AP Chemistry : Ch. 5 Notesmr. Ferwerda - Tecumsehhigh School5/20/08

AP Chemistry : Ch. 5 NotesMr. Ferwerda - TecumsehHigh School5/20/08

A. Gases

0. Characteristics :

a. expand spontaneously to fill its container (no definite volume)

b. gases are highly compressible

c. form homogeneous mixtures

d. individual molecules are relatively far apart and exert little influence on each other

1. Pressure

a. Devices used to measure gas pressure :

- barometer - device used to measure atmospheric pressure - mercury or aneroid

- manometer - used to measure the pressure of a contained gas - see Fig. 5.3

b. Units of gas pressure

- mm Hg - equal to the amount of air pressure needed to push a mercury column up 1 mm

- torr - named after Evangelista Torricelli - (inventor of barometer), equals 1 mm Hg

- standard atmosphere (atm) equals 760 mm Hg (or 760 torr)

- pascal (Pa) - SI unit of gas pressure (N/m2) = 101,325 Pa = 1 atm

- Pa are very small and not frequently used

Reading pressure using open manometers :

2. The Gas Laws of Boyle, Charles, and Avogadro

a. Four factors which determine the state of a gas :

- Pressure

- Temperature (always in K ; K = C +273)

- Volume

- amount (usually measured in moles)

3. The Ideal Gas Law

a. PV = nRT , where : R = universal gas constant (.08206 L·atm/K·mol)

- it is important to remember that the gas laws describe ideal gases, not real gases

- real gas behavior approaches ideal gas behavior at high temperatures and low pressures

- for calculations you may assume ideal gas behavior unless told otherwise

Note : The other above gas laws can be derived from the ideal gas law. e.g. Boyle's law : If n,R and T are constant, then under condition set one : P1V1 = nRT, and under condition set two P2V2 = nRT, or P1V1 = P2V2.

Consider a sample of gas at two conditions :(" a sample" = n is constant)

Condition set 1 Condition set 2

Constant n,R and T

Constant n , R and P

A the same conditions of T and P, the volume of a gas is doubled, what must happen to the number of moles?

There are 0.122 moles of oxygen gas at 200 K, 760 mm Hg and a volume of 2.0 L. How many moles will there be at 100K, 2.0 L and 760 mm Hg ?

a. 0.122 mol b. 0.244 mol c. 0.0610 mol d. 4.88 mol e. none of the above.

Forty eight grams of oxygen gas occupy 29 L at 350 K and 1.5 atm. What volume would 64 grams of oxygen occupy at the same conditions of T and P?

a. 14 L b. 24 L c. 38 L d. 58 L e. 73 L

b. Boyle's law : Volume and pressure are inversely related at constant temperature

- PV = k, (P1V1=nRT=P2V2) where k is a constant for a given sample of a gas at a specific temperature

- or, P1 x V1 = P2 x V2

- a gas that strictly obeys Boyle's law is an ideal gas

- Boyle's law only holds precisely at low pressures

A thirty gram sample of an unknown gas has a volume of 22.0 L at 750 mm Hg. What will the volume be at 1500 mm Hg?

a. 5.5 L b. 11.0 L c. 22.0 L d. 27.5 L e. 44.0 L

c. Charles's law : The Kelvin temperature and volume vary directly with each other at constant pressure.

- linear relationship

- V = bT, where T is in Kelvins and b is a

proportionality constant

- or, V1/T1 = V2/T2

- K = ºC + 273

- If Charles's law is extrapolated backwards to where V = 0, the value of absolute zero having a value of -273 K can be obtained

A 68 gram sample of hydrogen sufide gas has a volume of 2.0 L at 127 C. What will the volume of this sample of gas be at -73 C ?

a. .5 L b. 1.0 L c. 1.5 L d. 2.0 L e. 4.0 L

d. Combined gas law - P, V, and T change :

A sample of a gas has a volume of 1.5 L at 400 K and 368 mm Hg. What will its volume be at 800 K and 735 mm Hg?

a. .75 L b. 1.5 L c. 2.0 L d. 3.0 L e. 4.5 L

e. Avogadro's law : for a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas present.

- Or, equal volumes of gases at the same temperature and pressure have the same number of particles.

