Chemistry

Unit 8: Gas Laws

Chemistry

Learning Objectives Gas Laws

Essential knowledge and skills:

Explain the behavior of gases and the relationship between pressure and volume (Boyle’s Law), and volume and temperature (Charles’ Law).

Solve problems and interpret graphs involving the gas laws.

Essential understandings:

Atoms and molecules are in constant motion. Temperature is a measurement of the average kinetic energy in a sample. There is a direct

relationship between temperature and average kinetic energy. The kinetic molecular theory is a model for predicting and explaining gas behavior. Gases have mass and occupy space. Gas particles are in constant, rapid, random motion and exert

pressure as they collide with the walls of their containers. Gas molecules with the lightest mass travel fastest.

Relatively large distances separate gas particles from each other. Equal volumes of gases at the same temperature and pressure contain an equal number of

particles. Pressure units include atm, kPa, and mm Hg. An ideal gas does not exist, but this concept is used to model gas behavior. A real gas exists, has

intermolecular forces and particle volume, and can change states. The Ideal Gas Law states that PV = nRT.

The pressure and volume of a sample of a gas at constant temperature are inversely proportional to each other (Boyle’s Law: P1V1 = P2V2).

At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (Charles’ Law: V1/T1 = V2/T2).

The Combined Gas Law (P1V1/T1 = P2V2/T2) relates pressure, volume, and temperature of a gas. The sum of the partial pressures of all the components in a gas mixture is equal to the total

pressure of a gas mixture (Dalton’s law of partial pressures).

Kinetic Molecular Theory of GasesTutorial on KMT

Particles of matter (any type) are in constant motion! Because we know this we have a few assumptions that we make about gases, called the Kinetic Molecular Theory of Gases:

1. Particles of a gas move in constant, straight-line motion, until they collide. They move independently from each other.

2. Gases consist of a large number of tiny particles (molecules or atoms); these particles are very far apart, therefore gas is mostly empty space. There are no forces of _____________________ or ____________________ between particles of gases.

3. Collisions between particles of a gas and the container wall are __________ , which means there is no loss of energy.

4. The average kinetic energy of gas particles depends on the temperature of the gas. (It is _______________________ proportional)

2

Kinetic energy: the energy an object has because of its motion. Kinetic energy and temperature are directly proportional

We use Joules (J) to measure energy

Pressure is a force per unit area

P= FA

(units are n/m2)

1.00 atmosphere (atm) = 760.0 mmHg= 760.0 torr = 101.3 kPa (Kilopascals)

Gases exert pressure in all directions.

Atmospheric pressure changes with altitude:

as altitude pressure

Temperature is measure of the average Kinetic energy of the particles

We use Kelvin (absolute) scale and Celsius scale

Kelvin scale has no negative values°C + 273.0 = KK – 273.0 = °C

Must convert all temperatures to Kelvin °C + 273.0 = __?__ K

Absolute Zero: Kelvin 0 K or Celsius -273.0 °C

STP – “standard temperature and pressure”

What is STP?

* This is measured at Sea Level

Standard Temperature is 0C or 273 K and Standard Pressure is 1.00 atm = 760 Torr= 760 mmHg= 101.3 kPa= 101,300 Pa

Gas Pressure: A measure of the force that a gas exerts on its container

Barometer- is a widely used weather instrument that measures atmospheric pressure (also known as air pressure). A barometer measures atmospheric pressure by balance the weight of mercury in a glass tube against the weight of air in the atmosphere.

