Gas Law and Gas Behavior Meyer 2014 Ch. 12 and 13

Characteristics of Gases Gases are highly compressible and occupy the full volume of their containers. Gases exert pressure, P = F/A (force/area). Gases always form homogeneous mixtures with other gases. Actual gas atoms and molecules only occupy about 0.1 % of the volume of their containers.

The Composition of the Atmosphere Dry Atmosphere at Sea Level (% by Volume) Nitrogen 78.084 Oxygen 20.948 Argon 0.934 Carbon dioxide 0.033 Neon 0.00182 Hydrogen 0.0010 Helium0.0052 Methane 0.0002* Krypton 0.0001 Xenon 0.000008 Carbon monoxide, ozone, ammonia, nitrogen dioxide, sulfur dioxide <0.00001* * = variable depending upon pollution Water content in the atmosphere is variable in actual contexts, ranging to over 5% in hot steamy climates to <<1% in dry arid environments.

A Mercury Barometer The pressure exerted by the column of mercury … … must be the same as that exerted by the atmosphere.

Pressure Atmospheric Pressure and the Barometer . Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column. Units: 1 atm = 760 mmHg 760 torr 1.013  105 Pa 101.3 kPa 1000 Pa = 1kPa

Practice 456 Torr = ___?___ Atm 1689 mmHg= ___?___ Torr 156kPa = __?__ Atm .

Boyle’s Law: Pressure-Volume Relationship For a fixed amount of a gas at constant temperature, the volume of the gas varies inversely with its pressure. For a fixed amount of a gas at constant temperature, the product of pressure and volume is a constant. If you squeeze (increase pressure) a balloon gets smaller (volume decreases) P V or V P P1V1=P2V2 PinitialVinitial = PfinalVfinal

Example A helium-filled party balloon has a volume of 4.50 L at sea level, where the atmospheric pressure is 782 Torr. Assuming that the temperature remains constant, what will be the volume of the balloon when it is taken to a mountain resort at an altitude of 2500 m, where the atmospheric pressure is .89 Atm?

Charles’s Law: Temperature-Volume Relationship The volume of a fixed amount of a gas at constant pressure is directly proportional to its Kelvin (absolute) temperature. Absolute zero is the temperature obtained by extrapolation to zero volume. Absolute zero on the Kelvin scale = –273°C

Absolute Zero Absolute temperature is measured in Kelvin Never be a negative Kelvin Absolute zero is zero (0) Kelvin or -273 degrees C Molecular motion stops Degree C + 273 = Degree K

Charles’s Law: Temperature-Volume Relationship If the temperature goes up a balloon expands If the temperature goes down a balloon contracts T must be in Kelvin

Example A weather balloon has a volume of 900 liters at 25 degrees C. What would the volume be if the same balloon was -45 degrees C?

Gay Lussac’s Law: Temperature-Pressure Relationship If the temperature goes up the pressure goes up If the temperature goes down the pressure goes down T must be in Kelvin

Example A coke can has a pressure of 1.1 atm at 25 degrees C what would the pressure be if you left the coke can in your car and it warmed to 125 degree C?

Standard Temperature and Pressure: STP We define STP (Standard Temperature and Pressure) = 0C (273 K) = 1 atm STP is used often and represents a standard condition which gases can be compared to each other

The Combined Gas Law: Temperature-Pressure Relationship Puts the first three gas laws together in one law Allows for all three variables to be changed at once T must be in Kelvin

Example A pump is attempting to compress propane gas. The propane has an initial volume of 2500 liters, temperature of 30 degree C, and a pressure of one atm. If the pump manages to compress the propane to 1000 liters at 2.5 atm what is the temperature of the propane gas?

Example (opener) If a balloon contains 50 liters of gas at 25 degrees C and 1200 mmHg what would the volume of the gas be at STP?

Mixtures of Gases: Dalton’s Law of Partial Pressures Dalton’s law of partial pressures is used in dealing with mixtures of gases. The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the separate gases: Ptotal = P1 + P2 + P3 + … Partial pressure: the pressure a gas would exert if it were alone in the container.

Example The gases in a light bulb are at STP. If a light bulb contains three gases, xenon at a pressure of 450 mmHg, argon at a pressure of 50 mmHg, and neon gas. What is the pressure of the neon gas in atm?

Gas Mixtures and Partial Pressures Collecting Gases over Water

Water Vapor -Water vapor is a problem -The pressure of the water vapor changes with temperature -Must look up vapor pressure of water on a chart (refer to handout) Temperature (˚C) Vapor Pressure (mmHg) 19 16.5 20 17.54 21 18.7 22 19.8 23 21.1 24 22.4 25 23.8 26 25.2

Example Suppose that 120 ml of argon is collected over water at 22 degree C and the total pressure is 780 torr. Calculate the pressure of the dry argon gas?

The Ideal Gas Law: Adding Moles to the Gas Laws Ideal gas equation: PV = nRT R = gas constant = 0.08206 L•atm/mol-K V must be in Liters P must be in Atm T must be in Kelvin

Example If Emily had 1.4 moles of propane in a one liter bottle at 30 degrees C what is the pressure?

Example A helium balloon has a volume of 12 liters at a temperature of 20 degrees C and 749 mmHg. How many grams of helium are in the balloon?

Example Amy the adventurous astronaut needed an oxygen tank that contained 40 moles of oxygen at STP. What is the volume of the tank? (liters)