1 Molecular Composition of Gases Chapter 11

2 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

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

4 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:

5 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

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

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

8 You try A chemical reaction produces 2.56 L of oxygen gas at STP. How many moles of oxygen are in this sample? mol O 2

9 Example Suppose you need 4.22 g of chlorine gas. What volume at STP would you need to use? 1.33 L Cl 2

10 You try What is the mass of 1.33 x 10 4 mL of oxygen gas at STP? 19.0 g O 2

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

12 Review Boyles Law: Charles Law: Avogadro’s Law:

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

14 More math Convert a proportionality to an equality by multiplying by a constant

15 Therefore We can covert to

16 More neatly

17 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.

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

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

20 The ideal gas constant R Value depends on units SI units:

21 Other units

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

23 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

24 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

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

26 You try A researcher collects 9.09 x mol of an unknown gas by water displacement at a temperature of 16 °C and 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

27 Finding mass Number of moles (n) equals mass (m) divided by molar mass (M).

28 Example What mass of ethene gas, C 2 H 4, 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

29 You try NH 3 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 kg

30 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

31 Density

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

33 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

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

35 Example Xenon gas reacts with fluorine gas to produce the compound xenon hexafluoride, XeF 6. Write the balanced equation for this reaction. Xe(g) + 3F 2 (g)  XeF 6 (g) If a researcher needs 3.14 L of XeF 6 for an experiment, what volumes of xenon and fluorine should be reacted? 3.14 L of Xe and 9.42 L of F 2

36 Example Nitric acid can be produced by the reaction of gaseous nitrogen dioxide with water. 3NO 2 (g) + H 2 O(l)  2HNO 3 (l) + NO(g) If 708 L of NO 2 gas react with water, what volume of NO gas will be produced? 236 L

37 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

38 You try At STP, what volume of oxygen gas is needed to react completely with 2.79 x mol of carbon monoxide gas, CO, to form gaseous carbon dioxide? L

39 You try Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation: 3F 2 (g) + 2H 2 O(l)  6HF(g) + O 3 (g) What volumes of O 3 and HF gas would be produced by the complete reaction of 3.60 x 10 4 mL of fluorine gas? 1.20 x 10 4 mL O 3 and 7.20 x 10 4 mL HF

40 You try Ammonia is oxidized to make nitrogen monoxide and water 4NH 3 (g) + 5O 2 (g)  4NO(g) + 6H 2 O(l) At STP, what volume of oxygen will be used in a reaction of 125 mol of NH 3 ? What volume of NO will be produced? 3.50 x 10 3 L O 2 and 2.80 x 10 3 L NO

41 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

42 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) + 6H 2 O (l)  2NaAl(OH) 4 (aq) + 3 H 2 (g) What mass of aluminum would be needed to produce 4.00 L of hydrogen gas at STP? 3.21 g

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

44 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 Cl 2

45 Example A sample of ethanol burns in O 2 to form CO 2 and H 2 O according to the following reaction. C 2 H 5 OH + 3O 2  2CO 2 + 3H 2 O If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and 40.°C, what volume of CO 2 is produced when measured at STP? 73.3 mL CO 2

46 You try Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 L of N 2 O 5 reacts at STP, what volume of NO 2 is produced when measured at 64.5 °C and 1.76 atm? 7.02 L NO 2

47 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

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

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

50 Algebra time

51 Rate of effusion Depends on relative velocities of gas molecules.

52 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.

53 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

54 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

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

56 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

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