3

mercury (Hg) air

vacuum

The manometer—a device for measuring the pressure of a gas in a container. Atmospheric pressure pushes on the mercury from one direction, and the gas in the container pushes from the other direction.

tutorial on manometer problems

Pgas > Patm    Gas pressure = atmospheric pressure + h (height of the mercury)

Pgas < Patm Gas pressure = atmospheric pressure - h (height of the mercury)

A. Calculate the pressure of the unknown gas in atm of Manometer 1.

B. Calculate the pressure of the unknown gas in mm of Hg of Manometer 2.

C. Calculate the pressure in of the unknown gas in torr of Manometer 3.

4

Hg HEIGHT

DIFFERENCE

AIR

PRESSURE

CONFINED

GAS

Pressure Conversions

1.00 atm = 101.3 kPa = 760.0 Torr = 101,300 Pa = 760.0 mm Hg

EXAMPLE: Convert 75.0 kPa to Torr: (If this looks like an easy dimensional analysis problem that is because it is an easy dimensional analysis problem)

75 . 0kPa (760 Torr )(101 .3 kPa )

=562Torr

1. 6.2 atm = ? torr 2. 1.2 atm = ? kPa 3. 2.7 atm = ? torr

4. 105.6 mmHg = ? torr 5. 850 torr = ? atm 6. 1820 mmHg = ? atm

7. 48 mmHg = ? torr 8. 600 mmHg = ? kPa 9. 0.62 atm = ? mmHg

10. 3.22 atm = ? kPa 11. 526 mmHg = ? Pa 12. 192 kPa = ? torr

13. 1000 torr = ? atm 14. 150 kPa = ? torr 15. 19.7 kPa = ? atm

16. 1159 torr = ? mmHg 17. 75 kPa = ? atm 18. 159 kPa = ? torr

19. 15000 Pa = ? atm 20. 20 kPa = ? atm 21. 900 mmHg = ? torr

Which Gas Law?

Which Law Should I Use?

5

Boyle’s Law - Pressure and Volume (when temperature remains constant)

Boyles law explained

P1V 1=P2V 2

V1 = initial volumeV2 = final volumeP1 = initial pressureP2 = final pressure

Inverse Relationship between Volume and Pressure (As pressure increases, volume decreases and as pressure volume increases.) (Temperature is constant)

A sample of carbon dioxide occupies a volume of 3.50 liters at 125 kPa pressure. What pressure would the gas exert if the volume was decreased to 2.00 liters?

P1 = ? P2 = ?V1 = ? V2 = Boyle’s Law Worksheet

1. A sample of oxygen gas occupies a volume of 250.5 mL at 740.0 mmHg pressure. What volume will it occupy at 810. mmHg pressure?

2. A sample of carbon dioxide occupies a volume of 3.50 liters at 125 kPa pressure. What pressure would the gas exert if the volume decreased to 2.00 liters?

6

3. A 250. litre container of nitrogen had a pressure of 3.25 atm. What volume would be necessary to decrease the pressure to 1.08 atm?

4. Ammonia gas occupies a volume of 450. mL at a pressure of 727 mmHg. What volume will it occupy at standard pressure?

5. A 175 mL sample of neon had its pressure changed from 75.0 kPa, to 150. kPa. What is its new volume?

6. A sample of hydrogen at 1.5 atm had its pressure decreased to 0.50 atm producing a new volume of 750. mL. What was its original volume?

Charles’ Law - Volume and Temperature (when pressure is constant)

Charles law visualised

7

V 1

T 1=

V 2

T2

T1 = initial temperatureT2 = final temperature

Direct Relationship (As temperature increases, volume increases and as temperature decreases, volume decreases.) (Pressure does not change)

Oxygen gas is at a temperature of 40°C when it occupies a volume of 2.3 liters. To what temperature should it be raised to occupy a volume of 6.5 liters?

V1 = V2 = T1 = T2 =

Charles’ Law Worksheet

1. The temperature inside my refrigerator is about 4.0 °C. If I place a balloon in my fridge that initially has a temperature of 22.6 °C and a volume of 0.509 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator?

2. A man heats a balloon in the oven. If the balloon initially has a volume of 0.452 liters and a temperature of 20.4 °C, what will the volume of the balloon be after he heats it to a temperature of 250.0 °C?

3. On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250. mL bag at a temperature of 19.0 °C, and I leave it in my car which has a temperature of 60.0 °C, what will the new volume of the bag be?

8

4. A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2.58 L) at room temperature (25.3 °C), what will the new volume be if you put it in your freezer (-4.00 °C)?

