The Gaseous State of Matter Chapter 12 Hein and Arena Eugene Passer Chemistry Department Bronx Community College © John Wiley and Sons, Inc Version 2.0 12th Edition

Chapter Outline 12.2 The Kinetic Molecular Theory 12.9 Dalton’s Law of Partial Pressures 12.3 Measurement of Pressure of Gases 12.10 Avogadro’s Law 12.11 Mole-Mass-Volume Relationships of Gases 12.4 Dependence of Pressure on Number of Molecules and Temperature 12.12 Density of Gases 12.5 Boyle’s Law 12.13 Ideal Gas Law 12.6 Charles’ Law 12.14 Gas Stoichiometry 12.7 Gay-Lussac’s Law 12.8 Combined Gas Laws 12.15 Real Gases

12.2 The Kinetic- Molecular Theory

The Kinetic-Molecular Theory KMT is based on the motions of gas particles. A gas that behaves exactly as outlined by KMT is known as an ideal gas. While no ideal gases are found in nature, real gases can approximate ideal gas behavior under certain conditions of temperature and pressure.

Principle Assumptions of the KMT Gases consist of tiny particles. The distance between particles is large compared with the size of the particles themselves. Gas particles have no attraction for one another.

Principle Assumptions of the KMT Gas particles move in straight lines in all directions, colliding frequently with one another and with the walls of the container. No energy is lost by the collision of a gas particle with another gas particle or with the walls of the container. All collisions are perfectly elastic.

Principle Assumptions of the KMT The average kinetic energy for particles is the same for all gases at the same temperature, and its value is directly proportional to the Kelvin temperature.

Kinetic Energy

mH = 2 mO = 32 vH vO = 1 4 Kinetic Energy All gases have the same average kinetic energy at the same temperature. As a result, lighter molecules move faster than heavier molecules. mH 2 = 2 mO 2 = 32 vH 2 vO = 1 4

Diffusion The ability of two or more gases to mix spontaneously until they form a uniform mixture. Stopcock closed No diffusion occurs Stopcock open Diffusion occurs 12.1

Effusion A process by which gas molecules pass through a very small orifice from a container at higher pressure to one at lower pressure.

Graham’s Law of Effusion The rates of effusion of two gases at the same temperature and pressure are inversely proportional to the square roots of their densities, or molar masses.

What is the ratio of the rate of effusion of CO to CO2?

12.3 Measurement of Pressure of Gases

Pressure equals force per unit area.

The pressure resulting from the collisions of gas molecules with the walls of the balloon keeps the balloon inflated. 12.2

The pressure exerted by a gas depends on the Number of gas molecules present. Temperature of the gas. Volume in which the gas is confined.

A tube of mercury is inverted and placed in a dish of mercury. Mercury Barometer A tube of mercury is inverted and placed in a dish of mercury. The barometer is used to measure atmospheric pressure. 12.3

Average Composition of Dry Air Gas Volume Percent Gas Volume Percent N2 78.08% He 0.0005% O2 20.95% CH4 0.0002% Ar 0.93% Kr 0.0001% CO2 0.033% Xe, H2, and N2O Trace Ne 0.0018%

12.4 Dependence of Pressure on Number of Molecules and Temperature

Pressure is produced by gas molecules colliding with the walls of a container. At a specific temperature and volume, the number of collisions depends on the number of gas molecules present. For an ideal gas the number of collisions is directly proportional to the number of gas molecules present.

The pressure exerted by a gas is directly proportional to the number of molecules present. V = 22.4 L T = OoC 12.4

Dependence of Pressure on Temperature The pressure of a gas in a fixed volume increases with increasing temperature. When the pressure of a gas increases, its kinetic energy increases. The increased kinetic energy of the gas results in more frequent and energetic collisions of the molecules with the walls of the container.

Lower T Lower P Higher T Higher P Increased pressure is due to more frequent and more energetic collisions of the gas molecules with the walls of the container at the higher temperature. The pressure of a gas in a fixed volume increases with increasing temperature. Lower T Lower P Higher T Higher P 12.5

12.5 Boyle’s Law

At constant temperature (T), the volume (V) of a fixed mass of gas is inversely proportional to the Pressure (P).