- V = an, where n = number of moles and a = proportionality constant or

- this relationship is closely obeyed at low pressures

A 72 gram sample of hydrogen sulfide gas has a volume of 50. L at a certain temperature and pressure. At the same temperature and pressure, how many liters would a 96 gram sample occupy?

a. 17 L b. 33 L c. 50. L d. 67 L e. 87 L

f.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.

a. mathematically : Ptotal = P1 + P2 + P3 …. Where P1, P2 and P3 represent the partial pressure of each gas in the mixture.

b. The pressure of a gas is unaffected by the identity of a gas. Therefore :

- the volume of the individual gas particles is not important

- the forces between the particles is unimportant

c. The pressure of a gas is directly proportional to the moles of gas present, therefore the mole fraction of a gas is directly proportional to the partial pressure of a gas :

where a = one of the gases in a mixture of gases

d. When a gas is collected over water by water displacement the vapor pressure of the water needs to be subtracted from the total pressure of the container to obtain the pressure of the gas alone. (Ptotal = Pgas + PH2O)

If a gas is collected over water and the PH2O = 0.50 atm and the total pressure is 1.0 atm, what is the pressure of the gas collected?

f. Partial pressure of gases and mole fraction :since the pressure of a gas is directly proportional to the

number of moles present, mole fraction is equivalent to partial pressure :

What is the mole fraction of ethanol, C2H5OH, in an aqueous solution that is 46 percent ethanol by mass? (The molar mass of C2H5OH is 46 g; the molar mass of H2O is 18 g.)

(A)0.25(B)0.46(C)0.54(D)0.67(E)0.75

If the above sample was vaporized in a 2400 L vessel, what would the volume occupied by the ethanol be?

a. 300 L b. 600 L c. 1200 L d. 1800 L e. 2000 L

6. The Kinetic Molecular Theory of Gases - a model based on observations used to explain and predict the behavior of ideal gases.

a. The Kinetic Molecular Theory of gases states that :

- The particles of a gas are so small compared to the distances between particles that the volume of the individual particles can be assumed to be zero.

- The particles of a gas are in constant motion. Gas pressure is created by the collisions of the gas particles with the walls of the container. Collisions of gas particles are elastic - no kinetic energy is lost.

- The particles exert no forces on each other.

- The average kinetic energy of a collection of gas particles is directly proportional to the Kelvin temperature of the gas.

______gases obey all the gas laws under all conditions of temperature and pressure.

_____ (T/F) According to the KMT, the atoms or molecules making up ideal gases have no volume.

_____ (T/F) According to the KMT, the particles of ideal gases are in constant and random motion (creates gas pressure as particles strike walls of container)

_____ (T/F) According to the KMT, the particles of ideal gases exert attractive forces on each other.

Which of the following gases, ammonia or oxygen would behave less like an ideal gas?

_____ (T/F) According to the KMT, the average kinetic energy of the particles of a gas is directly proportional to its Celsius temperature.

______is the spreading of a gas into an evacuated chamber through a small opening.

4. Gas Stoichiometry

a. The molar volume of an ideal gas at STP is 22.42 L

b. STP - standard temperature and pressure (0 ºC and 1 atm)

c. Determination of the molar mass of a gas from an ideal gas law derivation : Molar mass = dRT/P, where d = density of a gas and R = universal gas constant.

5.
b. The relationship between kinetic energy and temperature is given by the following equation :

c. The root mean square velocity of a gas can be calculated using the following equation :

- where : urms = root mean square

R = universal gas constant (8.3145 J/K·mol)

M = mass of one mole of the particles in Kg

d. Gas particles travel at varying speeds due to collisions with other particles.

e. Mean free path - the average distance traveled by a particle between collisions

7. Effusion and Diffusion

a. Effusion - the passage of a gas through a tiny hole into an evacuated chamber.

- the rate of effusion of a gas is inversely proportional to the square root of the mass of the particles of a gas (Graham's law)

- Graham's law of effusion :

The rate of effusion of helium to oxygen will be

AP Chemistry : Ch. 5 NotesMr. Ferwerda - TecumsehHigh School5/20/08

(a) 1.4

(b) 2

(d) 3.2

(e) 8.0

AP Chemistry : Ch. 5 NotesMr. Ferwerda - TecumsehHigh School5/20/08

b. Diffusion - the mixing of gases due to the random motion of the particles of the gas

- much more complex to mathematically describe due to the collisions between particles

8. Real Gases

a. No gas exactly follows ideal gas behavior. Real gases best approach ideal gas behavior under conditions of high temperature and low pressure.

b. van der Waal's equation - describes the behavior of a real gas by correcting for the actual volume of gas particles and the forces between gas particles :

where : Pobs = observed pressure

V = volume of container

a(n/V)2 = pressure correction

V-nb = volume correction

a and b are proportionality constants obtained from observing the real gas

"a" increases as the size and polarity of molecules or atoms increase

"b" increases as the volume of the atom or molecule increases

Which of the following gases would have the highest "a" value?