5. Some students believe that teachers are full of hot air. If I inhale 2.23 liters of gas at a temperature of 18.0°C and it heats to a temperature of 38.0°C in my lungs, what is the new volume of the gas?

6. How hot will a 2.36 L balloon have to get to expand to a volume of 400. L? Assume that the initial temperature of the balloon is 25.0°C.

7. I have made a thermometer which measures temperature by the compressing and expanding of gas in a piston. I have measured that at 100.°C the volume of the piston is 26.3 L. What is the temperature outside if the piston has a volume of 15.0 L?

8. I have made a thermometer which measures temperature by the compressing and expanding of gas in a piston. I have measured that at 100. °C the volume of the piston is 20. L. What is the temperature outside if the piston has a volume of 15.5 L?

9

Gay-Lussac’s Law - Pressure and Temperature (when volume is constant)

Can Crush

* Why will your soda can burst open if you leave it in your car too long on very hot days? Why do closed jars or aerosol cans or beer kegs explode when they are tossed into a fire? These unruly behaviors are manifestations of Gay-Lussac's Law at work.

Direct Relationship (As temperature increases, pressure increases and as temperature decreases, pressure decreases.)

P1

T1=

P2

T 2

A gas has a pressure of 0.370 atm at 50.0 °C. What is the pressure at standard temperature? (STP =Remember 0 oC or 273 K) (Change 50.0 °C to Kelvin)

P1 = P2 = T1 = T2 =

Gay Lussac’s Law Worksheet

1. A rigid container has an initial pressure of 1.50 atm at 21.4 oC. What will the pressure be if the temperature is increased to 121oC?

2. The pressure inside a container is 770. mmHg at a temperature of 57.0 oC. What would the pressure be at 75.0 oC?

10

3. A rigid container is at a temperature of 112 oC. When heated to 224 oC, the pressure was 288 kPa. What was the initial pressure?

4. Use Gay-Lussac’s Law to explain why you should never throw a pressurized aerosol container into a fire. A fire’s temperature is approximately 400.oC.

Avogadro’s Law: Volume is ______________ related to moles.

V 1

n1=

V 2

n2

Example: A 12.2 L sample of gas contains 0.500 mol of O2 at 1.00 atm and 25.0°C. If 3.00 mol of O2 are added, what will be the new volume?

11

Avogadro’s Law Worksheet

1. Suppose 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to1.80 mol, what new volume will result (at an unchanged temperature and pressure)?

2. If 2.00 mol of gas occupies 4.50 L at STP. How much of the same gas will occupy 3.00 L at STP?

3. A propane tank containing 55.0 L has 2.46 moles of the gas. (C3H8 is propane!) What would be the number of moles if ½ of the gas is used?

4. Ammonia is manufactured for fertilizer. The truck hauling the ammonia can hold 450. kiloliters of the gas, which is 20. moles. If a buyer only needs to purchase 225 kiloliters of the gas, how many moles is the buyer receiving?

Avogadro’s Hypothesis and moles of gas at STP

5. The volume of 1 mole of any gas at STP is _________

6. What is the volume occupied by 2.58 moles of helium gas at STP?

7. How many moles are there in a 3.00 L sample of gas is collected at STP?

12

8. How many particles would there be in 5.25 L of gas collected at STP?

9. A sample of ammonia contains 0.500 mol. What volume at STP would the gas occupy?

10. If a balloon filled with carbon dioxide gas occupies a volume of 31.4 L at STP, what is the mass of the gas?

Combined Gas Law

Tutorial on Combined gas Law

Combined gas law states that pressure, temperature, and volume can be related to one another using the following equation: assuming the number of moles of gas remains constant

P1V 1

T 1=

P2V 2

T 2

consistent units, and Temperature must be in K!

Example: A sample of hydrogen gas has a volume of 65.0 L at a pressure of 0.992 atm and a temperature of 338 K. What volume will the hydrogen occupy at 0.984 atm and 298 K?