Graph of pressure versus volume Graph of pressure versus volume. This shows the inverse PV relationship of an ideal gas. 12.6

The effect of pressure on the volume of a gas. 12.7

Method A. Conversion Factors An 8.00 L sample of N2 is at a pressure of 500 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). Method A. Conversion Factors Step 1. Determine whether volume is being increased or decreased. Initial volume = 8.00 L Final volume = 3.00 L volume decreases  pressure increases

An 8. 00 L sample of N2 is at a pressure of 500 torr An 8.00 L sample of N2 is at a pressure of 500 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). Step 2. Multiply the original pressure by a ratio of volumes that will result in an increase in pressure. new pressure = original pressure x ratio of volumes

An 8. 00 L sample of N2 is at a pressure of 500 torr An 8.00 L sample of N2 is at a pressure of 500 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). Method B. Algebraic Equation Step 1. Organize the given information: V1 = 8.00 L P1 = 500 torr V2 = 3.00 L P2 = ?

Step 2. Write and solve the equation for the unknown. An 8.00 L sample of N2 is at a pressure of 500 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). Step 2. Write and solve the equation for the unknown.

Step 3. Put the given information into the equation and calculate. An 8.00 L sample of N2 is at a pressure of 500 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). Step 3. Put the given information into the equation and calculate.

12.6 Charles’ Law

Absolute Zero on the Kelvin Scale If a given volume of any gas at 0oC is cooled by 1oC the volume of the gas decreases by . If a given volume of any gas at 0oC is cooled by 20oC the volume of the gas decreases by .

Absolute Zero on the Kelvin Scale If a given volume of any gas at 0oC is cooled by 273oC the volume of the gas decreases by . -273oC (more precisely –273.15oC) is the zero point on the Kelvin scale. It is the temperature at which an ideal gas would have 0 volume.

Volume-temperature relationship of methane (CH4). 12.8

Charles’ Law At constant pressure the volume of a fixed mass of gas is directly proportional to the absolute temperature.

12.9 Effect of temperature on the volume of a gas. Pressure is constant at 1 atm. When temperature increases at constant pressure, the volume of the gas increases.

Method A. Conversion Factors Step 1. Change oC to K: oC + 273 = K A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250oC? Method A. Conversion Factors Step 1. Change oC to K: oC + 273 = K 75oC + 273 = 348 K 250oC + 273 = 523 K

A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3 A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250oC? Step 2: Multiply the original volume by a ratio of Kelvin temperatures that will result in an increase in volume:

Method B. Algebraic Equation A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250oC? Method B. Algebraic Equation Step 1. Organize the information (remember to make units the same): V1 = 255 mL T1 = 75oC = 348 K V2 = ? T2 = 250oC = 523 K

Step 2. Write and solve the equation for the unknown: A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250oC? Step 2. Write and solve the equation for the unknown:

Step 3. Put the given information into the equation and calculate: A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250oC? Step 3. Put the given information into the equation and calculate: V1 = 255 mL T1 = 75oC = 348 K V2 = ? T2 = 250oC = 523 K

12.7 Gay-Lussac’s Law

Gay-Lussac’s Law The pressure of a fixed mass of gas, at constant volume, is directly proportional to the Kelvin temperature.

Method A. Conversion Factors Step 1. Change oC to K: oC + 273 = K At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC ,what will be the pressure of the oxygen? Method A. Conversion Factors Step 1. Change oC to K: oC + 273 = K 40oC + 273 = 313 K 100oC + 273 = 373 K Determine whether temperature is being increased or decreased. temperature increases  pressure increases

At a temperature of 40oC an oxygen container is at a pressure of 2 At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC, what will be the pressure of the oxygen? Step 2: Multiply the original pressure by a ratio of Kelvin temperatures that will result in an increase in pressure:

A temperature ratio greater than 1 will increase the pressure At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC, what will be the pressure of the oxygen? A temperature ratio greater than 1 will increase the pressure

Method B. Algebraic Equation At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC, what will be the pressure of the oxygen? Method B. Algebraic Equation Step 1. Organize the information (remember to make units the same): P1 = 21.5 atm T1 = 40oC = 313 K P2 = ? T2 = 100oC = 373 K

Step 2. Write and solve the equation for the unknown: At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC, what will be the pressure of the oxygen? Step 2. Write and solve the equation for the unknown:

Step 3. Put the given information into the equation and calculate: At a temperature of 40oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100oC, what will be the pressure of the oxygen? Step 3. Put the given information into the equation and calculate: P1 = 21.5 atm T1 = 40oC = 313 K P2 = ? T2 = 100oC = 373 K

