THE GAS LAWS

Kinetic Theory (Gases) Assumptions

1. Gas particles do not attract or repel each other

2. Gas particles are much smaller than the distances between them

3. Gas particles are in constant, random motion

4. No kinetic energy is lost when gas particles collide with each other or the walls of their container

5. All gases have the same average kinetic energy at a given temperature

The Nature of Gases

• Actual gases do not follow suit with the assumptions

• The assumptions are based on 4 factors:– 1. number of particles present– 2. temperature– 3. pressure – 4. volume of sample

• If one variable changes, it affects the other three

Boyle’s Law

• Named for Robert Boyle (1627-1691)– Irish Chemist – Studied the relationship between volume and

pressure– Proved that volume of a gas and the pressure of the

gas are inversely proportional

• Boyle’s Law- the volume of a given amount of gas held at constant temperature varies inversely with the pressure.

Boyle’s Law Cont’d

• Mathematically the equation is as follows:

P1V1=P2V2

Example Problem 14.1

• A sample of helium gas in a balloon is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210kPa, what will the pressure be at 2.5L?

ANSWER:

V1=4.0L V2= 2.5L P1=210kPa P2=???

P1V1=P2V2

P2= (P1V1) = (210kPa)(4.0L)= 340kPa

V2 2.5L

Charles’ Law

• Named for Jacques Charles (French physicist)

• 1746-1823

• Studied volume and temperature

• Observed that as temperature increases so does the volume of a gas in a sample; therefore, it is a direct relationship

• (Temperature is measured in KELVIN)

Charles’s Law Cont’d

• The volume of a given amount of gas is directly proportional to its Kelvin temperature at constant pressure

V1=V2

T1 T2

Tkelvin= 273 + TCelsius

Example Problem 14.2

• A gas sample at 40oC occupies a volume of 2.32 L. If the temperature is raised to 75oC, what will the volume by assuming the pressure remains constant?

T1=40oC +273= 313K V1=2.32L

T2= 75oC + 273 = 348K V2= ???

V1 = V2 V2=T2V1 so V2= (348K)(2.32L)= 2.58L

T1 T2 T1 313K

Gay-Lussac’s Law

• Named for Joseph Gay-Lussac

• Explored relationship between pressure and temperature of a gas at a fixed volume

• Equation:P1=P2

T1 T2

Gay-Lussac’s Law Example

• The pressure of a gas in a tank is 3.20 atm at 22oC. If the temperature rises to 60oC, what will be the gas pressure in the tank?

P1=3.20 atm T1= 22oC + 273 = 295K

T2=60oC + 273 = 333K P2=???

P1=P2 P2=T2P1 P2= (333K)(3.20atm) = 3.61 atm

T1 T2 T1 295K

HOMEWORK due tomorrow

• Page 422 1-5

• Page 425 6-8

• Page 427 9-13

14.2 The Combined Gas Law

• Boyle’s, Charles’s and Gay-Lussac’s Law can be COMBINED into one law

P1V1 =P2V2

T1 T2

Example 14.4

• A gas at 110kPa and 30oC fills a flexible container with an initial volume of 2.0L. If the temperature is raised to 80oC and the pressure increased to 440 kPa, what is the new volume?

P1=110kPa T1= 30oC +273= 303K V1= 2.0L

P2= 440 kPa T2=80oC + 273= 353K V2=???

P1V1=P2V2 V2= P1V1T2 V2= (110kPa)(2.0L)(353K)= 0.58L

T1 T2 P2T1 (440kPa)(303K)

Avogadro’s Principle

• States that equal volumes of gases at the same temperature and pressure contain equal numbers of particles

• Molar volume is the volume that one mole occupies at 0oC and 1.00 atm of pressure

• These conditions are referred to as STP (Standard Temperature and Pressure)

• Conversion Factor = 22.4L/1mol

Example 14.5

• Calculate the volume that 0.881 mol of gas at STP will occupy.

XL = 0.881 mol x 22.4L = 19.7L

1mol

Example 14.6

• Calculate the volume that 2.0kg of methane gas will occupy at STP.

XL = 2.0kgx 1000g x 1mol x 22.4L = 2.8x103L

1 kg 16.05g 1 mol

14.4 The Ideal Gas Law

• In addition to temperature, pressure, and volume, the number of moles is another way to describe a gas

• In the previous gas laws, care was taken to observe a “fixed amount” of a gas

• If the number of moles of gas present is changed, one of the other variables is affected.

PV=nRT

• P = pressure• V= volume• n= number of moles of gas present• R= ideal gas constant• T= temperature

• The value of the ideal gas constant (R) is dependent on the units used for pressure

Numerical Values of R

Units of R Numerical Value of R

Units of P

Units of V Units of T

Units of n

L atm/mol K 0.0821 atm L K mol

L kPa/mol K 8.314 kPa L K mol

L mmHg/mol K 62.4 mm Hg L K mol

Real vs. Ideal Gases

• Ideal gas- takes up no space and has no intermolecular attraction

• In the real world, no true real gas is ideal

• In the real world, real gases have intermolecular attraction – Length of bonds– Types of atoms

Example 14.7

• Calculate the number of moles of gas contained in a 3.0L vessel at 300K with a pressure of 1.50 atm.

P=1.50 atmV= 3.0Ln=?R=0.0821Latm/molKT=300K

PV=nRT

n=PV/RT

n= (1.50 atm)(3.0L)(0.0821Latm/molK) (300K)

n= 0.18 mol