Molecular Composition of Gases Chapter 11 Chemistry Chapter 11

Gay-Lussac’s law of combining volumes of gases At constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers Chemistry Chapter 11

Example When 2 L of hydrogen react with 1 L of oxygen 2 L of water vapor are produced. Write the balanced chemical equation: Chemistry Chapter 11

You try When 1 L of hydrogen gas reacts with 1 L of chlorine gas, 2 L of hydrogen chloride gas are produced. Write the balanced chemical equation: Chemistry Chapter 11

Avogadro's Law Equal volumes of gases at the same pressure and temperature contain the same number of molecules Atoms can’t split  diatomic molecules Gas volume is proportional to the number of molecules Chemistry Chapter 11

Molar Volume 1 mole of any gas contains 6.022 x 1023 molecules. According to Avogadro’s law, 1 mole of any gas must have the same volume. Standard molar volume: volume of 1 mole of any gas at STP 22.4 L Chemistry Chapter 11

Example You are planning an experiment that requires 0.0580 mol of nitrogen monoxide gas. What volume in liters is occupied by this gas at STP? 1.30 L NO Chemistry Chapter 11

You try A chemical reaction produces 2.56 L of oxygen gas at STP. How many moles of oxygen are in this sample? 0.114 mol O2 Chemistry Chapter 11

Example Suppose you need 4.22 g of chlorine gas. What volume at STP would you need to use? 1.33 L Cl2 Chemistry Chapter 11

You try What is the mass of 1.33 x 104 mL of oxygen gas at STP? 19.0 g O2 Chemistry Chapter 11

Discuss Explain Gay-Lussac’s law of combining volumes State Avogadro’s law and explain its significance. Chemistry Chapter 11

Review Boyles Law: Charles Law: Avogadro’s Law: Chemistry Chapter 11

Math A quantity that is proportional to each of several quantities is also proportional to their product. Therefore: Chemistry Chapter 11

More math Convert a proportionality to an equality by multiplying by a constant Chemistry Chapter 11

Therefore We can covert to Chemistry Chapter 11

More neatly Chemistry Chapter 11

This means…. The volume of a gas varies directly with the number of moles and the temperature in Kelvin. The volume varies indirectly with pressure. Chemistry Chapter 11

What if… n and T are constant? n and P are constant? nRT is a constant, k Boyle’s Law n and P are constant? nR/P is a constant, k Charles’s Law Chemistry Chapter 11

What if… P and T are constant? RT/P is a constant, k Avogadro’s law Chemistry Chapter 11

The ideal gas constant R Value depends on units SI units: Chemistry Chapter 11

Other units Chemistry Chapter 11

Solving ideal gas problems Make sure the R you use matches the units you have. Make sure all your units cancel out correctly. Chemistry Chapter 11

Example A 2.07 L cylinder contains 2.88 mol of helium gas at 22 °C. What is the pressure in atmospheres of the gas in the cylinder? 33.7 atm Chemistry Chapter 11

You try A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12 °C. What is the reading on the pressure gauge in atmospheres? 14.3 atm Chemistry Chapter 11

Example A reaction yields 0.00856 mol of oxygen gas. What volume in mL will the gas occupy if it is collected at 43 °C and 0.926 atm pressure? 240. mL Chemistry Chapter 11

You try A researcher collects 9.09 x 10-3 mol of an unknown gas by water displacement at a temperature of 16 °C and 0.873 atm pressure (after the partial pressure of the water vapor has been subtracted). What volume of gas in mL does the researcher have? 247 mL Chemistry Chapter 11

Finding mass Number of moles (n) equals mass (m) divided by molar mass (M). Chemistry Chapter 11

Example What mass of ethene gas, C2H4, is contained in a 15.0 L tank that has a pressure of 4.40 atm at a temperature of 305 K? 74.0 g Chemistry Chapter 11

You try NH3 gas is pumped into the reservoir of a refrigeration unit at a pressure of 4.45 atm. The capacity of the reservoir is 19.4 L. The temperature is 24 °C. What is the mass of the gas in kg? 6.03 x 10-2 kg Chemistry Chapter 11

Example A chemist determines the mass of a sample of gas to be 3.17 g. Its volume is 942 mL at a temperature of 14 °C and a pressure of 1.09 atm. What is the molar mass of the gas? 72.7 g/mol Chemistry Chapter 11

Density Chemistry Chapter 11

You try The density of dry air at sea level (1 atm) is 1.225 g/L at 15 °C. What is the average molar mass of the air? 29.0 g/mol Chemistry Chapter 11

Stoichiometry Involves mass relationships between reactants and products in a chemical reaction For gases, the coefficients in the balanced chemical equation show volume ratios as well as mole ratios All volumes must be measured at the same temperature and pressure Chemistry Chapter 11

