GASES
(adapted from M. Milanes original handout)
GOALS
Use this as a reference and study guide for the AP exam in May.
-More focus on the why…
-Be able to produce written responses and explain what’s going on and why
-Use molecular drawings to explain what’s going on and why
-Think about what gases are doing/behaving at the molecular level
Properties of Gases
Property
Pressure
What is it?
Increase the area over which a force is applied and you decrease the pressure.
Definition
A force exerted over an area. The collisions
Unit
Pascal,
Atm (most common)
Torr = mmHg
Volume
Temperature
Amount
Measurement of space, many ways to find it
Measurement of kinetic energy, molecular motion
Based on Avogadro’s number cm 3 , L, dm
Kelvin moles
3 = 1L
Water Boils
Celsius
100
Temperature facts
Kelvin
373.15
Fahrenheit
212
Rankine
672
Water Freezes
Absolute Zero
0
-273.15
273.15
0
32
-460
492
0
What is vapor pressure?
How is vapor pressure, atmospheric pressure, and boiling temperature related? How is this relationship demonstrated by the fact that water boils at a lower temperature in areas of low atmospheric temperature? Why was I able to boil water using the frozen milk?
STP = 1 atm and 0 Celsius
Barometers
What is the function of this instrument
How does it work?
What is a manometer, and how does it work?

GAS LAWS
Robert Boyle
Pressure and Volume are inversely proportional
P
1
V
1
= P
2
V
2
Why do pressure and volume have an inverse relationship? Can you explain using words and a molecular drawing?
What’s the pressure when 10.0 L of argon at 5.00 atm is compressed to 5.0 L?
Charles Law and Absolute Zero
Temperature and Volume are directly proportional
V
1
/ T
1
= V
2
/ T
2
Why does volume directly change with temperature if pressure is staying constant? Be able to explain using words and molecular drawing.
What is the volume 3.75 L of Neon at 25 Celsius is heated to 35 Celsius?
Joseph Gay-Lussac
Pressure and Temperature are directly proportional
P
1
/ T
1
= P
2
/ T
2
Why does pressure directly change with temperature if volume is staying constant? Be able to explain using words and molecular drawings.
If a gas exerts 10.0 atmospheres at 25 Celsius what pressure will it exert at 50 Celsius?
Amadeo Avogadro
Equal volumes of gases at the same conditions (pressure, volume, temperature) you have the same number of particles = same number of moles
When the other properties are at the same conditions, the volume occupied by a gas is directly proportional to the number of moles present.
What is the volume of one mole of an ideal gas at 25 Celsius and 1.00 atmosphere?
Combined Gas Law
-
(P
1
V
1
)/T
1
= (P
2
V
2
)/T
2
-
17.5 L of Helium at STP is heated to 300 Kelvin and 2.00 atm. What is the new volume of the sample?
Ideal Gas Law
Putting all the gas laws together
PV = nRT
R = 62.4 Liter mm Hg/(mole K) = 0.08206 Liter atm/(mole K) = 8.31 kPa L/(mole K)
What units are required for each property?
1.
25.00 grams of neon are held at 2.99 atm and 400. Kelvin. What is the volume of the sample?

2.
If an ideal is held at STP and occupies 35.4 L how many moles of the ideal gas are present?
3.
What is the pressure exerted by 64.00 g of oxygen gas at 273 Kelvin in 1.00 liter?
4.
What pressure can be exerted by 100.0 g of Helium at 27 Celsius in a 10.0 liter container?
5.
What is the volume of one mole of an ideal gas at STP?
Gas Density and Determining Molar Masses
Application of Ideal gas laws o Molar mass of a gas
 Be able to derive empirical and molecular formulas using the IG law o Density of a gas
Can we solve the ideal gas law for molar mass or density even if we do not see it in the equation?
PV = nRT = m/MM x RT Density = m/V Density = P x MM / RT MM = g R T /P V
1.
What is the density of sulfur hexafluoride at STP?
2.
A gas is composed of 46.2% Carbon and 53.8% Nitrogen. At 25 Celsius and 751 torr, .05 grams of the gas occupies 0.500 L. What is the molecular formula of the gas?
3.
The Density of a certain gaseous fluoride of phosphorus is 5.63 g/L
Gas Stoichiometry
Molecules A ----------- Moles A ---------Mass A ----------Volume A
Molecules B ---------- Moles B ---------- Mass B -----------Volume B
1.
How many liters of carbon dioxide will form at STP from the reaction of 50.0 grams of CaCO
3
with excess Hydrochloric acid?
Reaction

Gas Mixtures & Mole Fraction
Dalton’s law of partial pressure
What is the mole fraction equation, and how is this equation related to the total pressure and the partial pressure exerted by each gas?
1.
Imagine mixing 1.0 g of Helium and 1.0 g of hydrogen in a 5.0 liter container at 25 Celsius. What are the partial pressures of each gas and the total pressure? What if it were 1.0 mole of each? Would you get the same ratios?
Collecting a gas over water
What additional data needs to be taken into consideration when applying PV = nRT to these questions?
What is vapor pressure?
2.
Hydrogen gas is collected by water displacement until the pressure in the gas collection tube matches the atmospheric pressure of 755 torr at 25 Celsius. What is the pressure of hydrogen gas in the tube if the vapor pressure of the water is 23.76 torr at this temperature?
Kinetic Molecular Theory
What Determines how fast molecules move?
Root Mean Square Velocity
Ū= √
3𝑅𝑇
𝑀
Diffusion
Effusion
1.
The rate of diffusion for an unknown gas is measured to be
24.0mL/minute. Under identical conditions methane diffuses at a rate of 47.8 mL/minute. What is the molar mass of unknown gas?

