Gas Laws Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Congratulations….you’re almost there! We’re almost to the end of HONORS CHEMISTRY!

Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. 5.1 Physical Characteristics of Gases

An “IDEAL” Gas An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.internal energytemperature

The Gas Laws There are FOUR variables needed to define the state of a gas: 1. Temperature (T) in Kelvin 2. Volume (V) 2. Volume (V) 3. Pressure (P) 4. Amount of gas in sample

Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = kPa (kilopascal) 5.2 Barometer Pressure = Force Area (force = mass x acceleration) Force is measured in NEWTONS (N)

Example: 0.45 atm = ________mmHg 795 torr = ____________atm 1200 mmHg = __________atm

Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm 5.2

Temperature Conversions When doing gas law problems, convert temperature to Kelvin (K) K = ºC Examples: A. 83.4ºC = ? K B. 460K = ? ºC

5 Simple Rules for solving Gas Law problems: 1.List everything you are given 2.Determine what is unknown 3.Convert any numbers that need to have specific units (ex. °C to K) 4.Plug in all known values 5.Solve for the unknown

Boyle's Law- Pressure-Volume Relationship The volume of a fixed amount of gas is inversely proportional to the pressure (assumes temp. constant)  High Pressure = Lower Volume  Low Pressure = Larger Volume P 1 V 1 = P 2 V 2

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg 5.3

Charles's Law- Temperature-Volume Relationship The volume of a fixed amount of gas is directly proportional to its temperature – (must be Kelvin temp. scale and assumes P stays constant)  As temperature increases, volume increases  As temperature decreases, volume decreases V 1 /T 1 = V 2 /T 2

As T increasesV increases 5.3

A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V L x K 3.20 L = = 192 K 5.3 V 1 /T 1 = V 2 /T 2 T 1 = 125 ( 0 C) (K) = K

Combined Gas Law Use when the number of moles of gas DO NOT change but pressure, temperature, and/or volume change. P 1 V 1 = P 2 V 2 T 1 T 2

Example: A sample of neon occupies 200mL at 100ºC. Find its volume at 0ºC assuming the pressure remains constant. T 1 =100ºC = K V 1 = 200 ml T 2 = 0ºC = K V 2 = ?

STP STP stands for Standard Temperature and Pressure At STP – Temperature = 0ºC = K – Pressure = 1 atm

Example: A sample of SO 2 at 18 o C and 1.95 atm occupies a volume of 5L. Calculate the volume at STP.

Avogadro's Law- Quantity-Volume Relationships The volume of a gas is directly proportional to the number of moles of the gas – provided temp. and pressure remains constant.  As moles increase, volume increases  As moles decrease, volume decreases

Ideal Gas Equation 5.4 Charles’ law: V  T  (at constant n and P) Avogadro’s law: V  n  (at constant P and T) Boyle’s law: V  (at constant n and T) 1 P V V  nT P V = constant x = R nT P P R is the gas constant = L ∙ atm/Mol ∙ K PV = nRT α means is proportional to

What is the volume (in liters) occupied by 0.4 moles of HCl at STP? PV = nRT V = nRT P V = 5.4

Example: How many moles of gas are present in a 1L container with a pressure of 0.95 atm and a temperature of 12°C?

Gas Stoichiometry In a combustion reaction, 15.0 L of ethane gas (C 2 H 6 ) are completely burned at an atmospheric pressure of 115 kPa and temperature of 452 K. Calculate the moles of carbon dioxide produced. 2C 2 H O 2 → 4 CO H 2 O

Gas Stoich Important Question: Is the Reaction STP? Why? STP then remember….22.4L = 1 mole If NOT then…..PV=nRT

Gas Stoichiometry What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 12 O 6 mol C 6 H 12 O 6 mol CO 2 V CO g C 6 H 12 O 6 1 mol C 6 H 12 O g C 6 H 12 O 6 x 6 mol CO 2 1 mol C 6 H 12 O 6 x = mol CO 2 V = nRT P mol x x K Latm molK 1.00 atm = = 4.76 L 5.5

Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)? PV = nRT n, V and R are constant nR V = P T = constant P1P1 T1T1 P2P2 T2T2 = P 1 = 1.20 atm T 1 = 291 K P 2 = ? T 2 = 358 K P 2 = P 1 x T2T2 T1T1 = 1.20 atm x 358 K 291 K = 1.48 atm 5.4

In a combustion reaction, 15.0 L of ethane gas (C 2 H 6 ) are completely burned at an atmospheric pressure of 115 kPa and temperature of 452 K. Calculate the liters of carbon dioxide produced. 2C 2 H O 2 → 4 CO H 2 O Vs In a combustion reaction, 15.0 L of ethane gas (C 2 H 6 ) are completely burned at STP. Calculate the liters of carbon dioxide produced. 2C 2 H O 2 → 4 CO H 2 O

Graham’s Law helps us compare the effusion/diffusion rates of two gasses Can substitute density for molar masses The rate ratio has no unit of measurement – Although rate is usually in m/s

What is Diffusion?? Molecules move from a high pressure location to a low pressure location The perfume diffuses because when it is sprayed, a high pressure area is created. Thus, the molecules slowly distribute to a low pressure area, distributing molecules evenly across the room. Other examples of this would be: – A sugar cube in a glass of water (unstirred), the sugar will distribute throughout the water to become sugar water. – Heat diffuses through the walls of a mug of hot chocolate

What is Effusion? Effusion is the process of when gas molecules escape through their container through tiny holes. – From a high pressure place to a low pressure place The Lighter the molecule, the faster it effuses

Example 2 Which is faster ? Carbon dioxide exiting a balloon or helium exiting a balloon?

Example 6 Which is faster? Nitrogen oxide (NO) or Hydrogen chloride?

Example 3 How much faster is Argon than Krypton?

Example 5 How much faster does Helium effuse than Krypton?

Example 7 How much faster is the rate of Nitrogen gas than Oxygen?

Example 4 Determine the speed of Xenon particles if Radon particles move at m/s

Example Determine the speed of hydrogen gas molecules if oxygen gas molecules travel at 25.0 m/s.

Hydrochloric gas is produced in a chemical laboratory. The chemist produced a total of 8.2 atm of HCl. If there were 1520 torr of Chlorine gas, what is the partial pressure of the Hydrogen gas, in kPa?

Example 2 You are filling a balloon with air (N 2, O 2, He). If you have 7 atm of Oxygen, 380 torr Helium, and 380 mm Nitrogen, how many kPa would make up the total pressure of the balloon?