STP : standard temperature and pressure 0 o C = 273 K kpa

Transcription

1 GAS LAWS Pressure can be measured in different units. For our calculations, we need Pressure to be expressed in kpa. 1 atm = 760. mmhg = kpa R is the Universal Gas Constant. Take note of the units: R = 8.31 kpa L moles K To convert o C to Kelvin degrees, you must add 273 to the o C STP : standard temperature and pressure 0 o C = 273 K kpa RTP : room temperature and pressure 25 o C = 298 K kpa Dalton's Law of Partial Pressures: -the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases P T = Pa + Pb + Pc Pz If the individual pressures of gases are given, and these gases are all mixed together, the new total pressure is equal to their individual pressures added together.

2 A hot air balloon will float on air Why? Why does air become less dense as it is heated? Charles proved this in an experiment: Charles' Law: -when the pressure and the number of moles of a gas are held constant, the volume of a gas is directly proportional to the Kelvin temperature. V 1 = V 2 T 1 T 2 Charles Law EXAMPLES: 1. A 250 ml sample of gas exists at 25 o C. What volume will the gas occupy at 50. o C if pressure remains constant? 2. Nitrogen gas occupies 400. ml at 100 o C. At what temperature would the gas occupy 200. ml?

3 Boyle's Law: -when the temperature and the number of moles of a gas are held constant, the volume of a gas is inversely proportional to the pressure applied on the gas. V 1 P 1 = V 2 P 2 Boyles Law EXAMPLES: 1. A sample of gas occupies 10.L at 105 kpa. At what pressure will it occupy 13.4 L? (Assume constant temperature). 2. A sample of gas occupies 9.8 L under a pressure of kpa. What will its volume be at 108 kpa? T vs P (no name for this relationship): -the pressure of a gas, at constant volume, is directly proportional to the absolute temperature. P 1 = P 2 T 1 T 2 EXAMPLE: 1. At constant volume, a gas exerts 500. kpa of pressure on a container's walls at 250. K. What will the pressure be at 350. K?

4 Ideal gas law: PV = nrt Where P is the pressure in kpa, V is the volume in litres, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin degrees. Note: R = 8.31 kpa L moles K IDEAL GAS: a state of matter above its boiling point but below its plasma point AND meets the following criteria: IDEAL GAS vs. REAL GAS no attractive forces between neighbouring molecules all molecules are perfect spheres molecules occupy zero volume (don't occupy any space) molecule collisions are perfectly elastic liquids and solids result from attractions between gas molecules consider H 2 O and CH 4 as two examples. Their VSEPR geometry shows that they are not perfect spheres! mass and volume are essential properties of matter energy loss during collisions causes chemical reactions HOWEVER, despite the inadequate nature of each assumption, the combination of these allows a good model, providing the gas is not near it condensing point. i.e. We can use the Ideal gas equation that makes these assumptions about gases since it doesn t really change our answer. Ideal Gas Law EXAMPLES: 1. What volume will 480 g of ammonia gas occupy at 125 o C and 180 kpa? 2. What pressure is exerted by 54.0 g of Xenon in a 1.00 L flask at 20 o C?

5 Combined gas law: memory hint: write the letters in alpha order for this calculation "tool" P T V Consider the ideal gas equation, PV = nrt. Now consider a certain number of moles of gas: n = PV RT If we want to compare this number of moles of a certain gas at two sets of conditions, we could say that : V 1 P 1 = V 2 P 2, since both of sides of this equation must equal n, the number of moles RT 1 RT 2 We can also into consideration, that R is a constant, and can therefore be eliminated from both sides of the equation: V 1 P 1 = V 2 P 2, T 1 T 2 EXAMPLES: 1. A sample of neon occupies 100.L at 27.0 o C at 133 kpa. What volume would it occupy at standard conditions? V1 = V2 = T1 = T2 = P1 = P2 = 2. A meteorological balloon occupies 140 litres at 39 o C and 95 kpa. What volume will it occupy at 85 o C and 121 kpa? V1 = V2 = T1 = T2 = P1 = P2 =

6 CLEARLY SHOW ALL WORK FOR EACH OF THESE QUESTIONS. BE SURE TO HIGHLIGHT THE FORMULA YOU ARE USING IN EACH CASE. Sig Figs Count! 1. The highest pressure ever produced in a laboratory setting was about 2.0 x 10 6 atm. If we have a 1.0 x 10-5 liter sample of a gas at that pressure, then release the pressure until it is equal to atm, what would the new volume of that gas be? 2. If I have an unknown quantity of a gas at a pressure of 0.50 atm, a volume of 25 liters, and a temperature of 300. K, how many moles of gas do I have? 3. Imagine a thermometer that measures temperature by the compressing and expanding of gas in a piston. If it is measured that at 100 o C the volume of the piston is 21 L. What is the temperature outside if the piston has a volume of 15 L? What would be appropriate clothing for the weather?

7 4. A tank is originally filled up at 120 K to a pressure rating of 4600 mmhg. The tank is stored in an area that raises its temperature to 450 K. Has the pressure of the tank increased or decreased? Why does this (increase or decrease) make sense? 5. A 2.79 g sample of gas occupies a space of 735 ml at 1.78 atm and -21 o C. What is the molar mass of the gas? What gas might it be? 6. Based on the postulates of the kinetic molecular theory, give the conditions of temperature and pressure that you believe would cause a real gas to best simulate an ideal gas. Explain your answer.