Chapter 16 – Gases

Chapter 16 – Gases 16.1 Pressure Gas pressure: force per unit area exerted by gas molecules colliding against the walls of the container. P increases when 1) number of collisions increase (more hits on the container walls) 2) energy of collisions increase (harder hits on the container walls) Vacuum: no gas molecules are present, so gas pressure equals zero Atmospheric pressure: pressure exerted by air molecules colliding with surfaces in environment.  decreases as altitude increases because air becomes less dense (thinner) Barometer: instrument invented by Torricelli to measure atmospheric pressure  Atmospheric pressure is 760 torr at sea level, lower at higher altitudes like Denver Standard atmospheric pressure: a column of mercury measuring 760 mm Hg. 1 atm  760 torr  760 mm Hg = 14.7 psi (approx.) Know how to convert from one unit of pressure to the other units. You should review properties of gases in chapter 1. You should also know standard temperature and pressure, STP = 1 atm and 0oC. 16.2 Greenhouse Gases Greenhouse gases are in the news daily it seems because they are so important to our future environment here on Earth. Greenhouse gases (GHG) are gases in the atmosphere they act like a blanket keeping heat here around planet Earth. In fact we would not here without GHG, so a certain amount of them is necessary for life. But we have been increasing the balance of GHG over the past century to the point where we are keeping more heat in than desired which is giving rise to global climate change. The main GHG that we are concerned about are carbon dioxide, CO2, methane, CH4, and nitrous oxide, N2O. The main sources of GHG increasing in our atmosphere are coal power plants, gasoline powered vehicles, and the meat industry. Our reliance on fossil fuels is changing our environment by slowly heating up our world. Scientific measurements show that global average temperatures are increasing, mean sea level is increasing, Artic and Antarctic ice is melting, glaciers are melting, 1 and GHG concentrations are increasing. Also predicted by climate change is an increase in severe weather events such as tornadoes, hurricanes, floods and drought. 16.3 Gas Laws Several different scientists studied gases and how they depend on different variables such as volume, V, pressure, P, and temperature, T. What happens to the pressure of a gas given the following changes? a. If Volume ↑, pressure_____. ↑ Thus, pressure and volume are _____ related. b. If Temperature ↑ , pressure _____. ↓ stays same not directly ↑ ↓ inversely stays same 2 Thus, pressure and temperature are _____ related. c. If # of gas molecules ↑, pressure _____. Thus, pressure and # of molecules are _____ related. not directly ↑ ↓ not inversely stays same directly inversely Boyle studied pressure volume relations and in 1662 determined that when T is held constant P1V1 = P2V2. Charles studied volume temperature relations and in the 1780’s determined that V V 1 2 when P is held constant T  T . And Gay Lussac studied pressure temperature relations and 1 2 in 1808 determined that P1 P2  . T1 T2 16.4 Combined Gas Law Instead of memorizing three separate gas laws from above, we can combine them into one law: P1V1 P2 V2  . But be careful, when using gas laws the temperature MUST be in Kelvin. Here are some T1 T2 guidelines for using the combined gas law: 1. List all of the measurements given, and label each as P1, V1, T1, etc. 2. Convert all temperatures to Kelvin, convert all pressures to the same units, and convert all volumes to the same units. 3. Starting with the Combined Gas Law P1V1 P2 V2  , omit variables that remain T1 T2 constant. If a variable is not given, assume it remains constant so it cancels out. 4. Isolate the unknown variable. The unknown variable must be alone on one side of =. 