Gases

13.1 Gases and Pressure Gases – constituent atoms and molecules that

have little attraction for one another Free to move in available volume

Some properties of gases Mixtures are always homogenous

Very weak attraction between gas molecules Identity of neighbor is irrelevant

Compressible – volume contracts when pressure is applied

0.10% of volume of gas is occupied by molecules Exert a measurable pressure on the walls of their

container

13.1 Units of Pressure Pressure – force exerted per unit area

SI unit equals Pascal (Pa) 1 Pa = 1 N/m2 (1 N = 1 (kg•m)/s2)

Alternative units Millimeters of mercury (mmHg) Atmosphere (atm)

1.0 atm = 760 mmHg = 101, 325 Pa 1.0 atm = 14.69 psi

Pressure Atmospheric pressure –

pressure created from the mass of the atmosphere pressing down on the earth’s surface

Standard atmospheric pressure at sea level – 760 mmHg

Measuring pressure Barometer – long thin

mercury filled tube sealed at once end and inverted into a dish of mercury

Downward pressure of Hg in column equals outside atmospheric pressure

Manometer – U-tube filled with mercury, with one end connected to the gas – filled container and the other end open to the atmosphere.

ExamplesThe pressure of the air in a tire is measured

to be 28 psi. Represent this pressure in atm, torr and pascals

On a summer day in Breknridge, Colorado, the atmospheric pressure is 325 mmHg. What is the pressure in atmostphere?

13.2 Pressure and Volume; Boyle’s LawShowing the relationship between pressure

and volumeP x V = k (constant value @ specific temp and

constant moles of gas)k = 1.40 x 103

P = 1/ V (inverse relationship)Can predict a new volume of pressure is

changed P1V1 = k = P2V2 P1V1 = P2V2

Calculate V2 =

Figures 13.6

ExamplesA sample of helium gas has a pressure of

3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. What is the volume of the new container? Assume constant temperature.

A sample of neon gas has a pressure of 7.43 atm in a container with volume of 45.1 L. This sample is transferred to a container with a volume of 18.4 L. What is the new pressure of the neon gas? Assume constant temperature

13.3 Volume and Temperature: Charles’s LawRelationship between Volume and

TemperatureV = bT (b is a constant)V / T = bCan predict the new volume or temperature(V1/T1)= (V2/T2)

V vs. T

ExamplesA 2.0 L sample of air is collected at 298K and

then cooled to 278 K. The pressure is held constant at 1.0 atm.Does the volume increase of decrease?Calculate the volume of the air at 278 K?

ExamplesConsider a gas with a volume of 5.65 L at

27oC and 1 atm pressure. At what temperature will this gas have a volume of 6.69 L and 1 atm pressure?

13.4 Volume and Moles: Avogadro’s LawRelationship between volume of gas and

number moles of gasV is directly proportional to nV = an or V / n = a (a = constant)Can predict the new volume or new moles of

gas at constant pressure and temperature(V1/n1) = (V2/n2)

V vs. n

ExamplesSuppose we have a 12.2 L sample containing

0.50 mol of oxygen gas, O2 at a constant pressure of 1atm and a temperature of 25oC. If all of this O2 is converted to ozone, O3, at the same temperature and pressure, what will be the volume of ozone formed?

ExamplesConsider two samples of nitrogen gas

(composed N2 molecules). Sample 1 contains 1.5 mol of N2 and has a volume of 36.7 L at 25oC and 1 atm. Sample 2 has a volume of 16. L at 25oC and 1 atm. Calculate the number moles of N2 in sample 2

13.5 The Ideal Gas law Different gasses show similar physical

behavior (unlike solid or liquid) Defined by four variables – pressure,

temperature, volume, and number of moles Relationship of variable – gas laws Ideal gas – behavior follows the gas laws exactly

Describes how the volume of a gas is affected by changes in pressure, temperature and amount.

PV = nRT; R = gas constant = 0.08206 L•atm

K•mol

ExamplesA sample of hydrogen gas, H2, has a volume

of 8.56 L at a temperature of 0oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. (Assume that the gas behaves ideally.)

ExamplesWhat volume is occupied by 0.250 mol of

carbon dioxide gas at 25oC and 371 torr?

A 0.250 mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas?

Combine Gas Law is an expression obtained by

mathematically combining Boyle’s and Charles’ law

P1V1 = P2V2 @ constant n T1 T2can predict P, V or T when condition is changed

ExamplesSuppose we have a 0.240 mol sample of

ammonia gas at 25oC with a volume of 3.5 L at a pressure of 1.68 atm. The gas compressed to a volume of 1.35 L at 25oC. Use the combined gas law to calculate the final pressure.

ExamplesConsider a sample of hydrogen gas of 63oC

with a volume of 3.65L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35oC. Calculate the new volume of the gas

13.6 Dalton’s Law of Partial PressureA. Gas laws apply to mixtures of gasesB. Dalton's law of partial pressure – Ptotal = P1 + P2 + P3 + ….. at constant V, Twhere P1, P2, ….refer to the pressure of the

individual gases in the mixture

C. Partial pressures refer to the pressure each individual gas would exert if it were alone in the container (P1, P2, …)1. Total pressure depends on the total molar amount of gas present

3. Ptotal = ntotal (RT/V)

ExamplesMixture of helium and oxygen are use in the

“air” tanks of underwater divers for deep dives. For a particular dive, 12 of O2 at 25oC and 1.0 atm and 46 L of He at 25oC and 1.0 atm were both pumped into a 5.0 L tank. Calculate the partial pressure of each gas and the total pressure in the tank at 25oC

ExamplesA 2.0 L flask contains a mixture of nitrogen

gas and oxgyen gas at 25oC. The total pressure of the gas mixture is 0.91 atm, and the mixture is known to contain 0.050 mol of N2. Calculate the partial pressure of oxygen and the moles of oxygen present

13.8 The Kinetic Molecular Theory of GasA. Model that can explain the behavior of

gases.Assumptions

1. A gas consists of particles in constant random motion

2. Most of the volume of a gas is empty spaces

3. The attractive and repulsive forces between molecules of gases are negligible

4. The total kinetic energy of the gas particles is constant at constant T

5. Average Ek α T

13.10 Gas Stoichiometry Stoichiometric calculations involves the

application of the ideal gas law One of the variables in the ideal gas law

equation is unknown.

ExampleE.g Pure oxygen gas was first prepared by

heating mercury(II) oxide, HgO2 HgO(s) 2 Hg(l) + O2(g)

What volume (in liters) of oxygen at STP is released by heating 10.57 g of HgO?

Step1: Calculate moles of HgOStep 2: Calculate mole O2Step 3: Calculate volume using Ideal gas

law

ExamplesConsider the reaction represented by the

equation P4(s) + 6 H2(g) 4H3(g)

What is the amount of P4 is required to react with 5.39 L of hydrogen gas at 27oC and 1.25 atm?

Molar volume and STPThe molar volume of an ideal gas is

22.4L/moleSTP = Standard Temperature (273K)

Pressure ( 1.0 atm)

examplesA sample of nitrogen gas has a volume of

1.75 L at STP. How many moles of N2 are present?

examplesQuicklime, CaO, is produced by heating

calcium carbonate, CaCO3. Calculate the volume of CO2 produced at STP from the decomposition of 152 g of CaCO3 according to the reaction

CaCO3(s) CaO(s) + CO2(g)