12.8 Combined Gas Laws

Standard Temperature and Pressure Selected common reference points of temperature and pressure. Standard Conditions Standard Temperature and Pressure STP 273.15 K or 0.00oC 1 atm or 760 torr or 760 mm Hg

A combination of Boyle’s and Charles’ Law. Used when pressure and temperature change at the same time. Solve the equation for any one of the 6 variables

calculate final volume ratio of pressures ratio of temperatures final volume = initial volume

increases or decreases volume ratio of pressures ratio of temperatures final volume = initial volume

increases or decreases volume ratio of pressures ratio of temperatures final volume = initial volume

A sample of hydrogen occupies 465 ml at STP A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Step 1. Organize the given information, putting temperature in Kelvins: oC + 273 = K 0oC + 273 = 273 K -15oC + 273 = 258 K

A sample of hydrogen occupies 465 ml at STP A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Step 1. Organize the given information, putting temperature in Kelvins: P1 = 760 torr P2 = 950 torr V1 = 465 mL V2 = ? T1 = 273 K T2 = 258 K

Method A Conversion Factors Step 2. Set up ratios of T and P A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Method A Conversion Factors Step 2. Set up ratios of T and P

Step 3. Multiply the original volumes by the ratios: A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Step 3. Multiply the original volumes by the ratios: P1 = 760 torr P2 = 950 torr V1 = 465 mL V2 = ? T1 = 273 K T2 = 258 K

Method B Algebraic Equation Step 2. Write and solve the equation for A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Method B Algebraic Equation Step 2. Write and solve the equation for the unknown V2.

Step 2 Put the given information into the equation and calculate. A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? Step 2 Put the given information into the equation and calculate.

12.9 Dalton’s Law of Partial Pressures

Each gas in a mixture exerts a pressure that is independent of the other gases present.

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture. Ptotal = Pa + Pb + Pc + Pd….

Ptotal = 0.5 atm + 0.6 atm + 1.30 atm = 2.40 atm A container contains He at a pressure of 0.50 atm, Ne at a pressure of 0.60 atm, and Ar at a pressure of 1.30 atm. What is the total pressure in the container? Ptotal = PHe + PNe+ PAr Ptotal = 0.5 atm + 0.6 atm + 1.30 atm = 2.40 atm

Collecting a Gas Sample Over Water The pressure in the collection container is equal to the atmospheric pressure. The pressure of the gas collected plus the pressure of water vapor at the collection temperature is equal to the atmospheric pressure.

Oxygen collected over water. 12.12

A sample of O2 was collected in a bottle over water at a temperature of 25oC when the atmospheric pressure was 760 torr. What is the partial pressure of the O2? The vapor pressure of water at 25oC is 23.8 torr.

Gay Lussac’s Law of Combining Volumes When measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. N2 1 volume + 3 H2 3 volumes → 2 NH3 2 volumes

Gay Lussac’s Law of Combining Volumes When measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. 12.14

12.10 Avogadro’s Law

Avogadro’s Law Equal volumes of different gases at the same temperature and pressure contain the same number of molecules.

hydrogen + chlorine  hydrogen chloride 1 volume 1 volume 2 volumes 1 molecule 1 molecule 2 molecules There are 2 molecules of hydrogen chloride. 1 mol 1 mol 2 mol Each molecule of hydrogen chloride contains at least 1 atom of hydrogen and 1 atom of chlorine.

hydrogen + chlorine → hydrogen chloride H2 + Cl2 → 2 HCl 1 volume 1 volume 2 volumes 1 molecule 1 molecule 2 molecules 1 mol 1 mol 2 mol hydrogen + chlorine → hydrogen chloride Each molecule of hydrogen and each molecule of chlorine must contain at least 2 atoms.

12.11 Mole-Mass-Volume Relationships of Gases

Volume of one mole of any gas at STP = 22.4 L. 22.4 L at STP is known as the molar volume of any gas.

12.13

The density of neon at STP is 0. 900 g/L The density of neon at STP is 0.900 g/L. What is the molar mass of neon?

