Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. 8.1 Properties of Gases Generally, molecules with fewer than five atoms from the first two periods in the periodic table are gases at room temperature. In addition, the following are also gases: H 2, N 2, O 2, F 2, and Cl 2 oxides of the nonmetals on the upper right corner of the periodic table: CO, CO 2, NO, NO 2, SO 2, and SO 3 noble gases Learning Goal Describe the kinetic molecular theory of gases and the units of measurement used for gases.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Kinetic Molecular Theory A gas consists of small particles that move rapidly in straight lines have essentially no attractive (or repulsive) forces are very far apart have very small volumes compared to the volume of the container they occupy have kinetic energies that increase with an increase in temperature

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Properties That Describe a Gas Gases are described in terms of four properties: pressure (P), volume (V), temperature (T), and amount (n).

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Volume The volume of a gas is the same as the volume of the container it occupies is usually measured in liters or milliliters increases with an increase in temperature at a constant pressure

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Temperature The temperature of a gas relates to the average kinetic energy of the molecules and is measured in the Kelvin (K) temperature scale. When the temperature of a gas is decreased, the molecules have fewer collisions increased, the molecules have more collisions

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Pressure Pressure is a measure of the gas particle collisions with sides of a container and is measured in units of millimeters of mercury (mmHg) or torr atmospheres (atm) pascals (Pa) or kilopascals (kPa) pounds per square inch (psi) Gas particles in the air exert pressure on us. It is called atmospheric pressure.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Barometers Measure Pressure A barometer measures the pressure exerted by the gases in the atmosphere indicates atmospheric pressure as the height in millimeters of the mercury column 760 mmHg = 1 atm = 760 torr The barometer was invented by Evangelista Torricelli. At exactly 1 atm, the barometer tube is exactly 760 mm high.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Atmospheric Pressure Atmospheric pressure is the pressure exerted by a column of air from the top of the atmosphere to the surface of Earth decreases as altitude increases is 1 atm at sea level

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Units for Measuring Pressure

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Altitude and Atmospheric Pressure Atmospheric pressure changes with variations in weather and altitude. On a hot, sunny day, the mercury column rises, indicating a higher atmospheric pressure. On a rainy day, the atmosphere exerts less pressure, which causes the mercury column to fall.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check 1. What is 475 mmHg expressed in atmospheres? A. 475 atm B atm C × 10 5 atm 2. The pressure in a tire is 2.00 atm. What is this pressure in millimeters of mercury? A mmHg B mmHg C mmHg

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution 1. What is 475 mmHg expressed in atmospheres? The answer is B, atm. 2.The pressure in a tire is 2.00 atm. What is this pressure in millimeters of mercury? The answer is B, 1520 mmHg.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check 1.The downward pressure on the Hg in a barometer is _____ the pressure of the atmosphere. A. greater than B. less than C. the same as 2.A water barometer is 13.6 times taller than a Hg barometer (d Hg = 13.6 g/mL) because A. H 2 O is less dense than mercury B. H 2 O is heavier than mercury C. air is more dense than H 2 O

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution 1. The downward pressure on the Hg in a barometer is _____ the pressure of the atmosphere. The answer is C, the same as. 2. A water barometer is 13.6 times taller than a Hg barometer (d Hg = 13.6 g/mL) because The answer is A, H 2 O is less dense than mercury.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. 8.2 Pressure and Volume: Boyle’s Law The inverse relationship between the pressure and volume of a gas is known as Boyle’s law. Changes occur in opposite directions. When volume increases, the pressure decreases provided the temperature and moles of the gas remain constant. Learning Goal Use the pressure–volume relationship (Boyle’s law) to determine the final pressure or volume when the temperature and amount of gas are constant.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Boyle’s Law Boyle’s law states that the pressure of a gas is inversely related to its volume when T is constant the product P × V is constant when temperature and amount of a gas are held constant if volume decreases, the pressure increases P 1 V 1 = P 2 V 2

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Boyle’s Law: PV = Constant Pressure × volume is a constant, provided that the temperature and amount of the gas remain the same. P 1 V 1 = 8.0 atm × 2.0 L = 16 atm L P 2 V 2 = 4.0 atm × 4.0 L = 16 atm L P 3 V 3 = 2.0 atm × 8.0 L = 16 atm L Boyle’s law can be stated as P 1 V 1 = P 2 V 2 (T is constant.)