Combined Gas Law Worksheet

1) If I initially have a gas at a pressure of 12.0 atm, a volume of 23.0 liters, and a temperature of 200. K, and then I raise the pressure to 14.5 atm and increase the temperature to 300. K, what is the new volume of the gas?

13

2) A gas takes up a volume of 17 liters, has a pressure of 2.35 atm, and a temperature of 299 K. If I raise the temperature to 350 K and lower the pressure to 1.52 atm, what is the new volume of the gas?

3) A gas that has a volume of 28 liters, a temperature of 45°C, and an unknown pressure has its volume increased to 34 liters and its temperature decreased to 35°C. If I measure the pressure after the change to be 2.0 atm, what was the original pressure of the gas?

4) A gas has a temperature of 14°C, and a volume of 4.5 liters. If the temperature is raised to 29°C and the pressure is not changed, what is the new volume of the gas?

5) If I have 17 liters of gas at a temperature of 67°C and a pressure of 88.89 atm, what will be the pressure of the gas if I raise the temperature to 94°C and decrease the volume to 12 liters?

6) I have an unknown volume of gas at a pressure of 0.5 atm and a temperature of 325 K. If I raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas?

7) If I have 21 liters of gas held at a pressure of 78 atm and a temperature of 900 K, what will be the volume of the gas if I decrease the pressure to 45 atm and decrease the temperature to 750 K?

14

8) If I have 2.9 L of gas at a pressure of 5.0 atm and a temperature of 50.0°C, what will be the temperature of the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3.0 atm?

Dalton's Law of Partial Pressures:

Dalton's law Tutorial!

The total pressure is the sum of the pressures created by the gases in the mixture.

Ptotal = P1 + P2 + P3 + .... + Pn

Each gas in a mixture creates pressure as if the other gases were not present.

The pressure each gas exerts in mixture is called its partial pressure.

Example Problem: A mixture of oxygen, hydrogen, and nitrogen gases exerts a total pressure of 278 kPa.  If the partial pressures of the oxygen and the hydrogen are 112 kPa and 101 kPa respectively, what would be the partial pressure exerted by the nitrogen.

The most common use of Dalton's Law is with water vapor.

A common method of collecting gas during an experiment is by trapping it "over water." An inverted bottle filled with water sits in a water bath. A tube from the reaction vessel conducts the gas into the bottle where it bubbles to the top and displaces water, which runs out the mouth of the bottle into the water bath.

15

However, there is an unavoidable problem. The gas saturates with water vapor and now the total pressure inside the bottle is the sum of two pressures - the gas itself and the added water vapor.

So we get rid of it by subtraction. This means we must get the water vapor pressure from somewhere.

Example:

A student collects oxygen gas by water displacement at a temperature of 16.0 oC. The total volume is 188.0 mL at a pressure of 92.3 kPa. What is the pressure of the oxygen collected? (90.5 kPa)

A chemist collects a sample of H2S(g) over water at a temperature of 27oC. The total pressure of the gas that has displaced a volume of 15mL of water is 207.33kPa. What is the pressure of H2S(g) collected? (203.76kPa)

This is because….

Gases mix homogeneously (form a solution) in any proportions Each gas in a mixture behaves as if it were the only gas present (assume no chemical reactions).

Try the following examples:

1. An organic chemist was considering the pressures exerted by three gases (let’s call them M, N, L) in a flask. The total pressure inside the flask was 456 mmHg. If gas M contributes 200 mmHg, and gas L contributes 10 mmHg, what is the pressure exerted by gas N.

16

2. An organic chemist was considering the pressures exerted by three gases (M, N, L) in a flask. The total pressure inside the flask was 644 mmHg. If gas M contributes to 21% of the pressure, and gas N contributes 54%, what percentage of the pressure is exerted by gas L? What is the pressure exerted by each gas individually in mm of Hg?

Mole Fraction (χ)

Mole Faction and Partial Pressures

𝛘A = moles A / [moles A + moles B + . . . . ]

mole % = 𝛘A x 100%

mixtures of gases: 𝛘A nA PA (constant temp)

so, χ=PA

PT

3. Four gases are found in an atmospheric sample of gas. The data below indicates their respective amount. Determine the mole fraction of each.

