AP Chapter 10

Gases

Physical Properties of Gases

Will fill any container Highly compressible Form homogeneous mixtures

Noble GasesDiatomic gasesGaseous compounds of Nonmetals

Characteristics:

Amount: measured in moles (n) Temperature: measured in Kelvin (K) Volume: measured in liters

Simple gas laws can use milliliters

Pressure: measured in 1 atmosphere (atm) 14.69 psi 760 mm Hg 101,325 Pascals (N/m2)

760 torr 1.01325 Bar

Barometer was invented in 1643 by Evangelista Torricelli (Torr)

Manometer is a device used to measure pressure difference between a gas and barometric pressure.

Standard Temperature Pressure (STP) is 0 oC and 1 atm.

Molar volume is the volume of one mole of gas at specific temperatures. STP – molar volume is 22.4 L

25 oC – molar volume is 24.5 L

Simple Gas LawsBoyle’s Law P1V1 = P2 V2

V 1/P

When graphing V and 1/P, the slope of the line = k

P V = k

P = pressure in atm or mm Hg

V = volume in liters or mL

k = slope

Charles Law V1 = V2

T1 T2

A plot of all gas extrapolated to a volume of zero, occurs at 0 K, (-273 oC) Absolute Zero

V T

V = volume in liters or mL

T = temperature in Kelvin

Pressure Temperature Law P1 = P2

T1 T2

Pre

ssure

Temperature

P T

P = pressure in atm or mm Hg

T = temperature in Kelvin

Avogadro’s Law V1 = V2

N1 N2V

olu

me

Moles

V NAvogadro’s

Hypothesis: Equal volumes of gas at the

same temperature and pressure contain

equal number of particles.

V = volume in liters or mL

N = number of moles

General Gas Law combines all of the

simple gas laws into one. P1V1 = P2V2

T1N1 T2N2

P = pressure in atm or mm Hg

V = volume in liters or mL

T = temperature in Kelvin

N = moles

Ideal Gas Law P V = n R T

P = pressure in atmV = volume in litersn = number of molesR = gas constant 0.08206 atm L/mol K

T = temperature in Kelvin

An Ideal gas is hypothetical, it assumes that the gas atoms or molecules have no volume and there is no interactions between particles.

Calculate the volume of H2(g) measured at 26 oC and 751 mm Hg, required to react with 28.5 L of CO(g) measured at 0 oC and 760 mm Hg in the following reaction:

CO (g) + H2 (g) C3H8 (g) + H2O (g)

Remember Avogadro’s hypothesis!

What volume of N2 (g) measured at 735 mm Hg and 26 oC is produced when 70.0 g of NaN3 (s) is decomposed in an air bag.

NaN3 (s) Na (s) + N2 (g)

A sample of methane gas having a volume of 2.80 L at 25 oC and 1.65 atm was mixed with a sample of O2 (g) having a volume of 35.0 L at 31 oC and 1.25 atm. The mixture was then ignited to form CO2 (g) and H2O (g). Calculate the volume of CO2 formed at a pressure of 2.50 atm and 125 oC.

CH4 (g) + O2 (g) CO2 (g) + H2O

(g)

The Ideal Gas Law can be converted to many forms to find other properties of gases.

Grams /molar mass = moles

P V = grams /molar mass R T

Molar mass = grams R T/ P V

Md R T / P

A gas has a pressure of 1.10 atm at a temperature of 300 K and a volume of 2.79 L. It has a mass of 2.00 g. What is it’s molar mass?

Molar mass = grams R T / P V

To find density of a gas

Density = mass /volume

Molar mass = grams R T / P V

Molar mass = (grams/volume)(R T/P)

Molar mass = d R T / P

d = MP/R T

d = MP / R T

What is the density of O2 (g) at 298 K and 0.987 atm?

Dalton’s Law of Partial Pressures – For a mixture of gases, in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.PT = P1 + P2 + P3 . . .

P = n(RT/V) PT = (n1 + n2 + n3 . . .)(RT/V)

Mole fraction (chi)

=

A = individual gasT = total gas mixture

Important characteristics of an ideal gas•Pressure is not exerted by identity of gas•Volume of individual gas particles is unimportant•Force of individual gas particles is unimportant

NA = PA = VA

NT PT VT

What is the pressure exerted by a mixture of 1.0 g H2 (g) and 5.0 g He (g) in a volume of 5.0 L and a temperature of 293 K?

What are the partial pressures of H2 and He in the mixture?

Mixtures of Helium and oxygen can be used in scuba diving tanks to help prevent “the bends”. For a particular dive, 46 L He at 25 oC and 1.0 atm and 12 L of O2 at 25 oC and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25 oC. (hint: calculate the total moles and pressure of each, then total pressure)

Collecting Gas of H2OPatm = PA + PH2O A = gas collecting

Example: If 35.5 mL of H2 (g) is collected over H2O at 26 oC and a pressure of 755 mm Hg, how many moles of HCl must be consumed?

Al(s) + HCl(aq) AlCl3 (aq) + H2

(g)

PH2O is temperature dependent

Determination of Gas Constant Lab

Mg (s) + HCl(aq) MgCl2 (aq) + H2 (g)

We want to collect exactly 30 mL of H2 (g)

How much Mg do we use? (exactly)How much HCl do we use? (use excess!)

Temp =

Pressure =

Kinetic Theory of Molecular Motion A gas is composed of a very large number of

extremely small (molecules or atoms) particles, in constant, random, straight line motion.

The total volume of the gas molecules is negligible compared to the volume used (mostly empty space).

