Pressure, Volume, TemperatureThe Gas Laws

Learning Objectives

• Understand the qualitative relationship between pressure (P) and volume (V) and temperature (T), when you have a gas

• Learn the three gas laws and how to apply then mathematically to solve problems

• Combine the gas laws into one equation, and solve problems where P, V, and T are no longer constant.

Boyle’s Law• Robert Boyle, studied the relationship

between pressure, p, and volume, V, in the mid-1600s.

• When he doubled the pressure on a sample of gas at constant temperature, its volume was reduced by one-half.

pressure

volume

Boyle’s Law: Graphically

-constant temperature-inverse relationship

Connection To Your Math Class

Asymptote- A line that continually approaches a given curve but does not meet it at any finite distance.

Greek word that means “not falling together”

Boyle’s Law: Formula

P1 = initial pressure

V1 = initial volume

P2 = final pressure

V2 = final volume

If you know three of the four, you can calculate the fourth.

P1V1 = P2V2

Boyle’s Law: Sample Problems

P1V1 = P2V2

A sample of oxygen gas has a volume of 150. ml when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature does not change?

Standard Problem

More Difficult Problem

It is hard to begin inflating a balloon. A pressure of 800.0 kPa is required to initially inflate the balloon 225.0 mL.  What is the final pressure in mm Hg when the balloon has reached it's capacity of 1.2 L??

Boyle’s Law: Sample Problem

P1V1 = P2V2A sample of oxygen gas has a volume of 150. ml when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature does not change?

P1V1 = P2V2

P2 = P2

P1V1 = V2

P2

V2 = (0.947)(150.) = 144 ml of O2

(.987)

P1 = 0.947 atmV1 = 150. mlP2 = 0.987 atmV2 = what problem is looking for

Charles’ Law• Jacques Charles discovered the relationship

between volume and temperature in 1787.

• The law states that the volume of a sample of gas at constant pressure varies directly with Kelvin temperature.

1783 - 1st hydrogen balloon

volume

temperature

Charles’s Law: Graphically

-constant pressure-directly proportional

Charles’s Law: Formula

V1

T1

= V2

T2

V1 = initial volume

T1 = initial temperature

V2 = final volume

T2 = final temperature

If you know three of the four, you can calculate the fourth.

Charles’s Law: Sample Problem

A sample of neon gas occupies a volume of 752 ml at 25oC. What volume will the gas occupy at 50oC if the pressure remains constant?

T2V1 T2V2

T1 T2

T2V1

T1

V2 = (752)(273 +50) = 815 ml Ne (273 + 25)

V1

T1

= V2

T2

= = V2

Gay-Lussac’s Law• Joseph Gay-Lussac is credited with discovering

relationship between pressure and temperature, but the discovery should actually go to Guillaume Amontons (1699).

• The law states that the pressure of a sample of gas at constant volume varies directly with Kelvin temperature.

pressure

temperature

Gay-Lussacs Law: Graphically

-constant volume-direct relationship

Gay-Lussac’s Law: Formula

P1

T1

= P2

T2

P1 = initial pressure

T1 = initial temperature

P2 = final pressure

T2 = final temperature

If you know three of the four, you can calculate the fourth.

Gay-Lussac’s Law: Sample Problem

The gas in an aerosol can is at a pressure of 3.00 atm at 25oC. The can warns not to allow the temperature to get above 52oC. What would the pressure of the can be at 52oC?

T2P1 T2P2

T1 T2

T2P1

T1

P2 = (3.00)(273 +52) = 3.27 atm (273 + 25)

P1

T1

= P2

T2

= = P2

LAWLAW RELATIONSHIRELATIONSHIPP

LAWLAW CONSTANTCONSTANT

Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n

Charles’Charles’ VV T T VV11/T/T11 = V = V22/T/T22 P, nP, n

Gay-Gay-Lussac’sLussac’s PP T T PP11/T/T11 = P = P22/T/T22 V, nV, n

The Combined Gas Law

The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

Sample Combined Gas Law Problem

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature (°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = 180 mL T1 = 302 K

P2 = 3.20 atm V2= 90 mL T2 = ??

604 K - 331oC

Pressure, Volume, Temperature

Let’s see what we already know about these three variables …

Gas Law Program

NOVA: Race for Absolute Zero

Try not to lose your head when you are doing chemistry

and

Why you should always wear your safety goggles