GAS AMOUNT IN MOLES

A 0.235

B 1.025

C 2.35

D 0.78

Total:

17

4. Four gases are found in an atmospheric sample of gas. The data below indicates their respective amount. Determine the mole fraction of each.

GAS AMOUNT IN GRAMS MOLAR MASS

He 23.5 4.00 g/mol

CO2 45.7 44.01 g/mol

CH4 32.3 16.05 g/mol

Steam 24.7 18.02 g/mol

5. Determine the partial pressure of oxygen, nitrogen, and argon using the following data. Total pressure of the system is 760 mmHg.

GAS AMOUNT IN MOLES

O2 20

N2 79

Ar 1

Total:

6. Determine the partial pressure of oxygen, nitrogen, and argon using the following data. Total pressure of the system is 760 mmHg.

18

GAS AMOUNT IN GRAMS MOLAR MASS

O2 45.6

N2 32.2

Ar 100.76

GAS DIFFUSION and EFFUSION

Difference between them!

Graham’s LawGraham’s Law states that the rates of diffusion/effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

Rate1

Rate2=√ Molar Mass2

Molar Mass1

Gases at same temperature and pressure have same kinetic energy As mass increases, the velocity decreases

*From KMT at any given temperature the molecules of all gases have the same average kinetic energy

Kinetic Energy = ½ mass x velocity2

On avg., carbon dioxide travels at 410 m/s at 25oC. Find avg. speed of chlorine at 25oC.

v1

v2=√ m2

m1 →

vCl2

vCO2

¿√ mCO2

mCl2

→ vCl2¿ vCO2 √ mCO2

mCl2

19

vCl2= 410 m/s √44 g

71 g= 320 m/s

**Hint: Put whatever you’re looking for in the numerator.

________________ tendency of molecules to move toward areas of lower concentrations until the concentration is uniform throughout

_________________is the movement of molecules through a tiny opening into an empty container.

Diffusion is related to effusion, and Graham's law can be used to approximate relative rates of diffusion. However, diffusion is complicated by collisions between molecules. Collisions make molecules change direction constantly, thereby impeding their linear progress. The mean free path is the average distance traveled by a molecule between collisions. The mean free path of molecules at atmospheric pressure is about 60 nm.

Using Graham’s Law, find the rate of effusion between the following gases:

Using Grahams Law in Calculations

Solve the following problems. Show ALL work including equations and units. Round all answers to the correct number of significant figures.

1. Circle the molecule in each pair that diffuses faster.

a. H2O or H2S b. NH3 or H2O c. CO2 or NO2

2. Calculate the ratio of effusion rates of NO and NO2.

3. Calculate the ratio of effusion rates of Ar and Kr.

4. A sample of N2O effuses from a container in 42 seconds. How long will it take the same amount of I2 to effuse from the same container under identical conditions?

5. Calculate the molar mass of a gas that effuses 2.5 times faster than carbon monoxide.

20

6. An uknown gas composed of diatomic molecules effuses at a rate that is only 0.355 times that of O2 at the same temperature. What is the molar mass of the unknown gas? What gas must it be???? (Hint, it is diatomic and homonuclear, which mean same element).

Ideal Gas law

Ideal Gas Law Calculation

PV = nRT

P = Pressure (in kPa, atm, or mmHg)V = Volume (in L)T = Temperature (in K) n = moles

Worked Example: A rigid steel container with a volume of 20.0 L, is filled with N2 gas to a final pressure of 200 atm at 27.0oC. Calculate the number of moles of N2 gas in the cylinder.P = 200. atmV = 20.0 L n = ?R =.0821 L atm / Kmol T = 27.0 oC + 273.0 = 300.0 K

1. 3.00 moles of a gas are placed in a 4.55 L container at 245 °C. What is the pressure in kPa?

21

2. 65.85 grams of nitrogen gas are placed in 17.5 L container. The pressure is 1988 mm Hg. What is the temperature, in °C?

