Chapter 11: Molecular Composition of Gases Coach Kelsoe Chemistry Pages 332–361

Section 11-3: Volume–Mass Relationships of Gases Coach Kelsoe Chemistry Pages 378–380

Section 11–3 Objectives State the law of combining volumes. State Avogadro’s law and explain its significance. Define standard molar volume of a gas, and use it to calculate gas masses and volumes. Use standard molar volume to calculate the molar mass of a gas.

Measuring and Comparing the Volumes of Reacting Gases In the early 19th century, French chemist Joseph Gay-Lussac studied gas volume relationships involving a chemical reaction between hydrogen and oxygen. He observed that 2 liters of hydrogen can react with 1 liter of oxygen to produce 2 liters of water vapor: Hydrogen gas + Oxygen gas  Water vapor 2 L 1 L 2 L 2 volumes 1 volume 2 volumes

Measuring and Comparing the Volumes of Reacting Gases In other words, this reaction shows a simple and definite 2:1:2 relationship between the volumes of the reactants and the product. The 2:1:2 relationship for this reaction applies to ANY proportions for volume – for example, 2 mL, 1 mL, and 2 mL; 600 L, 300 L, and 600 L; or 400 cm3, 200 cm3, and 400 cm3. Not every ratio will be a 2:1:2 ratio. These numbers can vary, but will always hold true for the same reactions.

Measuring and Comparing the Volumes of Reacting Gases Gay-Lussac also noticed simple and definite proportions by volume in other reactions of gases, such as in the reaction between hydrogen and chlorine gas. Hydrogen gas + Chlorine gas  HCl gas 1 L 1 L 2 L 1 volume 1 volume 2 volumes In 1808, Gay-Lussac summarized the results of his experiments in a statement known today as Gay-Lussac’s law of combining volumes of gases.

Measuring and Comparing the Volumes of Reacting Gases Gay-Lussac’s law of combining volumes of gases states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. This simple observation, combined with the insight of Avogadro, provided more understanding of how gases react and combine with each other.

Avogadro’s Law Remember an important point of Dalton’s atomic theory: atoms are indivisible. Dalton also thought that the particles of gaseous elements exist in the form of isolated single atoms. He believed that one atom of one element always combines with one atom of another element to form a single particle of the product.

Avogadro’s Law Accounting for some of the volume relationships observed by Gay-Lussac presented a problem for Dalton’s theory. For example, in reactions such as the formation of water vapor, it would seem that the oxygen involved would have to divide into two parts. In 1811, Avogadro found a way to explain Gay-Lussac’s simple ratios of combining volumes without violating Dalton’s idea indivisible atoms.

Avogadro’s Law Avogadro was able to do this by rejecting Dalton’s idea that reactant elements are always in monatomic form when they combine to form products. He reasoned that these molecules could contain more than one atom. Avogadro also put forth an idea known today as Avogadro’s law, which says that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Avogadro’s Law 1 mol H2 at STP = 22.4 L 1 mol O2 at STP = 22.4 L

Avogadro’s Law Let’s reconsider the reaction of hydrogen and chlorine to form hydrogen chloride gas. According to Avogadro’s law, equal volumes of hydrogen and chlorine contain the same number of molecules. Avogadro accepted Dalton’s idea that atoms of hydrogen and chlorine are indivisible, but rejected the idea that these elements are monatomic. He concluded that the hydrogen and chlorine components must each consist of two or more atoms joined together.

Avogadro’s Law + Hydrogen gas H2 1 Volume 1 Molecule Chlorine gas Cl2 Hydrogen Chloride gas 2HCl 2 Volumes 2 Molecules +

Avogadro’s Law Avogadro’s reasoning applied equally well to the combining volumes for the reaction of hydrogen and oxygen to form water vapor. The simplest hypothetical formula for oxygen indicated two oxygen atoms, which turns out to be correct. The simplest possible molecule of water indicated two hydrogen atoms and one oxygen atom per molecule, which is also correct. All elements that are gases near room temperature, except noble gases, exist as diatomic molecules.

Avogadro’s Law Avogadro’s law also indicates that gas volume is directly proportional to the amount of gas, at a given temperature and pressure: V = kn V = volume, n = number of moles of gas, k = constant

Molar Volume of Gases Remember that one mole of a molecular substance contains a number of molecules equal to Avogadro’s constant (6.022 x 1023). One mole of oxygen, O2, contains 6.022 x 1023 diatomic oxygen molecules and has a mass of 31.9988 grams. One mole of hydrogen, H2, contains 6.022 x 1023 diatomic hydrogen molecules but has a mass of only 2.01588 grams.

Molar Volume of Gases According to Avogadro’s law, one mole of any gas will occupy the same volume as one mole of any other gas at the same temperature and pressure, despite mass differences. The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas. It has been found to be 22.41410 L. For our calculations, we will use 22.4 as the standard molar volume.

Molar Volume of Gases Knowing the volume of a gas, you can use 1 mol/22.4 L as a conversion factor to find the number of moles, and therefore the mass, of a give volume of a given gas at STP. You can also use the molar volume of a gas to find the volume, at STP, of a known number of moles or a known mass of a gas.

Sample Problem 11–1 A chemical reaction produces 0.0680 mol of oxygen gas. What volume in liters is occupied by this gas sample at STP? Given: molar mass of O2 = 0.0680 mol Unknown: volume of O2 in liters at STP Using our conversion factor of 1 mol/22.4 L (or the reciprocal), we can solve for volume! 0.0680 mol x 22.4 L = 1.52 L O2 1 mol

Sample Problem 11–2 A chemical reaction produced 98.0 mL of sulfur dioxide gas, SO2, at STP. What was the mass (in grams) of the gas produced? Given: volume of SO2 at STP = 98.0 mL Unknown: mass of SO2 in grams We can’t convert directly from volume to mass, but we can convert from volume to moles to mass. 98.0 mL x 1 L x 1 mol SO2 x 64.07 g = 0.28 1000 mL 22.4 L 1 mol SO2

Vocabulary Avogadro’s law Gay-Lussac’s law of combining volumes of gases Standard molar volume of a gas