# CHEM 1000 Lecture Notes - Atmosphere (Unit), Ideal Gas, Gas Constant

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Chapter Six

Properties of Gases: Gas Pressure

•Gases expand to fill their container and assume the shape of their containers

•They diffuse into one another and mix in all proportions.

Four properties determine the physical behaviour of a gas:

1. The amount of the gas (in

moles)

2. The volume of the gas (in L)

3. The temperature of the gas (in

K)

4. Pressure of gas (in atm or KPa)

The Concept of Pressure:

Consider this. A balloon expands when inflated with air, but what maintains the

balloon’s shape? One good argument is that the molecules of the gas within the

balloon are in constant motion and thus colliding with each other as well as the walls

of the container, the balloon, keeping the balloon in shape.

However it is difficult to measure the total force exerted by a gas. So in

chemistry, we speak in terms of pressure. Pressure is the force per unit area. In

translation, it is the force divided by the area over which the force is distributed.

Liquid Pressure:

It is difficult to measure the pressure of gas directly. So it is done indirectly by

comparison with liquid pressure. Liquid pressure depends only on the height of the

liquid column and the density of the liquid. Thus the formula, g x h x d, can be

derived. Since g is a constant, liquid pressure is directly proportional to the liquid

density and the height of the liquid column.

Barometric Pressure: (read experiment briefly, not important) the height of

mercury in a barometer, a measure of barometric pressure, varies with

atmospheric conditions and altitude. The standard atmosphere (atm) is defined as

the pressure exerted by a mercury column of exactly 760 mm in height when the

density of mercury = 13.5951 g/cm3 (at 0 ºC). Therefore, it is justified to say 1 atm =

760 mmHg.

Manometers: just remember how that thing looks like, and these three situations:

1. Pgas = Pbar. 2. Pgas = P bar. +

P, ( P>0)Δ Δ

3. Pgas = P bar. +

P, ( P<0)Δ Δ

Boyle’s Law: For a fixed amount of gas at a constant temperature, the gas volume is

inversely proportional to the gas pressure.

P1V1 = n = P2V2

Charles’ Law: The volume of a fixed amount of gas at constant pressure is directly

proportional to the Kelvin (absolute temperature)*

V1/T1 = V2/T2

*All gases condense to liquids/solids before the temperature approaches absolute zero.

STANDARD CONDITIONS OF TEMPERATURE and PRESSURE:

0ºC = 273 K and the standard pressure is 1 atm = 760 mmHg.

AVOGARDO’S LAW

Avogadro’s equal volumes – equal numbers hypothesis can be stated in two ways:

1. Equal volumes of different gases compared at the same temperature and

pressure contain equal numbers of molecules.

2. Equal numbers of molecules of different gases compared at the same

temperature and pressure occupy equal volumes.

This can be restated in one general phrase known as the Avogadro’s Law:

At a fixed temperature and pressure, the volume of a gas is directly

proportional to the amount of gas. Therefore, 1 mol gas = 22.4 L gas (at STP).

The Ideal Gas Equation: combination of the previous three laws.

PV = nRT

A gas whose behaviour conforms to the ideal gas equation is called an ideal or

perfect gas.

R is a gas constant. Depending on the situation of the reaction, R can have four

different values:

1. 0.082057 L atm mol-1 k-1

2. 62.364 L Torr mol-1 k-1

3. 8.3145 m3 Pa mol-1 k-1

4. 8.3145 J mol-1 k-1

The General Gas Equation

(P1V1/n1T1) = (P1V1/n1T1)

If one or more of the variables remain constant during the reaction, it is acceptable to

remove them from the equation, thus having a more simplified equation and then

continue forward in achieving the final result.

Molar Mass Determination

PV = (mRT/M)

Gas Densities

d = m/V = (n x M)/ V = (n/V) x M

Therefore: d = m / v = (MP/RT)

The density of gases differs from that of solids and liquids in two important ways.

1. Gas densities depend strongly on pressure and temperature, increasing as the

gas pressure increases and decreasing as the temperature increases. Densities

of liquids and solids also depend somewhat on temperature, but they depend

far less on pressure.