Kinetic Molecular Theory and Gas Law Honors Packet. Name: Period: Date: Requirements for honors credit: Read all notes in packet

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1 Kinetic Molecular Theory and Gas Law Honors Packet Name: Period: Date: Requirements for honors credit: Read all notes in packet Watch the 10 Brighstorm videos shown on the right and take Cornell notes on separate sheets of paper and attach to packet. o Cornell notes must have 3 questions on side and a summary on the bottom for credit Do all problems Come see me in office hours for a minimum of 2 times to ask me questions, work on problems, and/or clarify concepts. Office hour visit 1: Date: Office hour visit 2: Date:

2 Kinetic Molecular Theory Notes Before you begin your studies of Kinetic Molecular Theory, you need to know what the word means. Kinetic refers to things in motion; molecular deals with molecules; a theory is a hypothesis that has been supported with experimental evidence. Now, we need to define terms. You know what these terms are, but for the discussion of this unit, we will define them differently than normal. Temperature is a measure of the average kinetic energy of the molecules in a sample. Since KE = ½ mv 2, the change in temperature of a sample is caused by a change in velocity (speed) of the molecules in that sample. Volume of a sample is the space that the particles take up (not much differently than it is normally thought of). Pressure of a gas sample is caused by the molecules of that sample colliding with the walls of the container. Pressure = Force / Area, so in order for a gas to exert more pressure on its container, there must be more collisions or more forceful collisions. Kinetic Molecular Theory is guided by the following assumptions: 1. The molecules of an ideal gas (an ideal gas is a gas that follows the assumptions of kinetic molecular theory) are in constant, random, straight-line motion. Gas molecules are constantly moving very, very fast and their direction is completely random. They move in straight lines within their container. 2. The molecules in an ideal gas can be considered dimensionless points. This assumption can be made because molecules are very, very small compared with the empty space in a gas sample. Therefore, you can assume that the volume of a gas sample is equal to the size of the container that it is held. 3. The collisions between molecules in an ideal gas with each other and the walls of its container are completely elastic. Elastic collisions mean that no energy is lost or gained when the molecules collide. 4. There are no attractive or repulsive forces in an ideal gas. This means that the molecules of an ideal gas do not like or hate each other, they are indifferent. If they pass by another gas molecule, they don t even notice them, they just go about their business. This assumption is totally false, but 2

3 as long as the molecules of the gas have plenty of space, they really won t interact with each other. Consequences of KMT (Kinetic Molecular Theory) When gas molecules follow these rules, the gas is said to be ideal. Most gases are ideal and will follow these rules. The only conditions under which these assumptions fail is when the gas sample is either under high pressure or at low temperatures. When a gas is compressed under high pressure, the gas is no longer mostly empty space, so assumption number 2 fails and the gas will condense to a liquid. When a gas is at low temperature, the molecules are moving slowly enough that they notice each other and assumption number 4 fails. Once the gas molecules realize that they are not alone, they start to feel attractive and/or repulsive forces and they will condense to a liquid. Scientists and Gas Laws Scientists started to conduct experiments with gases and they came up with equations to describe the relationships between the variables, temperature, volume, pressure, and moles of gas. Once you understand the assumptions of KMT and the definitions of the variables, the relationships make sense. Here are the scientists and their laws: Boyle s law If you hold temperature and the amount of molecules in a gas sample constant, the pressure of a sample of gas is inversely proportional to the volume. In equation form this law is P x V = Constant number. In English: If the speed of the molecules in a gas doesn t change (Temperature constant), if you change the amount of space the molecules have, you will change the amount of times they collide with the walls of the container. If you have less space, you have more collisions and vice versa. Charles Law If you hold the pressure and amount of molecules in a gas sample constant, the volume of a sample of gas is directly proportional to the temperature. In equation form this law is V/T = Constant number. In English: If the frequency of the molecules collisions with the walls doesn t change (Pressure constant), a change in the speed of the molecules requires a change in the amount of space they take up. If the molecules move faster, they need more room and vice versa. Gay-Lussac s Law If you hold the volume and amount of molecules in a gas sample constant, the pressure of a sample of gas is directly proportional to the temperature. In equation form this law is P/T = Constant number. 3

