General Properties of Gases. Properties of Gases. K is for Kelvin. C is for degrees Celsius. F is for degrees Fahrenheit PROPERTIES OF GASES GAS LAWS

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1 PROPERTIES OF GASES or GAS LAWS 1 General Properties of Gases There is a lot of empty space in a gas. Gases can be expanded infinitely. Gases fill containers uniformly and completely. Gases diffuse and mix rapidly. 2 Properties of Gases Gas properties can be modeled using math. The equations we will use relate these quantities: V = volume of the gas T = temperature n = moles of gas P = pressure 3 Temperature how hot or cold something is (a physical property) a measure of the average kinetic energy of a sample of matter. How fast the particles in a substance are moving 4 We will start by reviewing these quantities and the units they are measured in. Temperature measures MOTION Temperature K is for Kelvin o C is for degrees Celsius 5 Temperature is special because 6 We will sometimes use degrees celsius we sometimes will use kelvin. never always ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! Example K C F Boiling Point of Water O 212 O o F is for degrees Fahrenheit Body Temperature Freezing Point of Water O 0 O 98 O 32 O Absolute Zero o -459 O Page 1

2 Temperature Conversions Fahrenheit to Celsius o C = (5/9) ( o F - 32) Kelvin to Celsius: Celsius = K Kelvin Scale-absolute scale The Kelvin scale is experimentally derived: Place a gas in a cylinder with movable piston. V 8 Celsius to Fahrenheit o F = ((9/5) o C) + 32 Measure volume and temperature. T Kelvin Scale-absolute scale 9 Kelvin Scale-absolute scale 10 The best fit line intersects the T axis at o C Using a different gas gives a different line, but the same intercept: -273 o c V T o C = 0 Kelvin represents the temperature at which the gas has no volume and all molecular motion stops. It is purely theoretical and has never been reached. V T Kinetic Molecular Theory 3 Main Ideas: Moving Particle Theory Matter is made of tiny particles called atoms, which combine to form molecules. 12 Page 2

3 2. Atoms and molecules are in constant random motion (they are always moving) Atoms and molecules move faster as temperature rises. 14 Low Temperature (slower) High Temperature (faster) THREE STATES OF MATTER 15 Pressure atm is for atmospheres mm Hg is for millimeters of Mercury kpa is for kilopascal psi is for pounds per square inch torr is for torr 16 Pressure Pressure of air is measured with a BAROMETER Millimeters of Mercury (mm Hg) refers to this device and method of measuring atmospheric pressure. 1 atm = 760 mm Hg = 760 torr 17 Pressure Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) P of Hg pushing down related to Hg density column height 18 Page 3

4 Pressure Conversions 1 standard atmosphere (1 atm) 19 Pressure Conversions A. What is 475 mm Hg expressed in atm? 20 = 760 mm Hg = 760 torr = 14.7 psi = kpa 475 mm Hg x 1 atm 760 mm Hg = atm B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 760 mm Hg 29.4 psi x = 1.52 x 10 3 mm Hg 14.7 psi Pressure Conversions 21 And now, we pause for this commercial message from STP 22 A. What is 2.0 atm expressed in torr? OK, so it s really not THIS kind of STP STP in chemistry stands for Standard Temperature and Pressure B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kpa? Standard Pressure = 1 atm Standard Temperature = 0 deg C (273 K) Charles Law Jacques Charles ( ). 1823). Isolated boron and studied gases. Balloonist. Think about how thermometers work The hotter it gets, the more space the mercury or alcohol takes up. Gases seem to behave the same way; the hotter they get, the more space they take up. In other words, the temperature and volume of a gas are proportional. 23 Charles s Law If the pressure (P) is kept the same, and the number of moles of gas (n) are kept the same, then V α T (V and T are proportional.) V 1 T 2 = T 1 V 2 24 If the temperature goes up, the volume goes up! Page 4