12.12 Density of Gases

Density of Gases grams liters

Density of Gases depends on T and P

1 mole of any gas occupies 22.4 L at STP The molar mass of SO2 is 64.07 g/mol. Determine the density of SO2 at STP. 1 mole of any gas occupies 22.4 L at STP

12.13 Ideal Gas Law

V a P nT

atmospheres nT V a P

liters nT V a P

moles nT V a P

Kelvin nT V a P

Ideal Gas Constant nT V a P

Step 1. Organize the given information. A balloon filled with 5.00 moles of helium gas is at a temperature of 25oC. The atmospheric pressure is 750. torr. What is the balloon’s volume? Step 1. Organize the given information. Convert temperature to kelvins. K = oC + 273 K = 25oC + 273 = 298K Convert pressure to atmospheres.

Step 2. Write and solve the ideal gas equation for the unknown. A balloon filled with 5.00 moles of helium gas is at a temperature of 25oC. The atmospheric pressure is 750. torr. What is the balloon’s volume? Step 2. Write and solve the ideal gas equation for the unknown. Step 3. Substitute the given data into the equation and calculate.

Determination of Molecular Weights Using the Ideal Gas Equation

Calculate the molar mass of an unknown gas, if 0 Calculate the molar mass of an unknown gas, if 0.020 g occupies 250 mL at a temperature of 305 K and a pressure of 0.045 atm. V = 250 mL = 0.250 L g = 0.020 g P = 0.045 atm T = 305 K

12.14 Gas Stoichiometry

All calculations are done at STP. Gases are assumed to behave as ideal gases. A gas not at STP is converted to STP.

Gas Stoichiometry Primary conversions involved in stoichiometry.

Mole-Volume Calculations Mass-Volume Calculations

What volume of oxygen (at STP) can be formed from 0 What volume of oxygen (at STP) can be formed from 0.500 mol of potassium chlorate? Step 1 Write the balanced equation 2 KClO3  2 KCl + 3 O2 Step 2 The starting amount is 0.500 mol KClO3. The conversion is mol KClO3  mol O2  L O2

What volume of oxygen (at STP) can be formed from 0 What volume of oxygen (at STP) can be formed from 0.500 mol of potassium chlorate? 2 KClO3  2KCl + 3 O2 Step 3. Calculate the moles of O2, using the mole-ratio method. Step 4. Convert moles of O2 to liters of O2

The problem can also be solved in one continuous calculation. What volume of oxygen (at STP) can be formed from 0.500 mol of potassium chlorate? The problem can also be solved in one continuous calculation. 2 KClO3  2KCl + 3 O2

2 Al(s) + 6 HCl(aq)  2AlCl3(aq) + 3 H2(g) What volume of hydrogen, collected at 30.0oC and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? 2 Al(s) + 6 HCl(aq)  2AlCl3(aq) + 3 H2(g) Step 1 Calculate moles of H2. grams Al  moles Al  moles H2

Step 2 Calculate liters of H2. What volume of hydrogen, collected at 30.0oC and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? 2 Al(s) + 6 HCl(aq)  2AlCl3(aq) + 3 H2(g) Step 2 Calculate liters of H2. Convert oC to K: 30.oC + 273 = 303 K Convert torr to atm:

Solve the ideal gas equation for V What volume of hydrogen, collected at 30.0oC and 700. torr, will be formed by reacting 50.0 g of aluminum with hydrochloric acid? Solve the ideal gas equation for V PV = nRT

Volume-Volume Calculations

For reacting gases at constant temperature and pressure: Volume-volume relationships are the same as mole-mole relationships. H2(g) + Cl2(g)  2HCl(g) 1 mol H2 1 mol Cl2 2 mol HCl 22.4 L STP 22.4 L STP 2 x 22.4 L STP 1 volume 1 volume 2 volumes Y volume Y volume 2Y volumes

What volume of nitrogen will react with 600 What volume of nitrogen will react with 600. mL of hydrogen to form ammonia? What volume of ammonia will be formed? N2(g) + 3H2(g)  2NH3(g)

12.15 Real Gases

Ideal Gas An ideal gas obeys the gas laws. The volume the molecules of an ideal gas occupy is negligible compared to the volume of the gas. This is true at all temperatures and pressures. The intermolecular attractions between the molecules of an ideal gas are negligible at all temperatures and pressures.

Real Gases Deviations from the gas laws occur at high pressures and low temperatures. At high pressures, the volumes of the real gas molecules are not negligible compared to the volume of the gas At low temperatures, the kinetic energy of the gas molecules cannot completely overcome the intermolecular attractive forces between the molecules.

The End