3. A 7.0 L container is filled with 10.0 moles of a gas. The pressure is read at 4.00 atm, what is the temperature of the gas?

4. 155.0 grams of oxygen gas are put in a 4.50 L container at 35 °C. What is the pressure, in kPa?

5. What volume would be occupied by 3.0 moles of nitrogen gas under a pressure of 12156 kPa at 50oC?

6. How many moles of a gas will occupy 900 mL at a pressure of 599.8 kPa and -73oC?

7. 2.50 grams of XeF4 is introduced into an evacuated 3.00 liter container at 80.0 °C. Find the pressure in atmospheres in the container.

22

8. A lighter-than-air balloon is designed to rise to a height of 6 miles high with an atmospheric pressure of 210 mm Hg and the temperature is -40 °C. If the full volume of the balloon is 100,000.0 L, how many grams of helium will be needed to inflate the balloon?

9. What is the mass of 18.9 L of NH3 at 31.0°C and 97.97kPa?

10. 0.279 moles of O2 in a 1.85 L cylinder exert a pressure of 3.68 atm. What is the temperature in the cylinder?

Density and the Ideal Gas Law

1. At what Celsius temperature will argon have a density of 10.3 g/L and a pressure of 6.43 atm? (31 deg. C)

23

2. The density of an unknown gas at 20.0oC and 749 mm Hg is 1.31 g/L. Calculate the molar mass of the gas. (32.0 g/mol)

3. A 250.0 mL sample of a noble gas collected at 88.1 kPa and 7.50C has a mass of 0.37 g. What is the molar mass of the gas? Identify the gas.

4. What is the density of sulfur dioxide gas at 90.0 kPa at 45.0 ºC?

5. What is the density of Xenon gas at STP?

6. What is the molar mass of a compound if 2.00 liters of the gas weighs 2.57 grams at 25.0ºC and 0.420 atm.

24

 Gas Stoichiometry

Part 1

Part 2

Remember that stoichiometry involves using mole ratios to compare the amount of reactants used in a reaction to the amount of products made. Now that we know how the volume of a gas relates to the number of moles, we can solve more types of stoichiometry problems.

\

You can do limiting factor or % yield problems in the same manner as before in the stoichiometry unit.

Section 1

1. Consider the formation of nitrogen dioxide from nitric oxide and oxygen:2NO (g) + O2 (g) 2NO2 (g)

If 9.0 L of NO are reacted with excess O2 at STP, what is the volume in liters of the NO2 produced?

2. Methane, CH4, the principal component of natural gas, is used for heating and cooking. Write a balanced equation for its combustion. If 15.0 moles of CH4 are reacted, what is the volume of CO2 (in liters) produced at 23.0˚C and 0.985 atm?

25

Grams of substance X

given in problem

Moles of substance Y needed in

answer

Grams of substance Y needed in

answer

Multiply by molar mass of Y

Use mole ratio from balanced equation

Divide by molar mass of X

Moles of substance X

given in problem

Liters of substance X

given in problem

Liters of substance Y needed in

answer

Solve for n using PV=nRT

Solve for V using PV=nRT

Remember to convert all temperatures to Kelvin, and to use the proper R value depending on pressure units.R = 0.0821 L*atm/mol*K or

R = 8.314 L*kPa/mol*K

Section 2

3. Ammonium sulfate, (NH4)2SO4, can be prepared by a reaction of ammonia gas, NH3, and sulfuric acid, H2SO4. What volume of NH3 gas measured at 78˚C and a pressure of 1.66 atm will be needed to produce 5000.g of ammonium sulfate.

4. Carbon disulfide burns in oxygen to produce carbon dioxide gas and sulfur dioxide gas. Determine the mass of CS2 required to produce 15.7 L of SO2 gas at 25˚C and 99.4 kPa.