4 In English: If the amount of space doesn t change (Volume constant), a change in the speed of the molecules will result in a change in the collisions with the walls of the container. If the molecules move faster, they will hit the walls more often and with more force and vice versa. Avogadro s Law If you hold the temperature and pressure of a gas sample constant, the volume of a gas sample is directly proportional to the number of molecules. In equation form this law is V/n = Constant number. In English: If the speed of the molecules and the number of collisions with the walls of the container doesn t change, when you change the amount of molecules, the amount of space they take up will change. If you add more molecules, they take up more space and vice versa. Can you combine them? If you combine all of the gas laws together, you get a gas law for all situations, as long as the gas behaves ideally. Strangely, chemists refer to this law as the ideal gas law. P x V = n x R x T Pressure times Volume = amount of moles times the Ideal Gas Constant times Kelvin Temperature. The Ideal Gas Constant is located on the back of your periodic table. In fact, a summary of gas laws is located on the back of the periodic table. R = L atm/mol K OR 8.31 J/mol K L = Liters, atm = atmospheres, mol = moles, K = Kelvin, J = Joules = Liters x kilopascals The key for gas law calculations is to keep the units the same. So, you need to know what the different units for each variable are and how to convert between them. Pressure Atmospheres this unit is abbreviated (atm) and was invented to be the standard unit for pressure. Standard pressure is defined as 1 atmosphere. Pascals this unit is abbreviated (Pa) and is the force of 1 ant doing one push-up. You will see kilopascals used more often. Standard pressure is equal to kpa. Pounds per square inch this unit is abbreviated (psi) and is commonly used in the English system. Standard pressure is equal to 14.7 psi. Barometric height a barometer is used to measure atmospheric pressure. For a barometer, you measure the height of air supported by a column of mercury. Standard pressure is 760 mm Hg or inches Hg. 4

5 Volume Liters this is pretty much the only unit we will use for volume (L) Temperature Fahrenheit this is what we use in America, but no one else does. Celsius is more often used. Here s the equation to convert from Fahrenheit to Celsius: 0 C = 5/9( 0 F 32) Celsius this is the standard international unit for temperature. If you want to convert from Celsius to Fahrenheit: 0 F = 9/5 0 C + 32 Kelvin this is the unit you will use for gas law calculations. Kelvin is based on absolute zero, which is the temperature where all molecular motion will theoretically stop. A unit of Kelvin is equal to one degree Celsius, but they have different starting points for the scale. To convert from Celsius to Kelvin: K = 0 C

6 So now what to use it for (Sample Gas Law Calculations) Here are the equations you will use for these problems: Boyle s law: Charles Law: Gay-Lussac s Law: Avogadro s Law: P1V1 = P2V2 Ideal Gas Law: PV = nrt V1/T1 = V2/T2 P1/T1 = P2/T2 V1/n1 = V2/n2 Combined Gas Law: P1V1/T1 = P2V2/T2 1. A gas sample has a volume of 150 ml when the pressure is 135 kpa. If the temperature and amount of gas remains constant, what volume will the gas sample occupy at a pressure of 180 kpa? In order to do any gas law calculation, you need to identify the variables involved in the problem. Then you can determine the gas law that applies to the problem. The variables for this problem are: V1 = 150 ml P1 = 135 kpa P2 = 180 kpa V2 =? Now you can see that you will use Boyle s law for this problem. Set the unknown equal to X and solve for it, using the algebra you learned in middle school. P1V1 = P2V2 (135 kpa)(150 ml) = (180 kpa)x Divide both sides by 180 kpa to get X by itself. (135)(150)/(180) = X Punch the numbers into your calculator and you will have the answer. Only use as many digits (numbers) as you were given in the problem. X = 113 ml I rounded the number from because there were three digits in the numbers that were given to me in the problem. 6