5 Charles s s original balloon 25 Charles Law 26 T 1 V 2 = T 2 V 1 in other words V 1 / T 1 = V 2 / T 2 Modern long-distance balloon V and T Problem 27 Learning Check GL4 28 A balloon has a volume of 785 ml on a spring day when the temperature is 21 C. In the evening, the temperature of the gas cools to 12 C. What is the new volume of the balloon? A sample of oxygen gas has a volume of 420 ml at a temperature of 18 C. What temperature (in K) is needed to change the volume to 480 ml? 29 Charles Law and Absolute Zero 30 Charles Law and Absolute Zero Page 5

6 31 Charles Law: T and V 32 Charles Law explains the relationship between V and T for a gas when P and n are constant. It can be written as T = kv where k is a constant relating to the slope of the line on this graph ml of a gas is collected at kpa. Find the volume if the pressure goes to 705 mm Hg. Boyle s Law What happens if you increase the pressure of a gas? Well, naturally, since gases are compressible, the volume decreases. My law relates P and V, which are also proportional, as long as T and n are kept constant. 33 Boyle s s Law P α 1/V or PV = k This means P and V are INVERSELY PROPORTIONAL if n and T are constant (do not change). In other words, P goes up as V goes down. 34 Robert Boyle ( ). Son of Earl of Cork, Ireland. P 1 V 1 = P 2 V 2 Boyle s Law 35 Use this equation to calculate how a volume changes when pressure changes, or how pressure changes when volume changes. A bicycle pump is a good example of Boyle s s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. Boyle s s Law 36 P 1 V 1 = P 2 V 2 Page 6

7 Pressure and Volume Experiment Pressure Volume P x V (atm) (L) (atm x L) Boyle's Law P x V = k (constant) when T remains constant 37 Problems A gas is collected at a constant temperature of 29.0 o C with a pressure of 699 mm Hg and volume of 33.0 ml. Find the pressure if the volume goes to 50.0 ml? 38 P1V1= 8.0 atm x 2.0 L = 16 atm L P2V2= 4.0 atm x 4.0 L = 16 atm L P1V1 = P2V2 = k In other words, PV = k k is just the symbol for a constant. Its number value depends on the units you are using for of P and V. One more: 40.0 ml of a gas is collected at kpa. Find the volume if the pressure goes to 705 mm Hg. 39 Gay-Lussac s Law Of course, temperature and pressure of a gas must be related also I think that if temperature increases, pressure hmmm increases. as long as number of moles of gas and temperature stay the same, that is. 40 Gay-Lussac Lussac s Law If n and V are constant, then P α T P and T are directly proportional. P 1 P 2 = T 1 T 2 P/T = k Joseph Louis Gay- Lussac ( ) 1850) If one temperature goes up, the pressure goes up! 41 Gay-Lussac s Law P 1 / T 1 = P 2 / T 2 P α T P/T =k in other words T 1 P 2 = T 2 P 1 42 Page 7

8 43 44 Problems: A gas is collected at 40.0 o C and a pressure of 1.19 atm. Find the new pressure if the temperature drops to 22.0 o C. Kelvin!! Another problem: At constant volume, CO 2 is collected at 778 mm Hg with a temperature of 25.0 o C. Find the new temperature in K when the gas is under 97.1 kpa of pressure. Combined Gas Law The principles behind Charles Law, Boyle s Law and Gay-Lussac s Law can be related to each other: 45 Combined Gas Law The good news is that you don t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. 46 P 1 V 1 P 2 V 2 = T 1 T 2 Most Useful Form: P 1 V 1 T 2 = P 2 V 2 T 1 Combined Gas Law 47 Combined Gas Law Problem 48 If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! P 1 V 1 T 2 = P 2 V 2 T 1 Boyle s Law Charles Law Gay-Lussac s Law 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? Set up Data Table P 1 = atm V 1 = L T 1 = 302 K P 2 = 3.20 atm V 2 = L T 2 =?? Page 8

