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Gases Chapter 14 14.1 The Gas Laws • Kinetic Theory helps us understand the behavior of gases: 1st – All gases are made of tiny particles. 2nd – Gas particles are in constant, random motion. 3rd – All collisions between gas particles are perfectly elastic. In order to study Gases; one must keep track the types of units used in each problem. • Temperature: oC or K. • Pressure: kPa, mm Hg, Torr. or Atm. • Volume: mm3, cm3, m3, L, mL. • In this chapter we are dealing with Ideal Gases. Ideal Gas particles do not have a volume and no mutual attraction. STP - Standard Temperature & Pressure. • Standard Temperature is 0 oC (273 K) • Standard Pressure is 1 atm (760 mmHg) Boyle’s Law • Boyle’s Law states that at constant temperature, the pressure of a gas varies inversely with the volume of a gas. P1 V 1 = P2 V 2 • EX1: A gas has a volume 2.0 L and a pressure of 1.0 atm, what volume will the gas have at 4.0 atm? At constant temperature. • EX2: A gas has a volume 3 L and a pressure of 2.0 atm, what pressure will the gas have at 24 L? At constant temperature. • Practice Problem 1: A gas has a volume 50.0 L and a pressure of 8.0 atm, what volume will the gas have at 10.0 atm? • Practice Problem 2: A gas has a volume 20.0 L and a pressure of 5.0 atm, what pressure will the gas have at 25.0 L? Charles’ Law • At constant pressure, the volume of a gas varies directly with the temperature of a gas. V1 = V2 T1 T2 • All temperatures must be in Kelvin (K) K = oC + 273 • EX1: A gas has a volume 24 L and a temp of 27.0 °C, what volume will the gas have at 127.0 °C ? • EX2: A gas has a volume 30 L and a temp of 77.0 °C, what temp will the gas have at 120 L? • Practice Problem 1: A gas has a volume 50 L and a temp of 227 °C, what volume will the gas have at 127 °C? • Practice Problem 2: A gas has a volume 900 cm3 and a temp of 100.0 K, what temp will the gas have at 450 cm3? Gases Chapter 14 14.2 The Combined Gas Law & Avogadro’s Principle • The Combined Gas Law joins Boyle’s Law with Charles’s Law: P1 V 1 = P2 V 2 T1 T2 • All calculation must be in Kelvin!!! K = oC + 273. • EX1: A gas at 2.0 atm and 27.0 °C fills a flexible container with an initial volume of 3.0 L. If the temperature is raised to 127.0 °C and the pressure is increased to 4.0 atm, what is the new volume? • EX2: A helium-filled balloon at sea level has a volume of 2.0 L at 1.0 atm and 280 °C. If it is released and rises to an elevation at which the pressure is 1.5 atm and the temperature is 27 °C, what will be the new volume of the balloon? • Practice Problem 1: At 200 K and 1.00 atm pressure, a sample of gas occupies 30.0- mL. If the temperature is increased to 300.0 K and the entire gas sample is transferred to a 20.0-mL container, what will be the gas pressure inside the container? • Practice Problem 2: A sample of air in a syringe exerts a pressure of 100 kPa at a temperature of 27.0 °C. The syringe is placed in a warm water bath at 87.0 °C. The pressure of the air is increased to 120 kPa by pushing the plunger in, which reduces the volume to 0.20 -mL. What was the original volume of the air? • Practice Problem 3: An unopened, cold 2.00-L bottle of soda contains 46.0-mL of gas confined at a pressure of 1.30 atm at a temperature of 5.0 °C. If the bottle is dropped into a lake and sinks to a depth at which the pressure is 1.52 atom and the temperature is 2.09 °C, what will be the volume of the gas in the bottle? Gases Chapter 14 Molar Volume • Avogadro’s Principle: at equal temperatures and equal pressures, equal volumes of gases contain the same number of molecules. • 1 mole of any gas equals 22.4 liters at STP. Ideal Gas Equation PV = nRT • P = pressure measured in atmospheres (atm) • V = volume measured in liters (L) • n = moles measured in moles (mol) • R = gas constant (0.08 L-atm/mol-K) • T = temperature measured in Kelvin (K) • EX1: What pressure is exerted by a gas in a propane container with a volume of 2.0 L at 200 K and 5.0 mol? • Practice Problem 1: Find the volume of a gas with 10.0 moles at 500 K and 4.0 atm. • PP2: A typical float at the Macy’s Thanksgiving Parade has a volume of 1,800,000-L at 1.0 atm and 27 °C. Find the number of moles of gas in the float. • PP3: Find the temperature in Celsius for a gas held in a 2,000 mL balloon with 5.0 moles at 1520 torr. Molecular Mass Determination M = mRT PV • M = molecular mass in grams/mole (g/mol) • m = mass of sample in grams (g) • R = gas constant (0.08 L-atm/mol-K) • T = temperature in Kelvin (K) • P = pressure in atmospheres (atm) • V = volume in liters (L) • EX1: What is the molecular mass of a gas if 1.00 L has a mass of 2.0 grams at 200 K and 4.0 atm. • PP2: What is the molecular mass of a gas if 100 grams of it occupies 20.0 L at 5.0 atm at 500 K. • • PP2: What is the molecular mass of a gas if 100.0 centigrams of it occupy 200.0 mL at 380 mmHg and 500 K? Gases Chapter 14 Mass-Volume • Gas stoichiometry can be used to predict the products of a reaction. 1 mole = 22.4 L at STP Stoichiometry Solving Process • Find the balanced equation for the reaction. • Convert given amount to moles. • Use mole ratio to find moles of desired particle. • Convert moles of desired particle to correct unit. Mass-Volume Stoichiometry EX1: How many liters of ammonia are produced by the reaction of 56.0-grams of nitrogen gas (N2) with excess hydrogen gas (H2)? N2(g) + 3 H2(g) à 2 NH3(g) • Practice Problem 1: How many liters of water vapor (H2O) are created by the decomposition of 400-grams of ammonium nitrate (NH4NO3)? NH4NO3(s) à N2O(g) + 2 H2O (g) • Practice Problem 2: How many liters of chlorine gas (Cl2) are needed to completely react with 276 grams of solid sodium (Na)? 2 Na (s) + Cl2 (g) à 2 NaCl (s) Volume-Mass Stoichiometry • EX2: Find the mass of water that is produced by the reaction of 67.2-L of oxygen gas (O2) with excess hydrogen gas (H2) at STP. H2 (g) + O2 (g) à H2O (l) • Practice Problem 3: Calculate the mass of hydrogen gas (H2)needed to react with 224 -L of nitrogen gas (N2) at STP. N2 (g) + 3 H2 (g) à 2 NH3 (g) • Practice Problem 4: Calculate the mass of carbon dioxide (CO2) produced by the reaction of 1120-L of propane (C3H8) at STP. C3H8 + 5 O2 (g) à 3 CO2 (g) + 4 H2O (l) Volume-Volume Problems • EX3: How many liters of carbon dioxide (CO2) are produced by the reaction of 11.2-L of propane (C3H8)? C3H8 (g) + 5O2 (g) à 3CO2 (g) + 4H2O (l) • Practice Problem 5: How many liters of carbon dioxide (CO2) are produced by the reaction of 448-L of oxygen gas (O2)? C3H8 (g) + 5 O2 (g) à 3 CO2 (g) + 4 H2O (l)