AP Chemistry: Chapter 10 Notes
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Chapter 10: Gases
Pressure
barometer: an instrument that measures air pressure. It was invented in 1643 by Evangelista Torricelli.
manometer: an instrument that measures the pressure in a container
*mercury is used because of its high density. A column of water would be 13.5 times as high as a mercury column.
P = force/area
SI units are N/m2, which is called a Pascal (Pa)
1 atm = 760 mmHg = 760 torr = 101,325 Pa = 101.3 kPa = 14.7 lb/in2 (psi)
Boyles, Charles, and Avogardro’s Laws
These all came about by experimentation!
· Robert Boyle (1627-1691): pressure and volume are inversely related.
o PV = k or P1V1 = P2V2
o this holds true completely at low pressures
ideal gas: a gas that strictly obeys Boyle’s Law
v always check that the answers make physical sense! Should P,V behave that way?
· Jacques Charles (1746-1823): volume and temperature are directly related.
o V = bT or V1/T1 = V2/T2
o his graphs and data show that the volumes of all gases extrapolate to zero at -273.15°C, which is 0 Kelvin (can’t go below absolute zero because then gas volumes would be negative, which is physically impossible!).
· Amadeo Avogadro in 1811: equal volumes of gases at the same temperature and pressure have the same number of particles. In other words, for a gas at constant T and P, volume is directly proportional to the moles of gas.
Do Sample problem 10.3, page 374
Ideal Gas Law
PV = nRT where R =
The ideal gas law is an equation of state for a gas. A state is defined by P, V, T, and n. Knowing any three of those completely defines the gas, since the fourth property can be calculated from the ideal gas law.
v The ideal gas law is empirical—it is based on experimental measurements of gases! It expresses what real gases approach at high temperatures and low pressures. So ideal gases are hypothetical.
· Do Sample Problem 10.4, page 376.
Gas Stoichiometry
The molar volume of an ideal gas is 22.42 L at STP (standard temperature and pressure, 0°C and 1 atm)
The molar mass of a gas can be found by rearranging the ideal gas law: =
Dalton’s Law of Partial Pressures
Dalton studied gases before he came up with his atomic theory. The Law of Partial Pressures was 1803: for a mixture of gases in container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. This works because gas particles don’t really interact with each other!
PTOT = P1 + P2 + P3 + ...
P1 = P2 = P3 =
so if PTOT = P1 + P2 + P3 then PTOT = (n1 + n2 + n3) = nTOT
Therefore, pressure depends only on the quantity of the gas, not on the identity of the gas(es). So that means that the volume of a gas molecule must be negligible, and the intermolecular forces amongst gas particles are insignificant.
The mole fraction of a gas is c
c1 = n1/nTOT but since n1 = P1 and nTOT = PTOT then c1 = P1/PTOT
So the mole fraction of a gas is directly related to the partial pressure of that gas, and P1 = c1PTOT
v Do Sample Problems 10.10 and 10.11, page 383 - 384.
v read the Chemistry of Air Bags p. 209
v read Scuba Diving p. 211
Kinetic Molecular Theory of Gases
This is a model to try to explain why gases behave the way they do. It fits the most important experimental results but falls apart at some points.
1. the volume of gas particles is negligible
2. particles are in constant motion; their collisions with the container walls cause gas pressure
3. particles exert no force on each other
4. the average kinetic energy of the sample is directly proportional to the Kelvin temperature of the sample
Does KMT make sense?
- as volume is decreased, particles hit the walls more often, causing the pressure to go up. This agrees with Boyle’s Law (based on observations!)
- if temperature goes up at constant volume, the particles move faster and hit the walls with greater frequency and force. Thus pressure increases, and this agrees with Gay-Lussac’s Law!
- if temperature increases at constant pressure, particles also hit the walls with greater frequency and force. The only way to keep the pressure constant is to increase the volume. This agrees with Charles’s Law!
- if temperature and pressure are held constant and the number of moles of gas is increased, then the only way to keep pressure constant is to expand the volume of the container, so the particles will hit the walls with the same frequency as before.
v See the derivation of the ideal gas law on page 389.
Remember that as temperature increases, the most probable velocity (the one found the most often in a sample of gas) goes up. But also, the distribution (spread) of velocities in the sample also goes up! See Fig. 10.19.
Effusion and Diffusion
diffusion: the mixing of one gas into another
effusion: the passage of a gas through a small opening
Graham’s Law of Effusion: the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles:
· the bigger you are, the slower you effuse!
Diffusion is roughly related to Graham’s Law, but since gases must diffuse through air, which makes many more collisions happen, it is much more difficult/complex to calculate.
v Do Sample Problem 10.15, page 391.
Real Gases
Ideal gas behavior is what real gases approach under certain conditions: LOW pressure (< 1atm) and HIGH temperature. Johannes van der Waals came up with a model for real gases and adjusted the ideal gas law:
Volume: V is adjusted by accounting for the fact that atoms themselves have a small volume. V – nb where n = number of moles and b is an empirical constant (based on experimental data on the size of the gas particles).
Pressure: P is adjusted by the actual attraction that gases do fell for each other—they hit the walls slightly less often because of this attraction. P =
normally, P =
sub in the new definition of P: P =
sub in P’ = and V = nb:
This is rearranged to get the van der Waals equation:
[Pobs + ][V – nb] = nRT
v you must look up both a and b for different gases
v the key is to understand where these factors come from, why they are in the equation, and how they affect the values of P, V, and the final answer you are looking for.
Chemistry in the Atmosphere
The troposphere is the layer of the atmosphere closest to the earth’s surface, and is affected by humans’ activities. Nitrogen in the air reacts at the high temperatures in car engines with oxygen:
N2 + O2 ® 2NO
NO is oxidized in air: 2NO + O2 ® 2NO2
NO2 absorbs sunlight and breaks up: NO2 ® ·NO + ·O
The oxygen radical reacts with atmospheric oxygen: ·O + O2 ® O3 (ozone)
Ozone is reactive and can break up to form energized oxygen molecules: O2* and O*
These then react: O* + H2O ® 2·OH (hydroxyl radicals)
The radicals react further: ·OH + NO2 ® HNO3 (nitric acid)
Ozone can also react with other hydrocarbons to form pollutants.
Burning coal releases sulfur: S + O2 ® SO2
When solid particles are present, 2SO2 + O2 ® 2SO3
With water droplets, SO3 + H2O ® H2SO4 (aq) (acid rain)
A scrubber can be used to remove SO2 from the exhaust gases before they are emitted from a plant. Powdered limestone is blown into the combustion chamber to form lime, CaO:
CaCO3 (s) ® CaO (s) + CO2 (g)
CaO (s) + SO2 (g) ® CaSO3 (s)
Aqueous lime can then be sprayed into the exhaust gases to create a slurry (thick suspension) of CaSO3.
But scrubbing is expensive and produces tons of CaSO3, which is then land filled.
Buzin Fall 10