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Chemistry Link to Health: Boyle’s Law and Breathing During an inhalation, the lungs expand the pressure in the lungs decreases air flows toward the lower pressure in the lungs

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Chemistry Link to Health: Boyle’s Law and Breathing During an exhalation, lung volume decreases pressure within the lungs increases air flows from the higher pressure in the lungs to the outside

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Guide to Using Gas Laws

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Boyle’s Law Freon-12, CCl 2 F 2, was used in refrigeration systems. What is the new volume of an 8.0-L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant temperature and moles? SOLUTION: STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P 1 = 550 mmHg P 2 = 2200 mmHg P increases PROBLEM V 1 = 8.0 L V 2 = ? V decreases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Boyle’s Law STEP 2 Rearrange the gas law equation to solve for the unknown quantity. P 1 V 1 = P 2 V 2 Boyle’s law To solve for V 2, divide both sides by P 2. STEP 3 Substitute values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? A mmHg B mmHg C mmHg

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P 1 = 600. mmHg P 2 = ? P decreases PROBLEM V 1 = 12.0 L V 2 = 36.0 L V increases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 2 Rearrange the gas law equation to solve for the unknown quantity.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 12.0 L at 600. mmHg. What is the new pressure when the volume changes to 36.0 L at a constant T and n? STEP 3 Substitute values into the gas law equation and calculate. The answer is A, 200. mmHg.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check For a cylinder containing helium gas, indicate whether cylinder A or cylinder B represents the new volume for the following changes. (n and T are constant.) 1. pressure decreases 2. pressure increases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution For a cylinder containing helium gas, indicate whether cylinder A or cylinder B represents the new volume for the following changes. (n and T are constant.) 1. pressure decreases cylinder B 2. pressure increases cylinder A

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? A.60 mL B.120 mL C.240 mL

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? STEP 1 Organize the data in a table of initial and final conditions. Temperature and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P 1 = 850 mmHg P 2 = 425 mmHg P decreases PROBLEM V 1 = 120 mL V 2 = ?V increases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution If a sample of helium gas has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure is changed to 425 mmHg at a constant T and n? STEP 2 Rearrange the gas law equation to solve for the unknown quantity. STEP 3 Substitute values into the gas law equation and calculate. The answer is C.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C?

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n are constant), is the new volume represented by A, B, or C? At a higher pressure (T and n constant), the new volume is represented by the smallest balloon, A.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. 8.3 Temperature and Volume: Charles’s Law If we increase the temperature of a gas sample, kinetic molecular theory states that the motion (kinetic energy) of the gas particles will also increase. If the amount and pressure of the gas is held constant, the volume of the container will increase. Learning Goal Use the temperature–volume relationship (Charles’s law) to determine the final temperature or volume when the pressure and amount of gas are constant.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Charles’s Law In Charles’s law, the Kelvin temperature of a gas is directly related to the volume pressure and moles of gas are constant when the temperature of a sample of gas increases, its volume increases at a constant pressure

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Charles’s Law: V and T For two conditions, Charles’s law is written (P and n are constant.) Rearranging Charles’s law to solve for V 2, we obtain the following:

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check Solve Charles’s law expression for T 2.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution Solve Charles’s law expression for T 2 : Cross-multiply to give the following: V 1 T 2 = V 2 T 1 Isolate T 2 by dividing through by V 1 :

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Charles’s Law A balloon has a volume of 785 mL at 21 °C. If the temperature drops to 0 °C, what is the new volume of the balloon at constant pressure and moles? SOLUTION: STEP 1 Organize the data into a table of initial and final conditions. Pressure and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE V 1 = 785 mL V 2 = ? V decreases PROBLEM T 1 = 21 °C = 294 K T 2 = 0 °C = 273 T decreases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Charles’s Law STEP 2 Rearrange to solve for unknown quantity, V 2. STEP 3 Substitute the values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in degrees Celsius) will the volume of the oxygen be 640 mL? (P and n are constant.) A. 443 °C B. 170 °C C. −82 °C

