Download AP gas notes 2010

Gases
Common gases
 Molecular compounds: HCN, HCl, H2S, CO2, CO, CH4, N2O, NO2, NH3, SO2
 Nonmetals: N2, F2, O2, H2, He, Ne, Ar, Kr, Xe
Characteristics
 Small particles relatively far apart
 Indefinite shape and volume
 High expansion
 High compressibility
 Considered a fluid
 As temperature increases, gases expand
 High diffusion
Four factors That Describe the State of a Gas
1. Volume (V) - measured in L, ml, cm3, m3
2. Amount of gas ( n) – measured in moles
 moles = mass of sample/molar mass of sample
3. Temperature (T) – measured in Kelvin ; remember K = ºC + 273
4. Pressure ( P) – measured in Pa, kPa, torr, atm, mm Hg, bar
Pressure
 Pressure = force
area
defined as the force per unit area
in simple terms, molecules collide with container
walls
AIR
PRESSURE

A manometer is used to measure the
of a gas in a container; can be open or
closed
pressure
Hg HEIGHT
DIFFERENCE
Atmospheric Pressure
• pressure on the surface of the earth exerted by the gases of the atmosphere
• measured with a barometer
vacuum
air
pressure
•
•
at sea level, atmospheric pressure = 760 mm Hg
most abundant gases in the environment: N2 >O2 > CO2 >
mercury
(Hg)
Pressure Units
 SI Unit – Pascal (Pa)
 Other units and how they relate: 1atm(bar) = 760 mm Hg (torr)= 101.3 kPa
Example 1
Convert 875 mm Hg into atm? into torr? into kPa?
Gas Laws
1. Boyle’s Law (pressure-volume)
 Volume of a gas is inversely proportional to pressure at constant
temperature and moles; as one goes up, the other goes down
 PV = constant
Thus
V1 P1 = V2 P2
Example 2
20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.80 atm at
constant temperature and moles. What is the new volume?
2. Charles’ Law (volume –temperature)
 Volume of a gas is directly proportional with absolute temperature
(Kelvin) at constant pressure and moles; as one goes up, the other does as
well
 V /T = constant
Thus
V1 = V2
T1
T2
Example 3
What would the final volume be if 247 ml of gas at 22ºC is heated to 98 ºC,
if the pressure is held constant?
3. Gay – Lussac’s (Amonton’s) Law
 Pressure of a gas is directly proportional to absolute temperature(Kelvin)
at constant volume and moles
P/T = constant
Thus
P1 = P2
T1
T2
Example 4
A deodorant can have a volume of 175 ml and a pressure of 3.8 atm at 22 ºC.
What would the pressure be if the can was heated to 100. ºC
4. Avogadro’s Law
 Equal volumes of gases at same temperature and pressure contain equal
numbers of moles (molecules)
 Number of gas molecules are directly proportional to volume
 V / n = constant
Thus
V1 = V2
n1
n2
 0ºC and 1 atm : Standard Temperature and Pressure (STP)
 molar volume 1 mole of gas at STP contain 22.4 L and thus 6.02 x 1023
molecules
Helium
He
22.4 L
1 atm
0º C
4.00 g
6.02 x 1023 molecules
Nitrogen
N2
22.4 L
1 atm
0º C
28.0 g
6.02 x 1023 molecules
Methane
CH4
22.4 L
1 atm
0º C
16.0 g
6.02 x 1023 molecules
5. Gay-Lussac also observed the Law of Combining Volumes
 At a given temperature and pressure, volumes of gases react in whole number
ratios
 Coefficient in a balanced chemical equation = moles and now volume (only
when temperature and pressure are constant)
2 H2(g) + O2(g)  2 H2O (g)
100 ml 50 ml 100 ml
Example 5
What volume of NO will be produced by 1.38 L of oxygen when both volumes
are measured at the same temperature and pressure? 2 NO(g) + O 2(g) --> 2
NO (g)
6. Combined Gas Law – when all variables are changing but moles stays constant
V1 P1 = V2 P2
T1
T2
•
Cancel (i.e., ignore) any property that is not changing. (Assume
anything not explicitly mentioned in the problem is not changing.)
•
Units must be the same on both sides of the equal sign
•
Temperatures must be absolute (Kelvin).
Example 6
A sample of gas has a volume of 4.18 L at 29 ºC and 732 torr. What would
its volume be at 24.8 ºC and 756 torr?
7. Ideal Gas Law –used to describe an ideal gas “NOW”, not when variables are
changing


PV = nRT
Ideal gas- hypothetical gas that is calculated using the above equation;
actually very similar to real gas behavior when close to room temperature
and low pressures (1atm and less)
Assume gases obey all gas laws stated above unless otherwise stated

Ideal gas law constant(R) - changes depending on the units
Choose a value of R that has exactly the same units as the numbers you
are given in the problem. If this is not possible, you must convert the
units from the problem to units that agree with your R value.