5. How many grams of calcium nitride would be needed to produce 750.0 ml of ammonia at 212 kPa and 300.˚C using the equation Ca3N2 + 6H2O 3Ca(OH)2 + 2NH3 ? (2.48 g)

6. Oxygen masks for producing O2 in emergency situations contain potassium superoxide, KO2. If 5.15 liters of O2 at 35˚C and 99.5 kPa were wanted, how many grams of KO2 would be needed? The equation is 4KO2 + 2H2O + 4CO2 4KHCO3 + 3O2 (19.0 g)

26

7. The air pollutant nitric oxide, NO, is produced by automobile engines. It forms another pollutant, NO2, by reacting with O2. Determine the mass of NO2 produced if 26.25 liters of NO react at 150.˚C and 115.0 kPa with excess O2. The equation is 2NO + O2 2NO2 (39.5g)

8. Silver tarnishes in the presence of hydrogen sulfide and oxygen according to the reaction 4Ag + 2H2S + O2 2Ag2S + 2H2O How many liters of O2 at 100.˚C and 115. kPa would be needed to react with 10.00 grams of silver? (0.625 L)

9. The metabolic breakdown of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as gas:

C6H12O6 (s) + 6 O2 (g) 6 CO2 (g) + 6 H2O (l)Calculate the volume of dry CO2 produced at body temperature (37˚C) and 1.00 atm when 5.00 g of glucose is consumed in this reaction.

10. When coal is burned, the sulfur present in coal is converted to sulfur dioxide which is responsible for acid rain: S (s) + O2 (g) SO2 (g)If 2.54 kg of S are reacted with oxygen, calculate the volume in milliliters of SO2 gas formed at 30.5˚C and 1.12 atm.

27

Section 3

11. Ammonia is synthesized from the reaction of hydrogen gas and nitrogen gas: N2 + H2 NH3 If 5.0 liters of N2 and 7.0 L of H2 react at 21.0˚C and 100. kPa, how many liters of NH3 would be produced at 25˚C and 103.5 kPa?

12. In the reaction H2O + Cl2O 2 HOCl, if 4.00 L of H2O at 5.0˚C and 75 kPa react with 3.00 L of Cl2O at STP, how many grams of HOCl would be produced? (13.9 g)

13. Acetylene, C2H2, which is used as a fuel in welding torches is produced in a reaction between calcium carbide and water: CaC2 + 2H2O Ca(OH)2 + C2H2 Determine the liters of acetylene produced at STP if 10.50 g CaC2 reacts with 7.50 g H2O. (3.67 L)

14. In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide:C6H12O6 (s) 2 C2H5OH (l) + 2 CO2 (g)

If 5.97 g of glucose are reacted and 1.44 L of CO2 gas are collected at 293 K and 0.984 atm, what is the percent yield of the reaction?

28

Review Worksheet

Constants and Formulas (assume all variables not shown are constant)

Pressure Unit Conversions1 atm = 760 mmHg = 760 Torr = 101.325 kPaK = oC + 273.0

Constants

R = 8.314 L . kPa or mol . K0.0821 L . atm mol . K

Charles’ Law V1 = V2T1 T2

Gay-Lussac’s Law P1 = P2

T1 T2

Combined Gas Law P1V1 = P2V2

T1 T2

Boyle’s Law P1V1 = P2V2

Avogadro’s Law V1 = V2

n1 n2

STP: Standard T = 0 oC and Standard P = 1 atmMolar volume: 22. 4 L/mol at STP

Dalton’s Law of Partial Pressure

P1 + P2 +…..Pn = Ptotal

Conversion Practice

1. Convert: 560. mmHg to atm and kPa.

Boyle’s Law

1. A gas has a volume of 300. mL at 300. mm Hg. What will its volume be if the pressure is changed to 500. mm Hg?

2. A gas has a volume of 460. mL at 500. mm Hg. What will be the volume at 1.2 atm?

3. A gas has a volume of 5.00 liters at 3.67 atm. To expand the volume to 750.0 ml, what the new pressure (in atm) have to be?

Charles Law

4. A gas has a volume of 4.0 liters at 50.°C. What will its volume be (in liters) at 100.°C?

5. A gas has a volume of 350. mL at 45.°C. If the volume changes to 400. mL, what is the new temperature? (answer in °C )

Gay-Lussac’s Law

6. The gases in a hair spray can are at a temperature of 27.0°C and a pressure of 150. kPa. If the gases in the can reach a pressure of 300. kPa, the can will explode. To what temperature must the gases be raised in order for the can to explode? Assume constant volume.

