Gases

Chapter 14

14.1 The Gas Laws:

Kinetic Molecular Theory (Chapter 13): gases typically behave in a way that allows us to make assumptions in order to simplify their behavior and conclude basic mathematical relationships

Assumptions for ideal gases:

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 with the walls of their container (elastic collisions)

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

Variables that affect gases:

Volume (V) the amount of space the gas takes up

Pressure (P) a measure of the number of collisions the gas particles have with the container holding it

Temperature (T) a measure of the average kinetic energy of the gas particles

Moles (n) the amount of gas held in the container

Boyles Law:

Defined by Robert Boyle (1627-1691) while studying the relatedness of the volume and pressure of gases

States that: “the volume and pressure of a gas are inversely proportional when the temperature and amount of gas are held constant”

Mathematically stated:

P1V1=P2V2 Constant = T and n

the 1’s and 2’s are indicating starting vs. ending conditions

Charles’ Law:

Defined by Jacques Charles (1746-1823) while studying the relatedness of the volume and temperature of gases

States that: “the volume and temperature of a gas are directly proportional when the pressure and amount of gas are held constant”

Mathematically stated:

V1 = V2 constant = P and n

T1 T2

the 1’s and 2’s indicating starting vs. ending conditions

Kelvin Scale

A temperature scale with no negative values; allows for calculations with temperature

Tk = 273 + Tc

All temperatures must be converted to Kelvin when using Charles’ Law, even if they are already positive. Otherwise the formula becomes invalid.

Gay-Lussac’s Law:

Defined by Joseph Gay-Lussac while studying the relatedness of the pressure and temperature of gases

States that: “the pressure and temperature of a gas are directly proportional when the volume and amount of gas are held constant”

Mathematically stated:

P1 = P2 constant = V and n

T1 T2

the 1’s and 2’s are indicating starting vs. ending conditions

All temperatures must be converted to Kelvin when using Gay-Lussac’s Law, even if they are already positive. Otherwise the formula becomes invalid.

14.2 The Combined Gas Law and Avogadro’s Principle:

Combined Gas Law (Combination Law) – a synthesis of the 3 basic laws into one mathematical expression where the amount of gas is held constant

Mathematically stated:

P1V1 = P2V2 constant = n

T1 T2

Avogadro’s Principle – equal volumes of gases at the same temperature and pressure contain equal numbers of particles

Molar volume – the volume of one mole of ANY gas at 0°C and 1atm pressure

STP – standard temperature and pressure; zero degrees Celsius and 1 atmosphere of pressure

Conversion factors:1mole=22.4L(of gas @STP)=6.02x1023particles=molar mass

14.3 The Ideal Gas Law:

Ideal Gas – a gas that generally follows the assumptions; typically under non-extreme conditions

Real Gas – a gas that deviates from the 5 assumptions; typically under high pressures and/or low temperatures

Ideal Gas Law -

The relationship of pressure, volume, temperature, and number of moles of an ideal gas factoring in the Gas Constant

Mathematically stated:

PV = nRT R=gas constant=0.0821L.atm

mole.K

Applications of Ideal Gas Law:

PV = mRT and D=MP m=mass(g)

M RT M=molar mass

14.4 Gas Stoichiometry

Find volume @STP using 22.4L

Moles of given to moles of unknown

Find grams using

molar mass

Find particles

using 6.02x102

3

Not at STP Given: V,P andT

Find moles @STP using 22.4L

Moles of given to moles of unknown

Find moles using

molar mass

Find moles using

6.02x102

3

Not at STP

Find V using n, P and T V,P and

T