Houston Community College System Chemistry 1405 Chapter 5 The Physical Properties of Gases By Mounia Elamrani Blei / Odian ’ s General, Organic, and Biochemistry

Mounia ElamraniChapter 5 –The Physical Properties of Gases2 Objectives What is gas pressure and how is it measured? Describing the physical behavior of gases using gas laws Applying the gas laws Properties of gas mixtures Using gas laws to determine the molar mass Gases that dissolve in liquids

Mounia ElamraniChapter 5 –The Physical Properties of Gases3 5.1 Gas Pressure What gases are important for each of the following: O 2, CO 2 and/or He? A. B. C. D.

Mounia ElamraniChapter 5 –The Physical Properties of Gases4 Some Gases in Our Lives Air: oxygen O 2 nitrogen N 2 ozone O 3 argon Ar carbon dioxide CO 2 water H 2 O Noble gases: helium He neon Ne krypton Kr xenon Xe Other gases: fluorine F 2 chlorine Cl 2 methane CH 4 carbon monoxide CO nitrogen dioxide NO 2 sulfur dioxide SO 2 ammonia NH 3

Mounia ElamraniChapter 5 –The Physical Properties of Gases5 The Nature of Gases 1.Why can you put more air in a tire, but can ’ t add more water to a glass full of water? Gases are compressible 2. Why does a round balloon become spherical when filled with air? Gases fill a container completely and uniformly 3. Suppose we filled this room halfway with water. Where would pressure be exerted? Gases exert a uniform pressure on all inner surfaces of their containers 4. Gases have low densities D (solid or liquid) = 2 g/mL D (gas)= 2 g/L

Mounia ElamraniChapter 5 –The Physical Properties of Gases6 Barometers Pressure = Force / Area 760 mmHg 1 atm = 760 torr = 760 mm Hg Calculate:a) the pressure in atm of 563 mm Hg, b) the equivalent of atm in mm Hg and torr One atmosphere (1 atm) is the average pressure of the atmosphere at sea level and is the standard unit for pressure

Mounia ElamraniChapter 5 –The Physical Properties of Gases7 5.2 The Gas Laws Physical properties of gases depend on: Pressure (P) Volume (V) Absolute Temperature (T) Amount of gas in moles (n) The gas laws describe the behavior of gases in certain conditions, using only P, V, T, and n.

Mounia ElamraniChapter 5 –The Physical Properties of Gases8 5.2 The Gas Laws Pressure and Volume (Boyle ’ s Law) Temperature and Volume (Charles ’ Law) Temperature and Pressure (Gay-Lussac ’ s Law)

Mounia ElamraniChapter 5 –The Physical Properties of Gases9 5.3 Boyle ’ s Law: Pressure and Volume P1P1 P2P2 V1V1 V2V2

Mounia ElamraniChapter 5 –The Physical Properties of Gases Boyles ’ s Law: Pressure and Volume ExperimentPressureVolume P x V (atm) (L) (atm x L) _____ _____ _____ P1 x V1= 8.0 atm x 2.0 L = 16 atm L P2 x V2= 4.0 atm x 4.0 L = 16 atm L P1 x V1 = P2 x V2 = k

Mounia ElamraniChapter 5 –The Physical Properties of Gases Boyle ’ s Law: Pressure and Volume Boyle's Law: The pressure of a gas is inversely related to the volume when T does not change. Then the PV product remains constant: P x V = k (constant) when T remains constant Use this equation to calculate: - how a volume changes when pressure changes, or - how pressure changes when volume changes. new vol. = old vol. x Pfactor new P = old P x Vfactor

Mounia ElamraniChapter 5 –The Physical Properties of Gases12 PV Calculation Freon-12, CCl 2 F 2, is used in refrigeration systems. What is the new volume (L) of a 1.6 L sample of Freon gas initially at 50 mm Hg after its pressure is changed to 200 mm Hg at constant T? DATA TABLE Initial conditionsFinal conditions P 1 = 50 mm HgP 2 = 200 mm Hg V 1 = 1.6 LV 2 = ? ?

Mounia ElamraniChapter 5 –The Physical Properties of Gases13 Find New Volume (V2) Solve for V 2 : P 1 V 2 = P 2 V 2 V 2 = V 1 x P 1 /P 2 V 2 = 1.6 L x 50 mm Hg = 0.4 L 200 mm Hg

Mounia ElamraniChapter 5 –The Physical Properties of Gases14 Exercise A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T constant) Explain. 1) 3.2 L2) 6.4 L3) 12.8 L Problem 5.3 a 1.80L sample of gas at atm must be compressed to 1.40L at constant temperature. What pressure in atmospheres needs to be exerted to bring it to that volume?

Mounia ElamraniChapter 5 –The Physical Properties of Gases Charles ’ Law V = 125 mL V = 250 mL T = 273 K T = 546 K Observe the V and T of the balloons. How does volume change with temperature? At constant pressure, the volume of a gas is directly related to its absolute (K) temperature:

Mounia ElamraniChapter 5 –The Physical Properties of Gases16 Exercise A. Use Charles’ Law to complete the statements below: 1. If final T is higher than initial T, final V is (greater, or less) than the initial V. 2. If final V is less than initial V, final T is (higher, or lower) than the initial T. B. A balloon has a volume of 785 mL on a Fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon? C. A sample of oxygen gas has a volume of 420 mL at a temperature of 18°C. What temperature (in °C) is needed to change the volume to 640 mL?

Mounia ElamraniChapter 5 –The Physical Properties of Gases Gay-Lussac ’ s Law: P and T The pressure exerted by a confined gas is directly related to the temperature (Kelvin) at constant volume. P (mm Hg)T (°C) When temperature decreases, the pressure of a gas (decreases or increases). 2. When temperature increases, the pressure of a gas (decreases or increases).

