Module 8

Module 8

Gases

Substances that Exist as Gases

•At 25oC and 760 torr (1 atm), the following substancesexist as gases:

Elements

Compounds

NH3

HCl

NO2

HBr

SO2

O3(Ozone)

H2S

HCN

Cl2

CO2

CH4(methane)

Properties of Gases

•Compressibility-Gases can be compresses into smaller volumes.Their densities can be increased by applying pressure. If too muchpressure is applied they will become liquids or solids.

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

•Expansion-Gases expand without limits so that gas samplescompletely 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 usuallymeasured 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 gasesor those behaving very closely as ideal gases. An idealgas is considered to have the following characteristics:

a. each particle (atom or molecule) has a negligiblevolume

b. has no attractive forces

c. undergoes elastic collisions (they rebound aftercolliding and bounce back in the opposite direction withthe 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 tomeasure 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 opento the atmosphere (side P1) and the other arm (side P2 ) attached to a gastank. 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 is

58 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 andPressure (STP) and StandardMolar Volume

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

•At STP 1 mol of an ideal gas occupies22.4 L.

Gas Laws

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

Therefore, Volume isinversely related(inversely proportional) topressure. If the pressureof a gas at constanttemperature and numberof moles is doubled, thevolume will be cut in half.

Gas Laws

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

For example, if thetemperature (in K) of agas at constant pressureand composition istripled, the volume willtriple.

Gas Laws

•Avogadro’s Law- V n (constant T and P)

Example:

If the number of moles of a gas at constanttemperature and pressure is quadrupled,its volume will quadruple.

•At the same T & P equal volumes of gasescontain the same number of moles andmolecules (at STP 1 mol of gas occupies avolume of 22.4 L).

Combined Gas Law

•Taking into account Boyle’s, Charles’, and Avogadro’slaw 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 bothsides 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 MM

And: 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, thetotal pressure extended by a mixture ofideal gases is the sum of the partialpressures 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/V

PT = nART + nBRT + nCRT + … = (nA + nB + nC +…)(RT)

V V V VThere is a simple relation that exists between total pressure and individualpressures. Consider a sample containing gases A and B. Dividing PA by PTwe 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 ofone component to the number of total moles. The mole fraction can be anynumber between 0 and 1. Note that the sum of all mole fractions must equalto one. If two components are present, then:

XA + XB = 1

Rearranging the above equation (PA/PT = XA), we can express the partialpressure of A and B as:

PA = XAPT PB = XBPT

Therefore, in a sample containing two gases (A & B), the total pressure of thesample 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 overwater. The partial pressure exerted by the water vapor above the liquid iscalled its vapor pressure.

•Every liquid shows characteristic vapor pressures that vary withtemperature.

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

PT = Pgas + Pwater or Pgas = PT – Pwater

gas

gas + water vapor

Vapor pressure of water (Pwater) in torr near roomtemperature:

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 Effusionof Gases

•Diffusion is the intermingling of gases.

•Effusion is the leaking out of gasesthrough 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 ofCombining Volumes)

•At constant temperature and pressure, thevolumes of reacting gases can be expressed asthe simple whole number ratio of the moles ofgases that are reacting (V M at constant T andP).

•If the reaction is carried out at STP, then

1 mol gas = 22.4 L

H2(g) + Cl(2) 2HCl(g

1 mol 1 mol 2 mol

1 volume 1 volume 2 volumes

22.4 L 22.4 L 44.8 L At STP