Properties of Gases Gases have Gases Gases exert Gases fill their containers Behavior of Gases Gases are mostly The molecules in a gas are separate, very small and very Kinetic Theory of Matter: Gas molecules are in constant, chaotic motion Collisions between gas molecules are elastic (there is no energy gain or loss) The average of gas molecules is directly proportional to the absolute Gas pressure is caused by collisions of molecules with the walls of the container Measurement of Gases To describe a gas, its volume, amount, temperature, and pressure are measured. Volume: Amount: Temperature: Pressure: Units of Pressure: 1 atmosphere 1
Intro to Gas Laws: What you saw in the simulation Temperature vs Pressure Temperature and Pressure are related. (and vice versa) The causes an increase in kinetic energy/. This increased movement causes the particles to each other and the of the container and with more force, thus. Temperature vs Volume Temperature and Volume are related. (and vice versa) The causes an increase in the kinetic energy/molecular movement. The and collide with each other and the walls more often. As the walls move outward, there is more space and the particles (still moving with increased kinetic energy) collide with the walls less often and with less force. This leads to an expansion in volume and the pressure stays the same. Volume vs Pressure Volume and Pressure are related. (and vice versa) Pressure is the measurement of how hard the particles of a gas hit the walls of a container. As the volume shrinks, there is and the particles other particles and the walls harder and, thus increasing the pressure. SUMMARY OF GAS LAW RELATIONSHIPS: If you have a sample of gas and one variable is changed, then the other variables will also change according to the gas law relationships (see above): To figure out how much the other variable will change, you will need a multiplier The multiplier will be a ratio of the other variable that either increases the unknown or decreases the unknown based on the gas law relationships 2
To Solve a Gas Law Problem when you have a single sample of gas 1. Read the full problem 2. Make a chart for PVT initial and final 3. Fill in the chart using units and the problem Make sure each variable has the same units TEMPERATURE MUST ALWAYS BE IN KELVIN! oc + 273 K 4. Use gas law relationships to create an appropriate multiplier 5. Solve the problem Example1: A sample of gas occupies 12 L under a pressure of 1.2 atm. What would its volume be if the pressure were increased to 3.6 atm? (assume temp is constant) Example2: A sample of nitrogen gas occupies 117 ml at 100. C. At what temperature would it occupy 234 ml if the pressure does not change? (express answer in K and C) Example3: A rigid box contains a sample of helium gas at room temperature, 23.0 o C and a pressure of 760. mmhg. What is the new pressure of the box if the gas is cooled to freezing, 0.00 o C? Standard Temperature & Pressure (STP): 0 C (273 K) and 1 atm (760 torr, 760 mm Hg) The Combined Gas Law Sometimes it isn t just one variable that changes, sometimes two variables change at once, and you need to find out what happened to the third variable. Do everything exactly the same, but you will have two multipliers. o It is ok if one multiplier makes the number bigger and the other makes it smaller. Examples: 1. A sample of neon gas occupies 105 L at 27 C under a pressure of 985 torr. What volume would it occupy at standard conditions? 3
2. A sample of gas occupies 10.0 L at 240 C under a pressure 80.0 kpa. At what temperature would the gas occupy 20.0 L if we increased the pressure to 107 kpa? 3. A sample of oxygen gas occupies 23.5 L at 22.2 C and 1.3 atm. At what pressure (in mm Hg) would the gas occupy 11.6 L if the temperature were lowered to 12.5 C? Gases: Standard Molar Volume & The Ideal Gas Law Avogadro s Law: at the same temperature and pressure, equal volumes of all gases contain the same # of molecules (moles). Standard Molar Volume The Ideal Gas Law: shows the relationship among the pressure, volume, temp., and the # of moles in a sample of gas. Where, P V n T R (the units of R depend on the units used for P, V, and T) Examples: 1) What volume would 50.0 g of ethane, C2H6, occupy at 140 C under a pressure of 1820 torr? 2) Calculate: a) the # of moles in, and (b) the mass of an 8.96 L sample of methane, CH4, measured at standard conditions. 3) Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25 C. 4
Notes: Partial Pressures and mole Fraction In a mixture of gases each gas exerts the pressure it would exert if it occupied the volume alone. The total pressure exerted by a mixture of gasses is the sum of the partial pressures of the individual gases: Example: If 100.0 ml of hydrogen gas, measured at 25ºC and 3.00 atm, and 100.0 ml of oxygen, measured at 25ºC and 2.00 atm, what would be the pressure of the mixture of gases? Vapor Pressure of a Liquid: Temp (ºC) v.p. of water (mm Hg) Temp. (ºC) v.p. of water (mm Hg) 18 15.48 21 18.65 19 16.48 22 19.83 20 17.54 23 21.07 Example: A sample of hydrogen gas was collected by displacement of water at 25ºC. The atmospheric pressure was 748 mm Hg. What pressure would the dry hydrogen exert in the same container? (vapor pressure of water at 25 o C 23.76 mm Hg) Example: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 ml at 27ºC. The barometric pressure was 753 mm Hg. What volume would the dry oxygen occupy at STP? (vapor pressure of water at 27 o C 26.74 mm Hg) Example: A student prepares a sample of hydrogen gas by electrolyzing water at 25ºC. She collects 152 ml of H2 at a total pressure of 758 mm Hg. Calculate (a) the partial pressure of hydrogen, and (b) the number of moles of hydrogen collected. (vapor pressure of water at 25 o C 23.76 mm Hg) 5
Mole Ratio for Partial Pressure Example: A box holds 3.0 moles of hydrogen gas and 2.0 moles of oxygen gas. If the total pressure of the box is 10. atm, what is the pressure exerted by the hydrogen gas? Graham s Law of Diffusion & Effusion Rate of is how quickly different Rate of is how quickly a gas can Equation: Where Rate rate of diffusion/effusion for gas 1 or 2 MM molar mass of gas 1 or 2 Example: How many times faster will hydrogen effuse compared to methane, CH4? Example: Rank the following gases in terms of fastest to slowest effusion: Kr, He, Rn, N2 6