Gas Laws: Part 2

Avogadro’s Principle Equal volumes of gases at the same temperature and pressure contain equal number of molecules.

Volume-Volume Problem In one method of manufacturing nitric acid, ammonia is oxidized to nitrogen monoxide and water: 4NH3(g) + 5O2(g)  4NO(g) + 6H2O(l) What volume of oxygen will be used in a reaction of 2800L of NH3? What volume of NO will be produced? All volumes are measured under the same conditions.

Volume- Volume Problem You Try! Fluorine reacts violently with water to produce hydrogen fluoride and ozone according to the following equation: 3F2(g) + 3H2O(l)  6HF(g) + O3(g) What volume of O3 and HF gas would be produced by the complete reaction of 3.60 X 104 mL of fluorine gas? All gases are measured under the same condition.

Molar Volume = 22.4 L Molar Volume Defined - the volume occupied by one mole of a gas at S.T.P. Recall: 1 mole = 6.022 X 1023 molecules= molar mass = 22.4 L

Molar Volume Problems What is the volume, in liters, of 3.50 mol of F2 at STP? How many moles are contained in 5.60L of Cl2 at STP? Find the mass, in grams, of 2.80 L of CO2 at STP. Find the volume in liters of 3.50 g CO at STP.

Molar Volume Problems You Try! What is the volume, in liters, of 0.0400 mol of CO2 at STP? How many moles are contained in 0.125 L of Ne at STP? Find the mass, in grams, of 15.0 mL of SO2 at STP. Find the volume in liters of 0.0170 g H2S at STP.

22.4L/mol Determining the Density of a Gas at STP Molar Mass Density = _______________ Molar Volume 22.4L/mol 22.4L/mol Density of 1 mole of a gas at STP = Molar Mass/Molar Volume

Density = _______________ Density at STP Problem Calculate the density a gas will have at STP if its molar mass is 39.9 g/mol. Molar Mass Density = _______________ Molar Volume Density = 39.9 Density = 39.9g x 1 mol 1 mol 22.4L

Density at STP Problem You Try! What is the molar mass of a sample of gas that has a density of 1.09 g/L at STP? Molar Mass Density = _______________ Molar Volume Molar Mass = Density * Molar Volume Molar Mass = 1.09g x 22.4L 1 L 1mol

Ideal Gas Equation Recall: Boyle’s Law states Pressure and Volume are inversely proportional if temp. is held constant. (V = k times 1/P) Recall: Charles’ Law states volume and temperature are directly proportional if pressure is held constant. (V = kT) Avogadro’s Principle states at equal temperatures and equal pressures, equal volumes of gases contain the same number of molecules. ( V = kn) Therefore.... V = nkT/P or PV = nRT (Ideal Gas Equation)

Value of the ideal gas law constant R = PV/nT or at STP, R =(1atm)(22.4L)/(1 mol)(273K) = .0821atm.L/molK

P = pressure must be in atmospheres PV = nRT P = pressure must be in atmospheres V = volume (must be in liters) n = moles R = Gas Law Constant (.0821 atm. X L/mol X K) T = Temperature in Kelvin

Ideal Gas Law Problem #1 What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0L container at 298 K?

Ideal Gas Law Problem #2 How many moles of helium gas would it take to fill a balloon with a volume of 1000.0 cm3 (1 cm3 = 1mL) when the temperature is 320C and the atmospheric pressure is 752 mm of Hg?

Ideal Gas Law Problem #3 A tank with a volume of 658 mL contains 1.50 grams of neon gas. The maximum safe pressure that the tank can withstand is 4.50 X 102 kPa. At what temperature will the tank have that pressure?

Ideal Gas Law Problems: You Try! A large balloon contains 11.7 g of helium. What volume will the helium occupy at an altitude of 10 000 m where the atmospheric pressure is 0.262 atm and temperature is a -50o C. A paper label has been lost from an old tank of compressed gas. To help identify the unknown gas, you must calculate its molar mass. It is known that the tank has a capacity of 90.0 L and weighs 39.2 kg when empty. You find its current mass to be 50.5 kg. The gauge shows a pressure of 1780 kPa. When the temperature is 18oC . What is the molar mass of the gas in the cylinder?

Mass-Volume Stoichiometry at STP Steps in Solving Mass-Volume Stoichiometry Problems 1. Write a balanced equation. 2. Find the number of moles of a given substance. 3. Use the ratio of moles of a given substance to moles of a required substance to find the moles of a gas. --4. Express moles of a gas in terms of volume of a gas.

2Na(s) + 2H2O(l)  2 NaOH(aq) + H2(g) Sample Mass- Volume Problem Sodium reacts vigorously with water to produce hydrogen and sodium hydroxide according to the following equation: 2Na(s) + 2H2O(l)  2 NaOH(aq) + H2(g) If 0.027 g of sodium reacts with excess water, what volume of hydrogen at STP is formed?