30

7. Maybelline Cousteau’s backup oxygen tank reads 900 mmHg while on her boat, where the temperature is 27.0 oC. When she dives down to the bottom of an unexplored methane lake on a recently-discovered moon of Neptune, the temperature will drop down to –183.0 oC. What will the pressure in her backup tank be at that temperature?

Combined Gas Law

8. A gas has a volume of 39.0 liters at STP. What will its volume be at 4.05 atm and 25.0°C?

9. 400. mL of a gas is contained at 300. mm Hg and 0.00 oC. What will its volume be in mL at 140. mm Hg and 10.0°C?

10. 500. mL of gas is contained at STP. The volume changes to 560 mL at 20.0°C. What is the pressure (in atm)?

Avogadro’s Law and Molar Volume at STP (Remember 22.4 L/mol at STP)

11. 50.0 g of nitrogen (N2) has a volume of ___ liters at STP.

12. Consider the reaction: 2H2(g) + O2(g) 2H2O(g). What mass of oxygen is consumed at STP by 100.g H2? What volume of water forms if you have the exact stoichiometric ratio of hydrogen to oxygen? Assume the reaction condition stays at STP throughout.

31

13. What is the density of carbon dioxide at STP in two significant figures?

Dalton’s Law Worksheet

14. A metal tank contains three gases: oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 35.0 atm of O2, 5.0 atm of N2, and 25.0 atm of He, what is the total pressure inside of the tank?

15. Blast furnaces give off many unpleasant and unhealthy gases. If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.050 atm, and the partial pressure of hydrogen sulfide is 0.020 atm, what is the partial pressure of the remaining air?

16. If the air from problem 15 contains 22.0% oxygen, what is the partial pressure of oxygen near a blast furnace?

Graham’s Law Problems

17. A certain gas effuses 4 times as fast as oxygen gas. What is the molar mass of the unknown gas?

32

18. A compound effuses through a porous cylinder 5.71 times slower than helium. What is its molar mass? Identify the compound.

19. If 0.00251 mol of NH3 effuse through a hole in 2.47 min, how much HCl would effuse in the same time?

20. A sample of N2 effuses through a hole in 38.00 seconds. What must be the molecular mass of gas that effuses in 60.45 seconds under identical conditions? Can you identify the gas?

Ideal Gas Law

21. Find the pressure in mm Hg produced by 2.35 g of carbon dioxide in a 5.00 L flask at 18°C. (194 mm Hg)

22. How many grams of carbon monoxide must be placed into a 40.0 L tank to develop a pressure of 965 mm Hg at 23.0°C? (58.5 g)

Ideal Gas Law: Density and Molar Mass

23. At what Celsius temperature will argon have a density of 10.3 g/L and a pressure of 6.43 atm? (31 deg. C)

24. The density of an unknown gas at 20.0oC and 749 mm Hg is 1.31 g/L. Calculate the molar mass of the gas. (32.0 g/mol)

33

Gas Stoichiometry

25. ___Mg3N2(s) + ___ H2O(l) → ___MgO(s) + ___NH3(g)

a. Balance the above reaction.b. If 10.35 g of magnesium nitride is treated with 10.35 g of water, what volume of ammonia gas would be collected at 24.0˚C and 0.989 atm?

26. ___ Cl2(g) + ____ C2H2(g) _____ C2H2Cl4(l)

a. Balance the above reaction.b. What volume of Cl2 will be needed to make 75.0 grams of C2H2Cl4 at 24.0°C and 773 mm Hg?

27. ____ C8H18(l) + ____ O2(g) ____ CO2(g) + ____ H2O(g)

a. Balance the above reaction.b. How many grams of water would be produced if 20.0 liters of O2 gas were burned at a temperature of -10.0°C and a pressure of 1.35 atm?

34