Ideal gases versus Real Gases
Four assumptions:
1.
Molecules are in constant motion
2.
The size of the molecules is negligible compared to the distance between them
3.
Molecules do not interact with each other
4.
The Temperature is directly proportional to their kinetic energy
5.
When molecules collide they do so elastically
Which assumptions are not correct? Why?
If a gas were ideal what would a graph of the ideal gas law look like?
This is what it looks like for real gases:

Determination of molar mass by vapor density (lab)
Use: Acetone few drops into a flask, and place into boiling water
MW = mRT/PV m acetone
make sure you say measure mass by difference
R = known
T = 100 celsius
P = pressure in flask =pressure outside the flask
V = find volume of flask (fill with water and measure mass by difference)
Determination of the molar volume of hydrogen gas (lab)
Equipment: barometer, beaker, Erlenmeyer flask, test tubes, graduated cylinder, clamp, analytical balance, thermometer, rubber tubing
What’s it all about: A gas can either be simply be released from a canister or produced by a reaction and then collected, often over water. Knowing the moles of gas and knowing the volume, it is possible to determine
Molar Volume, i.e. the number of L per mole. At s.t.p. the molar volume of any gas is 22.4 L per mole. Look out for calculations that require the subtraction of water vapor pressure from total pressure of gas collected above water.
1) Calculate the theoretical number of moles H
2
gas produced.
Mg + 2 HCl  MgCl
2
+ H
2
according to the balanced reaction, the amount of hydrogen gas should equal the amount of moles of magnesium in the reaction.
0.00789 g/ 24.32 g/mol = 3.25 x 10 -4 moles Mg and thus H
2
2) Calculate the partial pressure of H
2
gas. Use Dalton’s law of Partial pressure. Check chart at 23 o C
Barometric = total pressure (735 mmHg) 735 mm Hg total
– 21.1 mmHg H
2
O = 713 mmHg H
2
3) Used combined gas law to convert gas volumes to those at STP.
P
1
V
1
/T
1
= P
2
V
2
/T
2
 let STP be 2 nd conditions V
2
= P
1
V
1
T
2
/T
1
P
2
V stp
= (713.9 mmHg) (0.00845L) (273 K)
(296 K) ( 760 mmHg) = 0.00732 L
4) Divide volume at STP by the number of moles to get an experimentally determined molar volume at
STP. 0.00732 L/3.25 x 10 -4 moles = 22.5 L/mole

AP Chemistry Readiness Gases Review Page 10 of 12
Copyright by Michael A. Morgan Except Former AP Questions Copyright by Educational Testing Service
From the 1994 exam
A student collected a sample of hydrogen gas by the displacement of water as shown by the diagram above. The relevant data are given in the following table.
GAS SAMPLE DATA
Volume of sample
Temperature
Atmospheric Pressure
90.0 mL
25˚C
745 mm Hg
Equilibrium Vapor Pressure of H
2
O (25˚C)
23.8 mm Hg
(a) Calculate the number of moles of hydrogen gas collected.
(b) Calculate the number of molecules of water vapor in the sample of gas.
(c) Calculate the ratio of the average speed of the hydrogen molecules to the average speed of the water vapor molecules in the sample.
(d) Which of the two gases, H
2
or H
2
O, deviates more from ideal behavior? Explain your answer.

AP Chemistry Readiness Gases Review Page 11 of 12
Copyright by Michael A. Morgan Except Former AP Questions Copyright by Educational Testing Service
From the 1999 exam
5. A student performs an experiment to determine the molar mass of an unknown gas. A small amount of the pure gas is release from a pressurized container and collected in a graduated tube over water at room temperature, as shown in the diagram above. The collection tube containing the gas is allowed to stand for several minutes, and its depth is adjusted until the water levels inside and outside the tube are the same. Assume that:
• the gas is not appreciable soluble in water
• the gas collected in the graduated tube and the water are in thermal equilibrium
• a barometer, a thermometer, an analytical balance, and a table of the equilibrium vapor pressure of water at various temperatures are also available.
(a) Write the equation(s) needed to calculate the molar mass of the gas.
(b) List the measurements that must be made in order to calculate the molar mass of the gas.
(c) Explain the purpose of equalizing the water levels inside and outside the gas collection tube.
(d) The student determines the molar mass of the gas to be 64 g mol
–1
. Write the expression (setup) for calculating the percent error in the experimental value, assuming that the unknown as is butane (molar mass 58 g mol
–1
). Calculations are not required.
(e) If the student fails to use information from the table of equilibrium vapor pressures of water in the calculations, the calculated value for the molar mass of the unknown gas will be smaller than the actual value. Explain.