a. CO2 b. NH3 c. CH4 d. HCN e. O2

Which of the following gases would have the highest "a" value?

a. H2 b. He c. Ne d. Ar e. Kr

Which of the following gases would have the highest "a" value?

a. N2 b. O2 c. CH4 d. C2H6 e. C3H8

Which of the following gases would have the highest "b" value?

a. N2 b. O2 c. CH4 d. C2H6 e. C3H8

9. Chemistry in the Atmosphere

a. Air pollution

- acid rain can also be formed when nonmetallic oxides (acid anhydrides) formed by burning nitrogen in the air or sulfur in coal react with water in the air :

S (from coal) + O2(g)  SO2(g)

2 SO2(g) + O2(g)  SO3(g)

H2O(l) + SO3(g)  H+(aq) + HSO4-(aq)

- other examples of acid anhydrides :

- H2O(l) + CO2(g)  H2CO3(aq)

- H2O(l) + SO2(g)  H2SO3(aq)

- H2O(l) + 2NO2(g)  H+(aq) + NO3-(aq) + HNO2(aq) *

* Note these are not redox reactions - oxidation states do not change - must balance.

Day 2

What is the density of a metal object given the following data :

mass of metal = 12.211 g

vol. of water before adding metal object = 14.2 mL

vol. of water with metal object = 14.9 mL

(a) 17.444 g/mL

(b) 17.44 g/mL

(d) 17 g/mL

(e) 20 g/mL

The correct net ionic equation for the reaction between silver acetate and barium chloride is :

(a) Ba + 2 C2H3O2- ---> Ba(C2H3O2)2

(b) Ag2+ + 2 Cl- ---> AgCl2

(d) Ba+ +C2H3O2- ---> BaC2H3O2

(e) Ba2+ + 2 C2H3O2- ---> Ba(C2H3O2)2

How many of the following salts are insoluble?

- ammonium acetate

- sodium sulfide

- calcium sulfate

- strontium sulfate

- iron(II) carbonate

- lead(IV) phosphate

- lithium phosphate

How many of the following salts are insoluble?

- cesium hydroxide

- magnesium hydroxide

- calcium hydroxide

- barium hydroxide

- aluminum hydroxide

How many of the following salts are insoluble?

- iron(II) sulfate

- barium sulfate

- calcium sulfate

- calcium fluoride

- lithium fluoride

- silver iodide

- potassium bromide

What is the mole fraction to partial pressure relationship in ideal gases?

A mixture consists of two gases with a total pressure of 3.0 atm. If one-third of the gas is chlorine and two-thirds are fluorine, what are the partial pressures of chlorine and fluorine?

Ideal gases vs real gases?

Ideal gases Real gases

If the volume of a gas exceeds the number calculated by the ideal gas law, which of the following factors can account for the discrepancy?

(a) the velocity of the gas particles

(b) the attractive forces between gas particles

(d) the volume of the gas particles

(e) the mass of the gas particles

Which of the following gases would behave less like an ideal gas?

Sulfur dioxideCarbon dioxide

Which of the following pairs would be the more ideal gas at identical conditions?

O2 or O3

CO2 or CO

Ne or Xe

Conditions at which real gases begin to approximate ideal gases?

Low Temperature or High Temperature

Low Pressure or High pressure

Low moles or High moles

Day 3 :

What is the density of fluorine gas at STP?

A 25.0 L tank is filled with helium to a pressure of 9.50 x 104 torr. How many 2.0 L balloons can the tank fill? (Assume 1.0 atm external pressure and no temperature change).

_____ (T/F) Mole fraction is directly related to the combined volumes and partial pressures of gases at equal conditions of T and P.

e.g. combining 2.0 L O2 + 1.0 L N2 at STP : XO2 = XN2 =

PO2 = PN2 =

A vessel contains oxygen and nitrogen gas. The partial pressure of the oxygen gas is 625 torr and the partial pressure of the nitrogen gas is 175 torr. What are the mole fractions of the two gases?

_____ (T/F) If carbon dioxide gas and nitrogen gas are in the same container (equal T, V and P), the molecules of each gas would have the same average kinetic energy.

_____ (T/F) If carbon dioxide gas and nitrogen gas are in the same container (equal T, V and P), the molecules of each gas would have the same average velocity.

