Chapter 10 Gases: Their Properties and Behavior

Air Pressure & Shallow Wells Gases •Are mostly empty space • Occupy containers uniformly and completely • The densities of gases are much smaller than those of liquids and solid and highly variable depending on temperature and pressure Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density Expand infinitely • Diffuse and mix rapidly Lower density Higher density

Gases Pushing gas molecules are constantly in motion as they move and strike a surface, they push on that surface push = force if we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting pressure = force per unit area Unit area Force Pressure:

The Pressure of a Gas result of the constant movement of the gas molecules and their collisions with the surfaces around them the pressure of a gas depends on several factors number of gas particles in a given volume volume of the container average speed of the gas particles

Measuring Air Pressure Chemistry: McMurry and Fay, 6th Edition Chapter 9: Gases: Their Properties and Behavior Measuring Air Pressure 2/17/2019 8:23:36 AM Units Pa (SI unit) torr mm Hg atm bar Conversions 1 atm = 760 mm Hg (exact) 1 torr = 1 mm Hg (exact) 1 bar = 1 x 105 Pa (exact) 1 atm = 101 325 Pa Barometer 1 atm = 14.7 psi Copyright © 2011 Pearson Prentice Hall, Inc.

Gases and Gas Pressure Monometer Pgas < Patm Pgas = Patm - PHg Chemistry: McMurry and Fay, 6th Edition Chapter 9: Gases: Their Properties and Behavior 2/17/2019 8:23:36 AM Gases and Gas Pressure Monometer Pgas < Patm Pgas = Patm - PHg Pgas > Patm Pgas = Patm + PHg Copyright © 2011 Pearson Prentice Hall, Inc.

Atmospheric Pressure Effects differences in air pressure result in weather and wind patterns the higher up in the atmosphere you climb, the lower the atmospheric pressure is around you at the surface the atmospheric pressure is 14.7 psi, but at 10,000 ft it is only 10.0 psi rapid changes in atmospheric pressure may cause your ears to “pop” due to an imbalance in pressure on either side of your ear drum

Chapter 9: Gases: Their Properties and Behavior 2/17/2019 The Gas Laws Numerous observations made in late 1600s showed that the properties of any gas can be define by four variable: pressure (P), temperature (T), volume (V), and amount or the number of moles (n), and a gas whose behavior follows the laws exactly is called an ideal gas. The Ideal Gas Law, PV = nRT, - models the behavior of ideal gases. Other gas laws can be derived from the Ideal Gas Law for either one set of conditions or for two sets of conditions (initial and final conditions). Copyright © 2008 Pearson Prentice Hall, Inc.

Boyle’s law 1 V a (constant n and T) P Chemistry: McMurry and Fay, 6th Edition Chapter 9: Gases: Their Properties and Behavior Boyle’s law 2/17/2019 8:23:36 AM What would happen if you were to increase the pressure of the gas by pushing the piston? pressure of a gas is inversely proportional to its volume constant T and amount of gas as P increases, V decreases by the same factor a V P 1 (constant n and T) One goes up, the other one goes down. Two sets of conditions P1 x V1 = P2 x V2 Copyright © 2011 Pearson Prentice Hall, Inc.

Boyles’ Law and Breathing During an inhalation, the lungs expand. the pressure in the lungs decreases. air flows towards the lower pressure in the lungs.

Charles’s Law What would happen if you were to raise the temperature of the sample while letting the piston move freely to keep the pressure constant? In Charles’s Law, the Kelvin temperature of a gas is directly related to the volume. P and n are constant. when the temperature of a gas increases, its volume increases. V a T For two conditions, Charles’s law is written V1 = V2 (P and n constant) T1 T2

Charles’s Law Charles’s Law can be used to approximate absolute zero. At a temperature of absolute zero (0K), theoretically an ideal gas has no volume.

Chapter 9: Gases: Their Properties and Behavior Avogadro’s Law 2/17/2019 If 1 mole of gas occupies 22.4L, how much volume will be needed for 2 mole of gas? V a n (constant T and P) = nfinal Vfinal ninitial Vinitial One goes up, the other one goes up. Copyright © 2008 Pearson Prentice Hall, Inc.

Combined Gas Law The combined gas law is a combination of Boyle’s law, Charles’ laws and Gay-Lussac’s law to interrelate temperature, volume and pressure.

Chapter 9: Gases: Their Properties and Behavior 2/17/2019 The Gas Laws Ideal Gas: A gas whose behavior follows the gas laws exactly. The physical properties of a gas can be defined by four variables: P pressure (atm) T temperature (calculation must be in Kelvin) V volume (L) n number of moles The Ideal Gas Law, PV = nRT, To derive gas laws for two sets of conditions, solve the Ideal Gas Law for R PV ---- = R nT R = 0.08206 K mol L atm Copyright © 2008 Pearson Prentice Hall, Inc.

Examples A 0.250 mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas?

Example What volume is occupied by 25.7 g of carbon dioxide gas at 25.0oC and 371 torr?

Chapter 9: Gases: Their Properties and Behavior 2/17/2019 The Ideal Gas Law since the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions T = 0 °C (273.15 K) Standard Temperature and Pressure (STP) for Gases P = 1 atm Standard pressure is actually 1 bar. Gas law problems must use Kelvin!!!!!! (1 atm) (1 mol) 0.08206 K mol L atm (273.15 K) P nRT = = 22.41 L Copyright © 2008 Pearson Prentice Hall, Inc.

Molar Volume solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L 6.022 x 1023 molecules of gas we call the volume of 1 mole of gas at STP the molar volume it is important to recognize that one mole of different gases have different masses, even though they have the same volume

Example Assuming ideal behavior, which of the following gas samples will have the greatest volume at STP? 1 g H2 b. 1 g O2 c. 1 g Ar

Examples What is the volume occupied by 2.75 moles of N2 gas at STP?

Identifying an Unknown by Using Gas Density to Find Molar Mass An unknown gas found bubbling up in a swamp is collected, placed in a glass bulb, and found to have a density of 0.714 g/L at STP. What is the molar mass of the gas?

Stoichiometric Relationships with Gases in reactions of gases, the amount of a gas is often given as a volume the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio when gases are at STP, use 1 mol = 22.4 L P, V, T of Gas A mole A mole B P, V, T of Gas B

Stoichiometric Relationships with Gases The reaction used in the deployment of automobile airbags is the high-temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3? 2Na(s) + 3N2(g) 2NaN3(s)

Examples How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP? O2(g) + 2 H2(g) → 2 H2O(g)

Partial Pressure when gases are mixed together, their molecules behave independent of each other the pressure of a single gas in a mixture of gases is called its partial pressure we can calculate the partial pressure of a gas if the sum of the partial pressures of all the gases in the mixture equals the total pressure Dalton’s Law of Partial Pressures PT = P1 + P2 + P3 +....

Mole Fraction the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction, c the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure

Example Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

Examples 1.02 L of O2 collected over water at 293 K with the partial pressure of H2 at 17.55 mmHg and a total pressure of 755.2 mmHg. Find mass O2.