9 Learning Check 49 One More Practice Problem 50 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? 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? Collecting a gas over water Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected over water, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton s Law of Partial Pressures becomes useful Dalton s s Law John Dalton Dalton s Law of Partial Pressure: In a mixture of two gases, the total pressure is simply the pressure of each gas in the mixture added together. Why it s useful: Often, we want to know the pressure of just one of those gases; ( partial pressure ) To get this, just subtract the pressure of the other gas from the total pressure: 53 Collection of a gas over water To make the total pressure of the gas mixture in the bottle equal to the atmospheric pressure, we adjust it so the water levels inside and outside the bottle are the same. When this is done, the partial pressure of the gas in the container is given by: 54 P gas = P atm -P H2O PB = Ptotal -PA Pbar is the barometer reading, and PH20 (the vapor pressure of water) is obtained from a table (p. 795), and depends on the temp. of the water. Page 9

10 Ideal Gas Law Temp C, F, K Pressure mm Hg, kpa, atm, psi, torr Volume ml, L, cm 3 55 IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory. Be sure you understand this equation! 56 Using PV = nrt V = Volume T = Temperature n = number of moles P = Pressure R is a constant, called the Ideal Gas Constant Depending on the units used, R has different values. When atm are used: R = L atm Mol K V = Liters T = Kelvin n = moles P = kpa OR When kpa are used: R = atm 57 L kpa Mol K Using PV = nrt How much N 2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 o C? Solution 1. Get all data into proper units V = 27,000 L T = 25 o C = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm And we always know R, L atm / mol K 58 Using PV = nrt How much N 2 is req d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 o C? Solution 2. Now plug in those values and solve for the unknown. PV = nrt RT n = RT (0.98 atm)(2.7 x 10 4 L) ( L atm/k mol)(298 K) n = 1.1 x 10 3 mol (or about 30 kg of gas) 59 Learning Check Dinitrogen monoxide (N 2 O), 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? 60 Page 10

11 Learning Check 61 EXAMPLES 62 A 5.0 L cylinder contains oxygen gas at 20.0 C and 735 mm Hg. How many grams of oxygen are in the cylinder? What is the volume of 1.00 mol of a gas at STP? 22.4 L of ANY gas AT STP = 1 mole GAS DENSITY High density 63 Low density Health Note When a scuba diver is several hundred feet under water, the high pressures cause N 2 from the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N 2 will form bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O 2 in scuba tanks used for deep descents. 64 Gases and Stoichiometry 2 H 2 O 2 (l) ---> > 2 H 2 O (g) + O 2 (g) Decompose 1.1 g of H 2 O 2 in a flask with a volume of 2.50 L. What is the volume of O 2 at STP? Bombardier beetle uses decomposition of hydrogen peroxide to defend itself. 65 EXAMPLES What is the volume of H 2 gas if 15.5 grams is collected at 25.0 o C with a pressure of.898 atm.? 66 Page 11

12 67 68 EXAMPLES PROBLEMS What is the pressure of 3.55 grams of CO 2 that is collected at 24.0 o C with a volume of 552 ml? 25.0 CM 3 OF HYDROGEN IS COLLECTED AT C WITH A PRESSURE OF 1.25 ATM. FIND THE NEW VOLUME IF THE PRESSURE DROPS TO.980 ATM AND THE TEMPERATURE DROPS TO C ANOTHER PROBLEM 78.5 cm 3 OF OXYGEN IS COLLECTED AT 42.0 O C WITH A PRESSURE OF 767mm. FIND THE NEW VOLUME AT STP. Combined: 35.0 cm 3 of N 2 is collected at.982 atm of pressure with a temperature of C. What is the new temperature in 0 C if the volume rises to 45.0 cm 3 and pressure rises to 788 mm? 71 One more combined: 65.5 ml of a gas is collected over water at 18 0 C with a pressure of.99 atm. Find the temperature in 0 C if the volume falls to 55.5 ml and the pressure changes to 77.5 kpa? Page 12

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