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in degrees Celsius) will the volume of the oxygen be 640 mL? (P and n are constant.) STEP 1 Organize the data into a table of initial and final conditions. Pressure and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE V 1 = 420 mL V 2 = 640 mL V increases PROBLEM T 1 = 18 °C = 291 K T 2 = ? T increases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in degrees Celsius) will the volume of the oxygen be 640 mL? (P and n are constant.) STEP 2 Rearrange to solve for unknown quantity, T 2. STEP 3 Substitute the values into the gas law equation and calculate. The answer is B.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check Use the gas laws to complete each sentence with increases or decreases. A.Pressure _______ when V decreases at a constant temperature and moles. B.When T decreases, V _______ at constant pressure and moles. C.Pressure _______ when V changes from 12 L to 24 L at constant temperature and moles. D.Volume _______when T changes from 15 °C to 45 °C at constant pressure and moles.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution Use the gas laws to complete each sentence with increases or decreases. A.Pressure increases when V decreases at constant temperature and moles. B. When T decreases, V decreases at constant pressure and moles. C. Pressure decreases when V changes from 12 L to 24 L at constant temperature and moles. D. Volume increases when T changes from 15 °C to 45 °C at constant pressure and moles.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. 8.4 Temperature and Pressure: Gay-Lussac’s Law Gay-Lussac’s law: When the Kelvin temperature of a gas doubles at constant volume and amount of gas, the pressure also doubles. Learning Goal Use the temperature–pressure relationship (Gay-Lussac’s law) to determine the final temperature or pressure when the volume and amount of gas are constant.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Gay-Lussac’s Law In Gay-Lussac’s law, the pressure exerted by a gas is directly related to the Kelvin temperature of the gas volume and amount of gas are constant

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check Solve Gay-Lussac’s law for P 2.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution Solve Gay-Lussac’s law for P 2. Multiply both sides by T 2 and cancel:

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Gay-Lussac’s Law A gas has a pressure at 2.0 atm at 18 °C. What is the new pressure when the temperature is 62 °C? (Volume and moles remain constant.) SOLUTION: STEP 1 Organize the data in a table of initial and final conditions. Volume and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P 1 = 2.0 atm P 2 = ? P increases PROBLEM T 1 = 18 °C T 2 = 62 °C T increases = 291 K = 335 K

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Gay-Lussac’s Law A gas has a pressure at 2.0 atm at 18 °C. What is the new pressure when the temperature is 62 °C? (Volume and moles remain constant.) STEP 2 Rearrange to solve for unknown quantity, P 2. Solve Gay-Lussac’s law for P 2 : STEP 3 Substitute the values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check A gas has a pressure of 645 torr at 128 °C. What is the temperature in degrees Celsius if the pressure increases to 824 torr? (V and n remain constant.)

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A gas has a pressure of 645 torr at 128 °C. What is the temperature in degrees Celsius if the pressure increases to 824 torr? (V and n remain constant.) STEP 1 Organize the data in a table of initial and final conditions. Volume and moles remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE P 1 = 645 torr P 2 = 824 torr P increases PROBLEM T 1 = 128 °C T 2 = ? T increases = 401 K

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A gas has a pressure of 645 torr at 128 °C. What is the temperature in degrees Celsius if the pressure increases to 824 torr? (V and n remain constant.) STEP 2 Rearrange to solve for unknown quantity, P 2. Solve Gay-Lussac’s law for T 2 : STEP 3 Substitute the values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check Explain why water boils at a lower temperature in the mountains than at sea level.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution Explain why water boils at a lower temperature in the mountains than at sea level. Atmospheric pressure in the mountains is less than at sea level. The vapor pressure of the water reaches the atmospheric pressure at a lower temperature.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. The Combined Gas Law The combined gas law uses the pressure–volume–temperature relationships from Boyle’s law, Charles’s law, and Gay-Lussac’s law where n is constant. Boyle’s law Charles’s law Gay-Lussac’s law Combined gas law