7 More sample problems 2. A 600 ml sample of gas is collected at a room temperature of 27 0 C. What volume will the sample have at C assuming the pressure of the gas remains constant? Start by writing down the variables that were given in the problem: V1 = 600 ml T1 = 27 0 C T2 = 0 0 C V2 =? Now you see two different things. You see that you will be using Charles law for this calculation and the temperature is in Celsius. Right away, you remember that you need to use Kelvin for gas law calculations! So you convert the Celsius temperatures to Kelvin: T1 = 27 0 C = 300K T2 = 0 0 C = 273K Now you can set the unknown equal to X and solve the equation. V1/T1 = V2/T2 600 ml/300 K = X/273 K Multiply both sides of the equation by 273 to get X by itself. (273)(600)/(300) = X Punch the numbers into your calculator and you will have the answer. Only use as many digits (numbers) as you were given in the problem. X = 546 ml Don t forget to write the proper units in for your answer! 3. What volume of gas would you expect to get from a 1.0-mole sample at STP? Start this problem just like any problem, by writing down the variables that are given in the problem. The challenge is with the term, STP. What does it mean? Well, STP stands for Standard Temperature and Pressure. Standard temperature is 0 0 C (or Kelvin) and standard pressure is 1 atmosphere. So now you can write down the variables in this problem. 7

8 P = 1 atm n = 1.0 mol T = K V =? When you look for the equation that corresponds to this problem, it looks like the ideal gas equation: PV = nrt. But what is R? I gave you 2 possible values for R earlier in the notes. Use the value of R that has the same units as the problem gives. R = L atm/mol K. Now you can solve the problem. PV = nrt (1 atm)x = (1.0 mol)( L atm/mol K)( K) Divide both sides by 1 atm to get X by itself. X = (1.0)(0.0821)(273.15)/(1) Punch the numbers into your calculator and you will have the answer. Only use as many digits (numbers) as you were given in the problem. X = 22.4 L Now you re done!! 8

9 Kinetic Molecular Theory and Gas Laws Problems Use the notes from the KMT packet to fill in the blanks on this worksheet. 1. Temperature is a measure of the energy of the molecules in a sample. 2. A gas exerts pressure on its container because the molecules with the walls. 3. Pressure = /. 4. According to the assumptions of KMT The molecules of an ideal gas are in,, - motion. The molecules of an ideal gas can be considered points because most of the volume of a gas is space. Collisions in an ideal gas are completely. There are no attractive or repulsive in an ideal gas. 5. The assumptions of KMT fail under high or low. 6. law relates pressure and volume in an equation. 7. law relates volume and temperature in an equation. 8. law relates pressure and temperature in an equation. 9. PV = nrt is referred to as the gas law. 10. Standard pressure is equal to atmospheres, kpa, psi, mm Hg, or in Hg. 11. Standard temperature is equal to 0 C or K. 12. Explain the Crushing Can demo by using gas laws. Watch this video Use a metaphor to explain any of the relationships described by the gas laws. 14. According to KMT, if 2 different gas molecules were at the same temperature and pressure, but one was large and the other small, who would win in a race? 9

10 More problems Define the following terms as they apply to Kinetic Molecular Theory: Pressure Temperature Volume n (moles) - Calculations 1. A gas sample has a volume of 150 ml when the pressure is 175 kpa. If the temperature and amount of gas remains constant, what volume will the gas sample occupy at a pressure of 120 kpa? 2. A 650 ml sample of gas is collected at a room temperature of 30 0 C. What volume will the sample have at C assuming the pressure of the gas remains constant? 3. An aerosol can of hair spray is filled to a pressure of 50.0 psi at a room temperature of C. Calculate the pressure inside the can if the can is placed in boiling water. 4. A balloon has a volume of ml at a pressure of mm Hg. Calculate the volume the balloon would have at standard atmospheric pressure if the temperature remains constant. 5. A car tire has a pressure of 30.0 psi at a temperature of C. Calculate the extremes of pressure caused by temperatures ranging from C ( F) on a cold winter day to C (122 0 F) while being driven on a hot summer day. 6. A gas sample has a volume of 480 ml at a temperature of 37 0 C and a pressure of 95.5 kpa. What volume would the gas occupy at STP? 7. If you collect 1.75-L of Hydrogen gas during a lab experiment, when the room temperature is 23 0 C and the barometric pressure is 105 kpa, how many moles of hydrogen will you have? 8. What volume of gas would you expect to get from a 1.5-mole sample at 35 0 C and 1.12 atm? 10

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