5. Solve for the unknown, making sure your final answer has the correct units and the correct number of sig figs. 6. Check if your final answer makes sense. Example Combined Gas Law Problem A variable volume container holds 24.3 L of N2 gas at 55 °C. What will the volume of the N2 gas be if the temperature falls to 17 °C? Change T to Kelvin: T1 = 55 + 273 = 328 K V1 = 24.3 L Omit P from combined gas law: T2 = 17 + 273 =290 K V2 = ? V1 V = 2 T1 T2 3 Solve for V2: V2 = V2 = V1T2 T1 (24.3L)(290 K ) = 21.5 L (328K )  T  V so makes sense  16.5 Ideal Gas Law The ideal gas law is an equation that is used to approximate the conditions of a gas. It was first published in 1834 by Emile Clapeyron. The equation is PV=nRT where n is number of moles of 𝐿 𝑎𝑡𝑚 gas and R is the gas constant 0.08206 𝑚𝑜𝑙 𝐾 . Note that to use this equation volume must be in liters, pressure in atmospheres, and temperature in Kelvin. This equation is used to find out the status of a gas whereas the combined gas law is used to determine variables of a changing gas. Example Ideal Gas Law Problem: What is the pressure of the GHG carbon dioxide if there is 55.3 grams at 42.7oC in a 12.4 L container? 1 𝑚𝑜𝑙 First we need moles of gas n so 55.3 g CO2 (44.01 𝑔) = 1.2565 moles CO2 Now check our units – we need Kelvin, so 42.7 + 273 = 315.7 K Now solve the equation for pressure P = And plug into the equation P = 𝑛𝑅𝑇 𝑉 (1.2565 𝑚𝑜𝑙)(0.08206 12.4 𝐿 𝐿 𝑎𝑡𝑚 𝑚𝑜𝑙 𝐾 (315.7 𝐾) = 2.63 atm Practice Problems 1. The tire pressure for tires used on most automobiles is about 32 psi. Express this pressure in atm, torr, and mm Hg. 2. A 250.0-mL sample of CO gas at 1.20 atm is compressed to 125.0 mL. Calculate the new pressure. 4 3. A sample of CO2 gas at 2.50 atm is cooled from 75˚C to 25˚C. Calculate the new pressure. 4. The gas in a 0.717 L cylinder exerts a pressure of 744 torr at 27 °C. What volume will it occupy at 48.6 atm and 547 °C? 5. A gas occupies 2.33 L at STP. What pressure (atm) will this gas exert if it is expanded to 6.19 L and warmed to 17 °C? At STP, the temperature = _________ and the pressure = _________. 6. What is the volume of 87.24 grams of nitrogen gas if the temperature is 25.5oC and the pressure is 0.893 atm? 5 7. What is the temperature of 2.45 grams of hydrogen gas if the volume is 17.35 liters and the pressure is 782 torr? Answers 1.  1 atm   = 2.2 atm  14.7 psi  32 psi   760 torr   = 1.7x103 torr = 1.7x103 mm Hg  14.7 psi  32 psi  2. V1 = 250.0 mL P1 = 1.20 atm V2 = 125.0 mL P2 = ? Omit T from combined law: P1V1 = P2V2 Solve for P2: P2 = 3. P2 = P1xV1 V2 1.20 atmx250.0 mL   2.40 atm 125.0 mL  V  P P1 = 2.50 atm T1 = 75 + 273 = 348 K P2 = ? T2 = 25 + 273 = 298 K Omit V from the combined gas law: Solve for P2: P2 = P2 = P1 P2  T1 T2 P1  T2 T1 2.50 atm 298 K   2.14 atm 348 K  T  P 6 4. V1 = 0.717 L V2 = ? T1 = 27 + 273 = 300 K P1 = 744 torr T2 = 547 + 273 = 820 K P2 = 48.6 atm  1 atm    Convert P1 to atm: P1 = 744 torr   760 torr  0.979 atm P1V1 P2 V2  T1 T2 Solve for V2: V2  V2  P1V1 T2  T1 P2 (0.979 atm)(0.717 L) (820 K) = 0.0395 L  (300 K) (48.6 atm) V  since P  a lot 5. At STP, the temperature = 273 K and the pressure = 1 atm. V1 = 2.33 L STP: T1 = 273 K P1 = 1 atm V2 = 6.19 L T2 = 17 + 273 = 290 K P2 = ? P1V1 P2 V2  T1 T2 Solve for P2: P2  P2  P1V1 T2  T1 V2 (1 atm)(2.33 L) (290 K) = 0.400 atm  (273 K) (6.19 L) P  since V  1 𝑚𝑜𝑙 6. 87.24g N2 (28.02 𝑔) = 3.1135 mol N2 gas P = 0.893 atm Solve for V = 25.5oC + 273 = 298.5 Kelvin so we are NOT changing so use ideal gas law PV = nRT 𝑛𝑅𝑇 1 𝑚𝑜𝑙 𝑃 (3.1135 𝑚𝑜𝑙)( 0.08206 = 𝐿 𝑎𝑡𝑚 )(298.5 𝐾) 𝑚𝑜𝑙 𝐾 0.893 𝑎𝑡𝑚 7. 2.45 g H2 (2.02 𝑔) = 1.21287 mol H2 gas = 85.4 L 1 𝑎𝑡𝑚 782 torr (760 𝑡𝑜𝑟𝑟) = 1.02895 atm 𝑃𝑉 Solve for T in ideal gas law PV = nRT, T = 𝑛𝑅 = (1.02895 𝑎𝑡𝑚)(17.35 𝐿) 𝐿 𝑎𝑡𝑚 (0.08206𝑚𝑜𝑙 𝐾 )(1.21287 𝑚𝑜𝑙) = 179 K 7