / P2

= (1.00 atm)(523 mL) / 1.97 atm = 265 mL

Example

A sample of gas has a volume of 150.0 mL at 0.947 atm. What is the volume if pressure decreases to 0.750 atm?

P1 = 0.947 atm V1 = 150.0 mL

P2 = 0.750 atm V2 = ?

P1V1 = P2V2

V2 = P1V1 / P2

= (0.947 atm)(150.0 mL) / 0.750 atm = 189 mL

Practice

A balloon with a volume of 456 mL at a pressure of 1.0 atm is submerged in water so that the new pressure is 3.3 atm. Assuming constant temperature, what is the new volume of the balloon?

1.4 x 102 mL or 140 mL

Charles’s Law

If the temperature changes, a gas will expand or contract to maintain constant pressure

At constant pressure, the volume of gas divided by temperature is constant

V / T = k V1 / T1 = V2 / T2

Example

A balloon with a volume of 15.5 L is inflated at 20.0 C. The balloon is cooled to 7.0 C. What will be the volume of the balloon?

V1 = 15.5 L T1 = 20.0 C = 293.0 K

V2 = ? T2 = 7.0 C = 280.0 K

V1 / T1 = V2 / T2 V2 = V1T2 / T1

V2 = (15.5 L)(280 K) / 293 K = 14.8 L

Practice

1.50 x 103 L of air is heated from 5.00 C to 30.0 C in a furnace. What is the new volume of the air?

1.63 x 103 L

Gay-Lussac’s Law

At constant volume, pressure is proportional to temperature

P = kT

P/T = k

P1/T1 = P2/T2

Example

A can containing gas at 101 kPa and 22 °C is heated to 55 °C. Calculate the pressure in the heated can.

P1 = 101 kPa T1 = 22 °C = 295 K

P2 = ? T2 = 55 °C = 328 K

P1/T1 = P2/T2

P2 = P1T2/T1 = (101 kPa)(328 K)/295 K = 112 kPa

Example

The pressure in tire at 20 °C is 29.8 psi. After being driven on a hot road, the temperature rises to 48 °C . What is the pressure in the hot tire?

P1 = 29.8 psi T1 = 20 °C = 293 K

P2 = ? T2 = 48 °C = 321 K

P1/T1 = P2/T2

P2 = P1T2/T1 = (29.8 psi)(321 K)/293 K = 32.6 psi

Practice

A sample of nitrogen has a pressure of 1.07 atm at 122 °C. The gas is cooled and the new pressure measured as 0.880 atm. What is the temperature of the cooled gas?

325 K or 52 °C

Avogadro’s Law

Equal volumes of gas under the same pressure and temperature have the same # of particles

Example:

He H2 CO2

Avogadro’s Law

The volume of a gas is proportional to the number of moles of particles

V = kn

k = constant

n = number of moles

Avogadro’s Law

But volume changes with different T and P!

Use standard temperature and pressure (STP)

• 0 °C and 1 atm pressure

At STP:

• volume of 1 mol of any gas = 22.41 L

• mass of 22.41 L of any gas = molar mass

• 22.41 L of any gas = 6.022 x 1023 particles

Example

1 mol of He, H2 and CO2 at STP

volume mass particles

He 22.41 L 4.0 g 6.022 x 1023

H2 22.41 L 2.0 g 6.022 x 1023

CO2 22.41 L 44.0 g 6.022 x 1023

He H2 CO2

Gas Law Recap

Boyle’s Law: P1V1 = P2V2 (constant T)

Charles’s Law: V1/T1 = V2/T2 (constant P)

Gay-Lussac’s Law: P1/T1 = P2/T2 (constant V)

Avogadro’s Law: V = kn

P T V C B G

Review

As popcorn heats up, the pressure inside the kernel builds. What law describes this pressure increase?

Gay-Lussac’s Law (P1/T1 = P2/T2, V is constant)

Once the popcorn kernel breaks open, its volume increases and the pressure drops. What law describes this?

Boyle’s Law (P1V1 = P2V2, T is constant)

Review

Video: What two gas laws are in play with this video clip?

Gay-Lussac’s law – heating with pressure increase

Boyle’s Law – Volume expansion when pressure drops