Molecules collide with each other and the walls of the container. Collisions occur very rapidly and are elastic (collisions result in pressure).

There are no forces of attraction between the molecules.

Molecules may gain or lose energy, but the total energy of the gas remains constant.

KE = ½ m v2

This is an illustration of the path of

one gas molecule over

time.

All molecules do not travel at the same speed! It is dependent on the mass of the molecule.

Kinetic energy depends only on temperature. If gases have an equal number of moles and their temperature is the same, they have equal amount of Kinetic energy. KE = ½ m v2

When molecules do not have the same temperature, the higher the temperature (KE), the faster the molecules.

3 cars are going down the highway. One at 40 mph, one at 50 mph, and one at 60 mph.What is the average speed (u)?

Root – mean – square velocity (urms) is weighted toward molecules with higher speeds.

urms =

From the car analogy, urms =

The formula is weighted toward molecules with higher speeds.

urms

R = 8.3145 J/mol K M = molar mass in kg/mole

urms = meters/sec T = Kelvin

u2

3 R T =To find the root mean

square velocity of a

gasM

__

Find the average speed of He (g) at 25 oC

Which is the greater speed, that of a bullet from a high–powered M-16 rifle (2180 mph) or the root–mean–square speed of H2 (g) molecules at 25 oC?

Kinetic energy of a gas can be calculated

K E = ½ m v 2

KE = (3/2) R T

R = 8.3145 J/mol K

T = Kelvin

(Per mole)

(Per molecule)

Not in text book

Pressure of a gas is caused by molecules hitting the walls of the container.

P = (1/3) (n/V) M u2

u2 = average of the squares of all the molecule speeds

n = number of molecules

M = mass of one molecule

Not in text book

Diffusion is the migration of a gas through other gases.Effusion is the rate of passage of a gas through an orifice (tiny hole).

Graham’s Law of Effusion

Rate of EffusionA = urms A = = Rate of Effusion B urms B

3 R T/ A

3 R T / B

B

A

When using Graham’s Law, always change information to rates before working with.

__

__

2.2 x 10-4 mol N2 (g) effuses through a tiny hole in 105 seconds. How much H2 (g) would effuse through the hole in the same amount of time?

A sample of Kr (g) escapes through a tiny hole in 87.3 sec. An unknown gas requires 42.9 seconds for the same amount. What is the molecular mass of the unknown gas?

Non – Ideal Gases (Real Gases)PV = nRT works well at low to moderate pressures and moderate to high temperatures.

Outside of that, adjustments must be made to the formula. At high pressures or low temperatures, gas turns into liquids.

Van der Walls equation:[P + a(n/V)2] (V – nb) = n R T

- The ideal gas particles have no forces of attraction but Real gas particles do have some forces of attraction which reduce the pressure a(n/V)2 = (proportionality constant) (moles/volume)2

- The ideal gas law describes gas which the particles are volumeless but Real gas particles take up space

- nb = (moles)(constant for that gas)See page 429

Atmospheric layers are based on temperature which fluctuates.

Pressure constantly decreases with altitude.

Composition of the atmospheric gases

Component mole fraction

N2 0.78084

O2 0.20948

Ar 0.00934CO2 0.000345

Ne 0.00001818He 0.00000524CH4 0.00000168

Kr 0.00000114H2 0.0000005

NO 0.0000005Xe 0.000000087

These numbers reflect the atmosphere at sea level, and with H2O disregarded.

Air pollution comes from 2 main sources1. transportation2. electricity production

1. Produces CO, CO2, NO, NO2, and unburned fuel

NO from cars NO2 in the atmosphere

NO2 + hv NO + O

O + O2 O3

O3 O2 + energy + O

O + H2O 2 OH

OH + NO2 HNO3 (acid rain)

2 NO2 + H2O NHO2(aq) + HNO3 (aq)

2 SO2 + O2 2 SO3

SO3 + H2O H2SO4 (aq) (acid rain)

Photochemical smog (NO2 and O3) combined with

sunlight (hv) cause chemical pollution

2. Pollutants from electricity production (especially coal containing sulfur)S + O2 SO2 will eventually H2SO4

Chimney scrubbers blow CaCO3 into combustion chambers of coalCaCO3 CaO (s) + CO2 (g)

CaO (s) + SO2 (g) CaSO3 (s)

which can be disposed of

Which gas has the greatest Kinetic energy?

Ideal Gas Law Bottle Lab

The average molar mass of “air” is 29.0 g/mol

Room temp. =

Atmospheric pressure =

room temp volume of bottle

pressure

1 Trial 1 etc2 Mass of bottle, syringe + air use scale to measure3 Volume of air in syringe look at4 Pressure inside bottle measure then calculate

(pressure on gauge + current pressure)(1atm/14.69 psi)=

5 mass of air calculate (Q#2)m = P V molar

mass/R T

6 mass of bottle +syringe calculate (Q#3)

column 2 – column 5 =7 moles of air in bottle n = mass of air/molar mass of air

8 pressure to mole ratio pressure inside/moles

of air

Questions + calculations

1 pressure inside bottle = column 42 mass of air = column 53 mass of bottle + syringe = column 2 – column 54 moles of air = column 75 ratio of atm/mole = column 4/column 7

6 graph y axis = pressure (atm) x axis = moles of air

(should end up a straight line y = mx + b)7 theoretical atm/mole ratio = R T/V

8 compare Calculate % accuracy

Avogadro’s Law: At the same temperature and pressure, equal volumes of gases contain the same number of particles.