_____ (T/F) All the molecules of carbon dioxide in a 2.00 L container at 400 K and .95 atm will have the same velocity.

_____ (T/F) All the molecules of carbon dioxide in a 2.00 L container at 400 K and .95 atm will have the same kinetic energy.

Oxygen has three isotopes O-16, O-17 and O-18. Calculate the relative rates of effusion between the lightest and heaviest forms of O2.

In an experiment to determine the relative rate of effusion of hydrogen gas to chlorine gas, a pair of Saline chemistry students introduced hydrogen gas into the tube, then read the directions. They then added chlorine gas to the tube. Comment of the accuracy of their probable results.

What is the molar mass of a gas which has a density of 2.96 g/L at 27 ºC at a pressure of 780. torr?

Which of the following oxides will help create acid rain? (are acid anhydrides)

CO2

MgO

CaO

SO3

2NO2

Na2O

Homework Hints

WS-5-1

#36

#37. Use above equation.

WS-5-2

#36 - Let x = mol BaO, then 0.412-x = mol CaO (set up : (153.3x) + ((56.08(0.412-x)) = 5.14

AP ChemistryName :

Chapter 5 Free response practiceDate :

Summary problems :

S1. 2 Al(s) + 2 KOH(aq) + 6 H2O(l) --> 2 KAl(OH)4(aq) + 3 H2(g)

A 1.016 g impure sample of aluminum is reacted with potassium hydroxide according to the above equation. The hydrogen gas is collected over water and measures 235 mL at 22.0 C and 762 mm Hg( The vapor pressure of water at 22.0 C is 19.8 mm Hg). What is the mass percent of the aluminum in the sample?

S2. A dry, 10.00 gram mixture of sodium carbonate, sodium hydroxide and sodium chloride is reacted with 1.2 L of 1.0 M HCl (an excess).

(a) After reacting 455 mL of carbon dioxide gas is collected over water at 25 C and 778 mm Hg (Vapor pressure of water at 25 C is 23.8 mm Hg). What is the percentage of sodium carbonate is in the mixture?

(b) The resulting solution is titrated with 1.20 M NaOH, requiring 95.0 mL to neutralize the excess acid. Calculate the percentages of sodium hydroxide and sodium chloride in the original mixture.

S3. A solid sample of XeF4 is placed in an evacuated 2.00 L vessel and vaporized at 285 C.

(a) What is the vapor pressure in the flask if XeF4 if no reaction occurs?

(b) If XeF4 partially decomposes according to the equation XeF4 <=> 2 XeF2, and the pressure oin the flask is found to be 1.10 atm, calculate the partial pressures of the XeF4 and the XeF2.

S3. The boiling point of ethanol is C. If the molar mass of ethanol is determined from the volume, mass, and pressure of ethanol at C, would the results likely show a mass that is too high, low or would they be accurate? Explain your answer.

S4. A mixture of equal moles of hydrogen gas and nitrogen gas and 10.0 mL of ammonia are placed in a 2.00 liter vessel at a 25 C. The total pressure is 1888 mm Hg. (The vapor pressure of ammonia is assumed to be 22 mm Hg at 25 C). If the reaction proceeds to produce as much ammonia as possible

(a) Calculate the number of moles of the excess reactant remaining.

(b) Calculate the total pressure in the container at the conclusion of the reaction (assume no temperature change).

S5. A student produces hydrogen gas by the reaction of zinc metal and hydrochloric acid. The following data were obtained :

Gas Collection Data
Volume of gas sample / 80.0 mL
Temperature / 25 C
Atmospheric Pressure / 755 mm Hg
Equilibrium vapor pressure of water at 25 C / 23.8 mm Hg

(a) Calculate the number of moles of hydrogen gas collected.

(b) Calculate the number of moles of water vapor in the gas sample.

(d) If there was a pinhole in the apparatus, what would happen to the H2: H2O gas ratio and why?

(e) Which gas, hydrogen or water vapor is more ideal and why?

S6. (a) Write the balanced equation form the combustion of propane (C3H8).

(b) Calculate the heat released when 450.0 grams of propane are burned (H comb. = 2220.1 kJ/mol)

(c) If all the heat from the combustion of 500. grams of propane is transferred to 15.0 kg of water at 22.0 C, what would the final temperature of the water be?

S7. In a rigid 500. mL container 0.150 mol of SO2 reacts with 0.150 mol of oxygen gas to form SO3.

(a) Write a balance equation for this reaction.

(b) Calculate the total pressure, at 298 K in the container when the reaction is complete.