Manipulation of R – to calculate the constant, remember at O·C and 1 atm,
1 mole of any gas is 22.4 L
.08206 L· atm/mol· K
or
62.4 L
·mmHg/ mol·K
“ most common”
Example 7
A 47.3 L container containing 1.62 mol of He is heated until the pressure
reached 1.85 atm. What is the temperature?
Example 8
How many grams of oxygen gas in a 10.0 L container can exert a pressure of
712 mm Hg at a temperature of 25.0ºC?
8. Other Calculations involving the ideal gas law
Determining Molar Mass (M)
PV = nRT
PV = mRT
M
Determining Density (D)



SO
M = mRT
M= DRT
SO
PV
P
As molar mass increases, density increases
As molar mass increases, pressure decreases
As molar mass increases, temperature increases
M= mRT
PV
D= MP
RT
Example 9
When 4.93 g of carbon tetrachloride gas are in a 1.00 L container at 400.0
K, the gas exerts a pressure of 800.0 mm Hg . What is the molar mass of
carbon tetrachloride?
Example 10
The density of an unknown gas is 1.23 grams per liter at STP. Calculate its
molar mass
Stoichiometry of Reactions Involving Gases

Use PV=nRT to get any and all gases to moles and then solve the problem using
stoichiometry
 Could also use molar volume if the gas was measured at STP
Example 11
How many grams of MnO2 are required to produce 1.200 L of Cl2 gas at 1.00
atm and 200. C?
MnO2 + 2 Cl-1 + 4 H+1 --> Mn+2 + Cl2 + 2 H2O
Example 12
Calcium oxide is produced by the thermal decomposition of calcium
carbonate. Calculate the volume of carbon dioxide at STP produced from
the decomposition of 152g calcium carbonate by the reaction. Write it
yourself!
Dalton’s Law of Partial Pressures
 Mixture of gas = blend of gases each retaining their individual properties
 Each exerts a specific pressure(called partial pressure) as it would by itself
 Total Pressure of gas mixture = sum of the partial pressures of each individual gas
PT = P1 + P2 + P3 ….
•
The total moles of a gas in a mixture can be found using the mole fraction(X)
MOLE FRACTION = moles of individual gas/total moles of gas in a miture
X= n1
nT
Since moles and pressure are proportional
P1 = X
OR
P1 = PTX
PT
Example 13
The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr.
a. What is the mole fraction of nitrogen?
b. What is the partial pressure of nitrogen if the container holding the
air is compressed to 5.25 atm?
•
•
Example14
A 12.0 L tank of gas has a temperature of 30.0°C and a total pressure of
1.75 atm. If the partial pressure of oxygen in the tank is 0.350 atm, how
many moles of oxygen are in the tank? How many total moles of gas are in
the tank?
Collecting Gas Over Water
gas being
collected
filled with
water, initially
collected gas
(w/H2O vapor, too)
gas from
reaction
H2O levels
even
before
reaction
during
reaction
reaction
complete
When collecting gas over water, water vapor will mix with the collected gas. Water vapor
has a pressure and must be accounted for when determining the pressure of the gas
collected. Its dependent on temperature.
PT = Pgas + Pwater
PT at various temperatures found in the Appendix
Example 15
2 KClO3 --> 2 KCl + 3 O2. The oxygen was collected by water displacement
at 22 ºC at a total pressure of 754 torr. The volume of the gas collected
was .650 L and the vapor pressure for water at 22 ºC is 21 torr. Calculate
the partial pressure of the oxygen gas collected and the mass of KClO3 in
the sample that decomposed.
Kinetic Molecular Theory
1. Gas particles are in constant random motion.
2. The volume of the gas particles is negligible compared to the volume of the
container. GASES HAVE NO VOLUME!
3. The attractive and repulsive forces between molecules are negligible. GASES
HAVE NO ATTRACTIONS/REPULSIONS!
4. Collisions of gas molecules are ELASTIC. NO KINETIC ENERGY IS LOST!
5. The Average Kinetic Energy of gas molecules is directly proportional to KELVIN
temperatures
At a given temperature, the gas particles of Sample A have the same KE
as the gas particles of Sample B.
Average Speed
 Molecules at the same temperature have the same average KE and same average
speed BUT
individual molecules move at varying speeds

KEparticle = ½ mv2 m= mass of molecule
1J = 1 kg· m2/s2
v= speed of the molecule
Root Mean Square Speed (RMS) ( u)
• The average speed of a molecule possessing average KE
 As average temperature increases, average KE and average speed increases
R = 8.3125 J/K· mol



Urms = 3RT/M M= molar mass (kg/mol)
T = Kelvin
Speed is directly related to absolute temperature but inversely related to molar
mass
The lower the molar mass, the higher the RMS
A gas mixture consisting of He and Xe are at the same temperature SO
They have greater, same, lower average KE
They have greater, same, lower average speed
Example 16
Calculate the RMS of carbon dioxide at 25ºC
Graham’s Law
The lighter the molecules, the faster they move; the heavier the particles, the slower they
move
•
Effusion – escape of a gas through a small hole or pore

Diffusion- spread of 1 substance throughout a second substance or space from
high concentration to low
Rates




r1 = M 2
r2 M 1
M= molar mass
We usually place the lighter mass as gas 1
If the ratio is greater than 1, gas 1 is effusing faster than gas 2
effusion rate is faster for lighter molecules; same for diffusion
diffusion is slightly slower due to collisions of molecules
Example 17
Calculate the ratio of effusion rates of molecules from SO2 to NO2
Real gases deviate from ideal gas behavior
• All real gases, to some degree, behave differently from ideal gas behavior because
particles of a real gas occupy space and exert attractive forces.
• The deviations are most recognizable when gases are at extremely low
temperatures or at very high pressures ( > 10 atm)
• This is due to the small KE of the particles and the particles will be closer
together.
 Real gases (Noble gases and diatomic molecules) ALWAYS show ideal gas
behavior
 The more polar a molecules is, the greater the deviation because of the greater
attractive forces- See van der Waal’s equation
Use of van der Waals Equation
 High pressure – molecules are closer together  increases the likelihood of
attraction
 Low temperature- movement decreases  increases the likelihood of attraction
 Amount of deviation depends on the type of gas
The constants a and b are unique for each gas! (See the book for them)
a (molecular attraction) & b( molecular volume)
Example 18
Calculate the pressure exerted by .3000 mol He in a .2000L container at -25
°C
A. using the ideal gas law equation
B. using the vander waals equation- constants are taken from the book
within the chapter