Volume-Volume calculations From volume of one gas to volume of another gas Use volume ratios just like mole ratios in chapter 9 Chemistry Chapter 11

Example Xenon gas reacts with fluorine gas to produce the compound xenon hexafluoride, XeF6. Write the balanced equation for this reaction. Xe(g) + 3F2(g)  XeF6(g) If a researcher needs 3.14 L of XeF6 for an experiment, what volumes of xenon and fluorine should be reacted? 3.14 L of Xe and 9.42 L of F2 Chemistry Chapter 11

Example Nitric acid can be produced by the reaction of gaseous nitrogen dioxide with water. 3NO2(g) + H2O(l)  2HNO3(l) + NO(g) If 708 L of NO2 gas react with water, what volume of NO gas will be produced? 236 L Chemistry Chapter 11

You try What volume of hydrogen gas is needed to react completely with 4.55 L of oxygen gas to produce water vapor? 9.10 L Chemistry Chapter 11

You try At STP, what volume of oxygen gas is needed to react completely with 2.79 x 10-2 mol of carbon monoxide gas, CO, to form gaseous carbon dioxide? 0.312 L Chemistry Chapter 11

You try Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation: 3F2(g) + 3H2O(l)  6HF(g) + O3(g) What volumes of O3 and HF gas would be produced by the complete reaction of 3.60 x 104 mL of fluorine gas? 1.20 x 104 mL O3 and 7.20 x 104 mL HF Chemistry Chapter 11

You try Ammonia is oxidized to make nitrogen monoxide and water 4NH3(g) + 5O2(g)  4NO(g) + 6H2O(l) At STP, what volume of oxygen will be used in a reaction of 125 mol of NH3? What volume of NO will be produced? 3.50 x 103 L O2 and 2.80 x 103 L NO Chemistry Chapter 11

Volume-mass and mass-volume Converting from volume to mass or from mass to volume Must convert to moles in the middle Ideal gas law may be useful for finding standard conditions Chemistry Chapter 11

Example Aluminum granules are a component of some drain cleaners because they react with sodium hydroxide to release both heat and gas bubbles, which help clear the drain clog. The reaction is: 2NaOH(aq) + 2Al(s) + 6H2O (l)  2NaAl(OH)4(aq) + 3 H2(g) What mass of aluminum would be needed to produce 4.00 L of hydrogen gas at STP? 3.21 g Chemistry Chapter 11

Example Air bags in cars are inflated by the sudden decomposition of sodium azide, NaN3 by the following reaction: 2NaN3(s)  3N2(g) + 2Na(s) What volume of N2 gas, measured at 1.30 atm and 87 °C, would be produced by the reaction of 70.0 g of NaN3? 36.6 L Chemistry Chapter 11

You try What volume of chlorine gas at 38°C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl? 3.54 L Cl2 Chemistry Chapter 11

Example A sample of ethanol burns in O2 to form CO2 and H2O according to the following reaction. C2H5OH + 3O2  2CO2 + 3H2O If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and 40.°C, what volume of CO2 is produced when measured at STP? 73.3 mL CO2 Chemistry Chapter 11

You try Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 L of N2O5 reacts at STP, what volume of NO2 is produced when measured at 64.5 °C and 1.76 atm? 7.02 L NO2 Chemistry Chapter 11

Review Diffusion: the gradual mixing of gases due to their random motion Effusion: gases in a container randomly pass through a tiny opening in the container Chemistry Chapter 11

Rate of effusion Depends on relative velocities of gas molecules. Velocity varies inversely with mass Lighter particles move faster Chemistry Chapter 11

Kinetic energy Depends only on temperature Equals For two gases, A and B, at the same temperature Each M stands for molar mass Chemistry Chapter 11

Algebra time Chemistry Chapter 11

Rate of effusion Depends on relative velocities of gas molecules. Chemistry Chapter 11

Graham’s law of effusion The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Chemistry Chapter 11

Graham’s law Graham experimented with densities of gases, not molar masses. Density and molar mass are directly proportional So we can replace molar mass with density in the equation Chemistry Chapter 11

Use of Graham’s law Finding the molar mass Compare rates of effusion of a gas with known molar mass and a gas with unknown molar mass Use Graham’s law equation to solve for the unknown M Used to separate isotopes of uranium Chemistry Chapter 11

Example Compare the rates of effusion of hydrogen and helium at the same temperature and pressure. Hydrogen diffuses about 1.41 times faster Chemistry Chapter 11

Example Nitrogen effuses through a pinhole 1.7 times as fast as another gaseous element at the same conditions. Estimate the other element’s molar mass and determine its probable identity. 81 g/mol, krypton Chemistry Chapter 11

You try Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of carbon dioxide. 17 g/mol Chemistry Chapter 11