Module 8

Gases

Substances that Exist as Gases• At 25oC and 760 torr (1 atm), the following substances

exist as gases:

Elements Elements Compounds Compounds

H2 He HF NH3

N2 Ne HCl NO2

O2 Ar HBr SO2

O3(Ozone) Kr HI H2S

F2 Xe CO HCN

Cl2 Rn CO2 CH4

(methane)

Properties of Gases• Compressibility-Gases can be compresses into smaller volumes.

Their densities can be increased by applying pressure. If too much pressure is applied they will become liquids or solids.

• Indefinite shape and volume-A gas can be made to fit the vessel in which it is placed.

• Expansion-Gases expand without limits so that gas samples completely and uniformly occupy the volume of a container.

• Miscibility or diffusion-Gases diffuse into each other completely.• Low density-Because the density of a gas is small, it is usually

measured in g/L.

• The average kinetic energy (KE) of gaseous molecules is directly proportional to their absolute temperature (KE

Provided that T is the same, KE of different gas molecules is equal.

• The amounts and properties of gases are described in terms of T (Temperature in K), P (pressure), V (Volume they occupy), and n (number of moles present).

Characteristics of Ideal Gases

• The equations that will be used apply only to ideal gases or those behaving very closely as ideal gases. An ideal gas is considered to have the following characteristics:

a. each particle (atom or molecule) has a negligible volume

b. has no attractive forces c. undergoes elastic collisions (they rebound after

colliding and bounce back in the opposite direction with the same speed).

• Real gases can behave as ideal gases by avoiding: a. extremely low temperatures b. very small volumes c. very high pressures

Pressure• Pressure is defined as force per unit area.• The common units of pressure are: a. atmosphere (atm) b. torr c. mm of mercury (mm Hg) d. Pascal e. bar• 1.00 atm = 760 torr = 760 mm Hg =

1.01 x 105 Pa = 1.01 bar.• At sea level the pressure is 760 torr.

Above sea level it is less than 760 torr. Below sea level it is greater than 760 torr.

Barometer

• The barometer is a device used to measure pressure:

h mm Hg)

Patm

mercury surface

Schematic of a barometer

Patm = h

Manometer• A manometer is a partially filled glass tube of mercurey with one arm open

to the atmosphere (side P1) and the other arm (side P2 ) attached to a gas tank. It can be used to measure the pressure of gas inside of a container.

The difference in the height of mercury from one arm of a manometer to the other is58 mm. If the atmospheric pressure is 1.02 atm, then what is the pressure (in torr) of the gas in the tank that is attached to the manometer?

Pgas = Patm + h

Pgas = 1.02 atm x (760 mm Hg/1 atm) + 63 mm = 839 mm Hg = 839 torr

Standard Temperature and Pressure (STP) and Standard

Molar Volume

• STP = 0.00oC (273.15K) and 1 atm (760 torr)

• At STP 1 mol of an ideal gas occupies 22.4 L.

Gas Laws

• Boyle’s Law: V 1/P (at constant T and n)

Therefore, Volume is inversely related (inversely proportional) to pressure. If the pressure of a gas at constant temperature and number of moles is doubled, the volume will be cut in half.

0

20

4060

80

100

120140

160

180

0 10 20 30 40 50

P (atm)

Vo

lum

e (L

)

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50

P (atm)

1/V

(1/

L)

Gas Laws

• Charles’ Law: V T(K) (at constant P and n)

For example, if the temperature (in K) of a gas at constant pressure and composition is tripled, the volume will triple.

0

50

100

150

200

250

0 100 200 300 400 500

T (K)V

(L

)

Gas Laws

• Avogadro’s Law- V n (constant T and P) Example:If the number of moles of a gas at constant

temperature and pressure is quadrupled, its volume will quadruple.

• At the same T & P equal volumes of gases contain the same number of moles and molecules (at STP 1 mol of gas occupies a volume of 22.4 L).

Combined Gas Law

• Taking into account Boyle’s, Charles’, and Avogadro’s law we arrive at the combined Gas Law:

P1V1 = P2V2 If n is constant: P1V1 = P2V2

n1T1 n2T2 T1 T2

Any unit of P and V as long as they are the same on both sides of the equation. T1 and T2 must be in K.

Ideal Gas Equation

• The ideal gas equation is as follows:

PV = nRT R is the ideal gas constant.

It can have the units:

.0821 L x atm or 62.4 L x torr

K x mol K x mol

Molar Mass and Density of Gases

• Since PV = nRT and n = g/MM and d = g/V, then: PV = g R T and V = g x R x T MM P x MMAnd: d = g = g x P x MM V g x R x T

d = P x MM R x T

Dalton’s Law of Partial Pressures

• At constant volume and temperature, the total pressure extended by a mixture of ideal gases is the sum of the partial pressures of those gases.

Gas A Gas B Gas A & B

PA=200 torr PB=150 torr PT = PA + PB = 350 torr

Place A and B in same container

At constant T and V conditions.

Dalton’s Law of Partial Pressures• PT = PA + PB + PC + …= Since PV = nRT then P= nRT/VPT = nART + nBRT + nCRT + … = (nA + nB + nC +…)(RT) V V V V

There is a simple relation that exists between total pressure and individual pressures. Consider a sample containing gases A and B. Dividing PA by PT we obtain:

nA RT PA = V = nA = XA Where XA is PT (nA + nB)RT nA + nB the mole V fraction of A. Mole fraction is a dimensionless quantity that expresses the ratio of moles of

one component to the number of total moles. The mole fraction can be any number between 0 and 1. Note that the sum of all mole fractions must equal to one. If two components are present, then:

XA + XB = 1 Rearranging the above equation (PA/PT = XA), we can express the partial

pressure of A and B as:

PA = XAPT PB = XBPT

Therefore, in a sample containing two gases (A & B), the total pressure of the sample is given by:

PT = PA + PB = XAPT + XBPT

Vapor Pressure of Water• Gases that are insoluble and don’t react with water can be collected over

water. The partial pressure exerted by the water vapor above the liquid is called its vapor pressure.

• Every liquid shows characteristic vapor pressures that vary with temperature.

• If a gas is collected over water it is saturated with water vapor, and at atmospheric pressure (PT = atmospheric pressure):

PT = Pgas + Pwater or Pgas = PT – Pwatergas gas + water vapor

Vapor pressure of water (Pwater) in torr near room temperature:

Temp (oC) Pwater Temp (oC) Pwater Temp (oC) Pwater

20 17.5 23 21.1 26 25.2

21 18.7 24 22.4 27 26.7

22 19.8 25 23.8 28 28.4

Graham’s Law: Diffusion and Effusion of Gases

• Diffusion is the intermingling of gases.

• Effusion is the leaking out of gases through a small hole or orifice.

• RateA/RateB = (MB/MA)1/2

The rate is the rate of effusion:

V/t mL / s or L / min, etc..

Gay-Lussac’s Law (Law of Combining Volumes)

• At constant temperature and pressure, the volumes of reacting gases can be expressed as the simple whole number ratio of the moles of gases that are reacting (V M at constant T and P).

• If the reaction is carried out at STP, then 1 mol gas = 22.4 L

H2(g) + Cl(2) 2HCl(g1 mol 1 mol 2 mol

1 volume 1 volume 2 volumes

22.4 L 22.4 L 44.8 L At STP