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Summary of Gas Laws

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35 °C and 646 mmHg pressure. What is the volume (in milliliters) of the gas at −95 °C and a pressure of 802 mmHg? (n is constant.) SOLUTION: STEP 1 Organize the data into a table of initial and final conditions. Moles of gas remain the same. ANALYZE Conditions 1 Conditions 2 THE P 1 = 646 mmHg P 2 = 802 mmHg PROBLEM V 1 = 675 mL V 2 = ? T 1 = 35 °C T 2 = − 95 °C = 308 K = 178 K

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Combined Gas Law A gas has a volume of 675 mL at 35 °C and 646 mmHg pressure. What is the volume (in milliliters) of the gas at −95 °C and a pressure of 802 mmHg? (n is constant.) STEP 2 Rearrange to solve for unknown quantity, V 2. STEP 3 Substitute the values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check A sample of helium gas has a volume of L, a pressure of atm, and a temperature of 29 °C. At what temperature (in degrees Celsius) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm? (n remains constant.)

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of helium gas has a volume of L, a pressure of atm, and a temperature of 29 °C. At what temperature (in degrees Celsius) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm? (n remains constant.) STEP 1 Organize the data into a table of initial and final conditions. Moles of gas remain the same. ANALYZE Conditions 1 Conditions 2 THE P 1 = atm P 2 = 3.20 atm PROBLEM V 1 = L (180 mL) V 2 = 90.0 mL T 1 = 29 °C T 2 = ? = 302 K

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of helium gas has a volume of L, a pressure of atm, and a temperature of 29 °C. At what temperature (in degrees Celsius) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm? (n remains constant.) STEP 2 Rearrange to solve for unknown quantity, T 2.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution A sample of helium gas has a volume of L, a pressure of atm, and a temperature of 29 °C. At what temperature (in degrees Celsius) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm? (n remains constant.) STEP 3 Substitute the values into the gas law equation and calculate.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. 8.6 Volume and Moles: Avogadro’s Law The molar volume of a gas at STP is about the same as the volume of three basketballs. The volume of 1 mole of gas is 22.4 liters. Learning Goal Use Avogadro’s law to calculate the amount or volume of a gas when the pressure and temperature are constant.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Avogadro’s Law: Volume and Moles In Avogadro’s law, the volume of a gas is directly related to the number of moles (n) of gas T and P are constant

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Avogadro’s Law If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume (in liters) will 1.2 moles of helium occupy at the same temperature and pressure? A L B. 1.8 L C. 2.4 L

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Avogadro’s Law If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume (in liters) will 1.2 moles of helium occupy at the same temperature and pressure? SOLUTION: STEP 1 Organize the data into a table of initial and final conditions. Pressure and temperature remain constant. ANALYZE Conditions 1 Conditions 2 Know Predict THE V 1 = 1.5 L V 2 = ? V increases PROBLEM n 1 = 0.75 mole n 2 = 1.2 moles n increases

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Avogadro’s Law If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume (in liters) will 1.2 moles of helium occupy at the same temperature and pressure? STEP 2 Rearrange to solve for unknown quantity, V 2. STEP 3 Substitute the values into the gas law equation and calculate. The answer is C.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Standard Temperature and Pressure The volumes of gases can be compared at STP, Standard Temperature and Pressure, when they have the same temperature standard temperature (T ) 0 °C or 273 K the same pressure standard pressure (P ) 1 atm (760 mmHg)

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Molar Volume, STP At standard temperature and pressure (STP), 1 mole of a gas occupies a volume of 22.4 L, which is called its molar volume. Use this equality as a conversion factor for gas at STP: 22.4 L = 1 mole gas

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Molar Volume

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Guide to Using Molar Volume

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Molar Volume What is the volume occupied by 2.75 moles of N 2 gas at STP? SOLUTION: STEP 1 State the given and needed quantities. Pressure and temperature remain constant. STEP 2 Write a plan to calculate the needed quantity. Moles N 2 Volume N 2 ANALYZE GIVEN NEED THE 2.75 moles N 2 gas Volume N 2 gas PROBLEM at STP at STP Molar Volume

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Calculations Using Molar Volume What is the volume occupied by 2.75 moles of N 2 gas at STP? STEP 3 Write conversion factors including 22.4 L/mole at STP. At STP, 22.4 L = 1 mole N 2 STEP 4 Set up the problem with factors to cancel units.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check 1. What is the volume at STP of 4.00 g of CH 4 ? A LB LC L 2. How many grams of He are present in 8.00 L of gas at STP? A gB gC g

