Download Unit 11 Notes

Chapter 11: Gases
I.
Gases and Pressure
A. In order to fully describe a gas, we must have the measurements of
volume, temperature, pressure and number of molecules of gas.
B. Pressure and Force
1. Pressure is defined as the force per unit area of a surface.
P=force/unit area.
2. The SI unit of force is the newton (N). A high school textbook
weighs between 15-20 N. A small apple is about 1 N.
3. Pressure depends on surface area as well as force. For example, a
textbook lying flat exerts less pressure than one standing up.
4. Gas particles exert pressure on any surface they touch.
5. The atmosphere of the earth exerts pressure. Atmospheric
pressure at sea level is equal to about the weight of 1.03 kg per
cm2 of surface.
6. Measuring Pressure
a. A barometer is a device used to measure atmospheric
pressure.
1. A tube, nearly a vacuum, is inverted into a dish of mercury.
2. Atmospheric pressure pushes down on the surface of the Hg
in the dish, pushing some of it up the column.
3. Atmospheric pressure supports a column of 760 mm of Hg.
b. A manometer is used to measure the pressure of a confined
gas.
1. The difference in the height of mercury in the two arms of
the U-tube is a measure of the gas pressure in the container.
2. See Figure 4 on page 363.
7. Units of Pressure
a. There are several units of pressure: mm of Hg, torr,
atmosphere (atm), and Pascal (Pa).
b. Pascal is the SI unit of pressure.
c. 760 mm Hg = 760 torr = 1 atm = 101325 Pa = 101.3 kPa.
8. Standard Temperature and Pressure (STP): standard conditions of
temp and pressure agreed on by scientists to be 0oC (273 K) and
1atm (760mm Hg, 760 torr, 101.3 kPa).
C. Dalton’s Law of Partial Pressures: the total pressure of a mixture of
gases is equal to the sum of the partial pressures of the component
gases.
1. A partial pressure is the pressure of the gas in a mixture.
2.
3.
4.
Discovered by John Dalton. Assumes no interaction between the
gases. Holds true regardless of the number of gases present.
Mathematically, Ptot = P1+P2+P3+...
Gases Collected by Water Displacement
a. Many times in a lab setting, gases are collected over water.
b. See Figure 5 on page 366.
c. Water vapor, like other gases exerts pressure.
d. To calculate the pressure of the gas, subtract the pressure of
the water from atmospheric pressure.
e. The water vapor pressure depends on temperature, and can be
found in a standard reference table.
II. The Gas Laws
A. The Gas Laws are simple mathematical relationships between the
volume, pressure, temperature, and amount of a gas.
B. Boyle’s Law: States that the volume of a fixed mass of gas varies
inversely with the pressure at constant temperature.
1. Discovered by Robert Boyle. He noticed that be doubling the
pressure, the volume would be cut in half.
2. Pressure is caused by molecules hitting the walls of the container.
If the walls are smaller, the molecules hit them more often.
3. Mathematically, P*V = k (k is a constant). If T and the amount are
held constant, then P1V1 = k and P2V2 = k. Therefore, P1V1 = P2V2.
4. Practice, Practice, Practice.
C. Charles’ Law: States that the volume of a fixed mass of gas at
constant pressure varies directly with the Kelvin temperature.
1. Discovered by Jacques Charles. He noticed that all gases expand to
the same extent when heated through the same temperature
interval. He found this amount to be 1/273 of the volume per
degree C. The same applies if the gas is cooled.
2. Absolute Zero: ~-273 oC, given the value of 0 K. The point at
which all molecular motion stops.
3. Mathematically, V = kT. If amount and pressure are held constant,
V1 = kT1, and V2 = kT2. Therefore, V1/T1 = V2/T2.
4. Practice, Practice, Practice.
D. Gay-Lussac’s Law: States that the pressure of a fixed amount of gas
at constant volume varies directly with the Kelvin Temperature.
1. Discovered by Joseph Gay-Lussac.
2. Pressure is caused by molecules hitting the walls, decrease T, slow
them down, not as many hit the walls.
3.
4.
E.
Mathematically, P=kT. If V and amount are constant, P1 = kT1, and
P2 = kT2. Therefore, P1/T1 = P2/T2.
Practice, Practice, Practice.
Combined Gas Law: expresses the relationship between pressure,
volume, and temperature of a fixed amount of gas.
1. Simply a combination of the previous three gas laws.
2. Mathematically, PV/T = k. If amount is constant, P1V1/T1 = k and
P2V2/T2 = k. Therefore, P1V1/T1 = P2V2/T2.
3. All of the other 3 gas laws can be derived from this form.
4. Practice, Practice, Practice.
III. Gas Volumes and the Ideal Gas Law
A. Gay-Lussac’s Law of Combining Volumes of Gases: at constant T
and P, the volumes of gaseous reactants and products can be expressed
as ratios of whole numbers. These whole numbers are same as the
coefficients from balancing the equations.
B. Avogadro’s Law: equal volumes of gases at the same T and P contain
equal numbers of molecules.
C. The standard molar volume of a gas is 22.4 liters. At STP 1 mole of a
gas will occupy 22.4 L of volume.
D. Gas Stoichiometry
1. Because of Avogadro’s Law and Gay-Lussac’s Law of Combining
Gases, we can do stoichiometry for gases as well as solids and
liquids.
a. Volume-Volume is a simple 1 step conversion, once the reaction
is balanced. The coefficients from the reaction are used as the
factor.
b. Volume-mass conversions are done in a few more steps.
1. Use ideal gas law to get from V of A to moles of A.
2. Moles of A to moles of B as before.
3. Moles of B to mass of B as before.
4. Can also be done in reverse.
2. Practice, Practice, and more Practice.
E.
Ideal Gas Law: mathematical relationship among the pressure,
volume, temperature, and number of moles of a gas.
1. Mathematically, PV=nRT. P=pressure, V=volume, T=temperature,
n=# of moles, and R = ideal gas constant.
2.
3.
4.
The value of the ideal gas constant depends on the units that are
used for P, V, and T.
R=0.0821 (L*atm)/(mol*K)
R=62.4 (L*mmHg)/(mol*K)
R=8.314 (kPa*L)/(mol*K).
Practice, Practice, Practice.
IV. Diffusion and Effusion
A. Diffusion: the gradual mixing of two or more gases due to their
spontaneous, random motion.
B. Effusion: process whereby the molecules of a gas confined in a
container randomly pass through a tiny opening in the container.
C. Graham’s Law of Effusion
1. Rates of effusion and diffusion depend on the relative velocities of
the molecules. Velocity varies inversely with the square root of
the molar mass. (KE=1/2mv2)
2. Graham’s Law of Effusion: the rates of effusion of gases at the
same temperature and pressure are inversely proportional to the
square roots of their molar masses.
3. Rate A = (MMB)1/2
Rate B
(MMA)1/2