Mounia ElamraniChapter 5 –The Physical Properties of Gases18 P and T Problem A gas has a pressure at 2.0 atm at 18°C. What will be the new pressure if the temperature rises to 62°C? (V constant) T 1 = 18°C T 2 = 62°C

Mounia ElamraniChapter 5 –The Physical Properties of Gases19 Learning Check GL6 Complete with: 1) Increases 2) Decreases3) Does not change A. Pressure _____, when V decreases B. When T decreases, V _____. C. Pressure _____ when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume _____when T changes from 15.0 °C to 45.0°C (constant P and n)

Mounia ElamraniChapter 5 –The Physical Properties of Gases Avogadro ’ s Law: Volume and Moles How does adding more molecules of a gas change the volume of the air in a tire? When a gas is at constant T and P, the V is directly proportional to the number of moles (n) of gas

Mounia ElamraniChapter 5 –The Physical Properties of Gases The Combined Gas Law Combining these different equations gives us the Combined Gas Law

Mounia ElamraniChapter 5 –The Physical Properties of Gases22 Combined Gas Law Problems Use the combined gas law to solve problems that give the same substance in 2 sets of conditions: 1. Set up a data table 2. Write an equation that will solve for the unkown 3. Do the math and record your answer with proper sig. fig. A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? A gas has a volume of 675 mL at 35°C and atm pressure. What is the temperature in °C when the gas has a volume of L and a pressure of 802 mm Hg?

Mounia ElamraniChapter 5 –The Physical Properties of Gases The Universal Gas Law Combining all the gas laws results in the: Universal Gas Law

Mounia ElamraniChapter 5 –The Physical Properties of Gases24 Standard Temperature and Pressure (STP) The volumes of gases can be compared when they have the same temperature and pressure (STP). Standard temperature:0°C or 273 K Standard pressure:1 atm (760 mm Hg) At STP, 1 mole of any gas has a volume of 22.4 L Molar Volume = 22.4L The ideal gas constant is then determined to be:

Mounia ElamraniChapter 5 –The Physical Properties of Gases25 Exercises Problem 5.9: Exhaled air contains CO 2 at a pressure of 28.0 torr. The capacity of a human lung is about 3.00L. Body temperature is 37.0 °C. Calculate the mass of CO 2 in the lung before expiration. Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mmHg) in the tank in the dentist office?

Mounia ElamraniChapter 5 –The Physical Properties of Gases The Universal Gas Law and Molecular Mass The relationship between moles and mass through molar mass gives us a new equation relating gas laws and molecular mass: Solving for (M) gives: D=density of the gas

Mounia ElamraniChapter 5 –The Physical Properties of Gases27 Exercises Problem 5.10: The density of O 2 at 15.0°C and 1.00 atm is 1.36 g/L. Calculate its molecular mass. Problem 5.11: Determine the molecular ass of argon, when 14.10g of argon occupies L at STP.

Mounia ElamraniChapter 5 –The Physical Properties of Gases Daltons ’ Law of Partial Pressures Partial Pressure is: The pressure each gas in a mixture would exert if it were the only gas in the container Dalton's Law of Partial Pressures states that: The total pressure exerted by a gas mixture is the sum of the partial pressures of the gases in that mixture. P Total = P 1 + P 2 + P

Mounia ElamraniChapter 5 –The Physical Properties of Gases29 Gases in the Air The % of gases in air Partial pressure (STP) 78.08% N mmHg 20.95% O mmHg 0.94% Ar 7.1 mmHg 0.03% CO mmHg P AIR = P N2 + P O2 + P Ar + P CO2 = 760 mmHg

Mounia ElamraniChapter 5 –The Physical Properties of Gases30 Partial Pressures The total pressure of a gas mixture depends on the total number of gas particles, not on the types of particles. 0.5 mole O mole He mole Ar 1 mole H 2 P = 1 atm

Mounia ElamraniChapter 5 –The Physical Properties of Gases31 Exercises A. If the atmospheric pressure today is 745 mm Hg, what is the partial pressure (mm Hg) of O 2 in the air? 1) ) 156 3) 760 B. At an atmospheric pressure of 714, what is the partial pressure (mm Hg) N 2 in the air? 1) 557 2) 9.143) Problem 5.13: Hydrogen was collected over water at 25.0°C and a total pressure of 755 torr. The vapor pressure of water at that temperature is 23.8 torr. The amount of hydrogen collected was mol. What was the volume of the gas?

Mounia ElamraniChapter 5 –The Physical Properties of Gases Henry ’ s Law: Gases Dissolve in Liquids Some gases can dissolve in water The amount of gas dissolved increases when the (partial) pressure of the gas increases: C H = Henry ’ s law constant is specific to each gas at a specific temperature, and has units of:

Mounia ElamraniChapter 5 –The Physical Properties of Gases33 Exercises Problem 5.14: The C H for pure nitrogen in water at 20.0°C and 1.00 atm pressure of N 2 is: mL N 2 /mL H 2 O. Calculate its solubility in water at that temperature and pressure. Problem 5.15: The solubility of pure nitrogen in water at 20.0°C and 1.00 atm pressure of N 2 is: mL N 2 /mL H 2 O. It constitutes about 80% of air. Calculate its solubility when air is in contact with water at 20.0°C and 1.00 atm of pressure.

Mounia ElamraniChapter 5 –The Physical Properties of Gases34 End of Chapter Problems 5.2b, , 5.14, 5.16, 5.20, 5.26, , 5.34, 5.36