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution STEP 1 State given and needed quantities. 1.What is the volume at STP of 4.00 g of CH 4 ? Pressure and temperature remain constant. 2. How many grams of He are present in 8.00 L of gas at STP? Pressure and temperature remain constant. ANALYZE GIVEN NEED THE 4.00 grams CH 4 (g) Volume CH 4 (g) PROBLEM at STP at STP ANALYZE GIVEN NEED THE 8.00 L He(g) grams of He(g) PROBLEM at STP at STP

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution STEP 2 Write a plan to calculate the needed quantity. 1.What is the volume at STP of 4.00 g of CH 4 ? mass CH 4 moles CH 4 volume CH 4 2.How many grams of He are present in 8.00 L of gas at STP? volume He moles He mass He Molar Mass Molar Volume Molar Volume Molar Volume Molar Volume Molar Mass

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution STEP 3 Write conversion factors including 22.4 L/mole at STP. 1. What is the volume at STP of 4.00 g of CH 4 ? 22.4 L = 1 mole of CH 4 1 mole of CH 4 = g CH 4

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution STEP 3 Write conversion factors including 22.4 L/mole at STP. 2. How many grams of He are present in 8.00 L of gas at STP? 1 mole of He = 4.00 g He 22.4 L = 1 mole of He

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution STEP 4 Set up the problem with factors to cancel units. 1. What is the volume at STP of 4.00 g of CH 4 ? The answer is A, 5.60 L. 2. How many grams of He are present in 8.00 L of gas at STP? The answer is C, 1.43 g.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Partial Pressure The partial pressure of a gas is the pressure that each gas in a mixture would exert if it were by itself in the container. Core Chemistry Skill Calculating Partial Pressure

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Dalton’s Law of Partial Pressures Dalton’s law of partial pressures indicates that pressure depends on the total number of gas particles, not on the types of particles the total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases P T = P 1 + P 2 + P

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Total Pressure For example, at STP, 1 mole of a pure gas in a volume of 22.4 L will exert the same pressure as 1 mole of a gas mixture in 22.4 L. Gas mixtures 1.0 mole N mole O mole He 1.0 mole 0.5 mole O mole He 0.2 mole Ar 1.0 mole 1.0 atm

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Air is a Mixture of Gases The air we breathe is a mixture of different gases contains mostly N 2 and O 2, and small amounts of other gases What we call the atmospheric pressure is actually the sum of the partial pressures of the gases in the air.

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Guide to Solving for Partial Pressure

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solving for Partial Pressure A scuba tank contains O 2 with a pressure of atm and He at 855 mmHg. What is the total pressure, in millimeters of mercury, in the tank? (Volume and temperature are constant.) SOLUTION: STEP 1 Write the equation for the sum of the partial pressures. P total = P O 2 + P He STEP 2 Rearrange the equation to solve for the unknown pressure. Convert units to match. P total = P O 2 + P He

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solving for Partial Pressure A scuba tank contains O 2 with a pressure of atm and He at 855 mmHg. What is the total pressure, in millimeters of mercury, in the tank? (Volume and temperature are constant.) STEP 3 Substitute known pressures and calculate the unknown partial pressure. P total = P O 2 + P He P total = 342 mmHg mmHg = 1.20 × 10 3 mmHg

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Study Check For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium? (Volume and temperature are constant.) A. 520 mmHg B mmHg C mmHg

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium? (Volume and temperature are constant.) STEP 1 Write the equation for the sum of the partial pressures. P total = P O 2 + P He STEP 2 Rearrange the equation to solve for the unknown pressure. Convert units to match. P He = P total − P O 2

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Twelfth Edition© 2015 Pearson Education, Inc. Solution For a deep dive, a scuba diver uses a mixture of helium and oxygen with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mmHg, what is the partial pressure of the helium? (Volume and temperature are constant.) STEP 3 Substitute known pressures and calculate the unknown partial pressure. P He = 6080 mmHg – 1280 mmHg = 4800 mmHg The answer is C, 4800 mm Hg.