Mass-Volume Problem- You Try! 2NH3(g) + CO2(g)  (NH2)2CO(s) + H2O(g) Urea, (NH2)2CO is an important fertilizer that is manufactured by the following reaction: 2NH3(g) + CO2(g)  (NH2)2CO(s) + H2O(g) What volume of NH3 at STP will be needed to produce 8.50 X 104 kg of urea?

Steps in Solving Volume-Mass Stoichiometry Problems at STP Volume- Mass Problems Steps in Solving Volume-Mass Stoichiometry Problems at STP 1. Write a balanced equation. 2. Change volume of gas to moles of gas. 3. Determine the ratio of moles of a given substance to moles of required substance. 4. Express moles of required substance as grams of required substance.

Sample Volume Mass Problem Dinitrogen monoxide can be prepared by heating ammonium nitrate, which decomposes according to the following equation: NH4NO3(s)  N2O (g) + 2H2O(l) What mass of ammonium nitrate should be decomposed in order to produce 250. mL of N2O measured at STP?

Volume- Mass Problem- You Try! Oxygen can be generated in the laboratory by heating potassium chlorate. The reaction is represented by the following equation: 2KClO3(s)  2KCl(s) + 3O2(g) What mass of KClO3 must be used in order to generate 5.00 L of O2, measured at STP

Using Stoichiometry Under Nonstandard Conditions When given a volume under nonstandard conditions and asked to find grams of a reactant or product. Use PV = nRT to convert volume of known to moles of known. 2. Compute grams of unknown by stoichiometry.

Practice Problem on Using Stoichiometry Under Nonstandard Conditions The principal source of sulfur is in the form of deposits of free sulfur occurring in volcanically active regions. The sulfur was initially formed by the reaction between the two volcanic vapors SO2 and H2S to form H2O(l) and S (s). What volume of each gas, at 730 mm of Hg and 22oC, was needed to form a sulfur deposit of 4.50 X 105 kg on the slopes of a volcano in Hawaii?

SO2 + H2S  H2O(l) + S (s). What volume of each gas, at 730 mm of Hg and 22oC, was needed to form a sulfur deposit of 4.50 X 105 kg on the slopes of a volcano in Hawaii? PV = nRT  V = nRT P P = n = T = R = 0.0821 V = 730 mm Hg X ATM = 0.96 ATM 760 mm Hg 4.50 X 105 kg X 1000g = 4.50 X 108 g S 1 kg X 1 mol S = 1.41 X 107 mol S 32g S 22oC + 273 k = 295 K P = n = T = ? V = 1.41 X 107 mol S * 0.0821 * 295 K = 3.54 X 108 L of each gas 0.96 ATM

Practice Problem on Using Stoichiometry Under Nonstandard Conditions- You Try! A 3.25-g sample of solid calcium carbide (CaC2) reacts with water to produce acetylene gas (C2H2) and aqueous calcium hydroxide. If the acetlylene is at 17oC and 740 mm of Hg, how many mL of acetylene were produced? CaC2 + H2O  C2H2 + Ca(OH)2

Using Stoichiometry Under Nonstandard Conditions When given a mass of a reactant or product and asked to find the volume of another reactant or product under nonstandard conditions.... Compute moles of unknown by using stoichiometry. 2. Use PV = nRT to find volume of unknown.

Practice Problem on Using Stoichiometry Under Nonstandard Conditions What volume of oxygen gas in liters can be collected at 0.987 atm pressure and 25oC when 30.6 g of KClO3 decompose by heating according to the following equation? 2KClO3(s)  2KCl(s) + 3O2(g)

Practice Problem on Using Stoichiometry Under Nonstandard Conditions- You Try! How many liters of gaseous carbon monoxide at 27oC and 0.247 atm can be produced from the burning of 65.5 g of carbon according to the following equation: 2C(s) + O2(g)  2CO(g)

Diffusion & Effusion: i.e. How farts spread! The constant and random motion of gases causes them to spread out a fill any container in which they are placed. Diffusion: The gradual mixing of two gases. Effusion: gases molecules passing through tiny opening Effusion: Can be used to estimate The molar mass of a gas.

Graham’s Law of Gaseous Effusion The rate of effusion of gases at the same temperature and pressure are inversely proportional to the square root of their molar masses.

Practice Problem: Graham’s Law of Gaseous Effusion Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure. Answer: Hydrogen effuses 3.98 times faster

Answer: Carbon dioxide Graham’s Law: You Try! Compare the rate of effusion of carbon dioxide with that of hydrogen chloride at the same temperature and pressure. Answer: Carbon dioxide effuses about 0.9 times as fast as HCl

The End