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Applying the ideal gas equation Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 1 of 19 Using the Gas Laws Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 2 of 19 Avogadro’ Hypothesis: • Equal volumes of different gases at the same T and P contain equal numbers of molecules (or, equal numbers of moles of gas). Neglecting history (Avogadro’s elegant experiments!), we can apply the Ideal Gas Law Equation to two gases (Gas 1 and Gas 2). • n1 = P1V1/RT1 and n2 = P2V2/RT2 • If P1=P2 and V1=V2 and T1=T2 then n1=n2 Class Example – Avogadro’s Hypothesis: • At a given T and P, 8.00 g of oxygen gas (O2(g)) has a volume of 8.00 L. At the same T and P 10.0 L of a gas having the molecular formula XO2 has a mass of 20.0 g. Identify element X. Partial Solution: Apply Avogadro’s Hypothesis Here: Number of moles of = Number of moles of O2(g) per liter XO2(g) per liter # Moles O2(g) per liter = 0.250 mol/8.00L = 0.0313 mol∙L-1 “Aside”: Moles O2 = 8.00g/(32.0 g.mol-1) = 0.250mol Completion of “XO2 example” in class Ideal Gas Law and Molecular Formulas: • In high school you used % composition data for compounds to derive corresponding empirical formulas. The Ideal Gas Law Eqtn can be used to determine molar masses. Combining an empirical formula with a molar mass allows a molecular formula to be determined. Empirical formulas specify relative numbers of atoms of each element. Knowing “too much chemistry” Can lead you astray. How? Molecular Formulas using PV=nRT • Elemental analysis shows that a compound containing carbon, hydrogen and fluorine , CxHyFz, is 63.17 % carbon, 3.53 % hydrogen and 33.30 % fluorine by mass. At 44.2 oC a 2.400 g sample of this substance is completely evaporated in a previously empty 2.50 L container and a gas pressure of 22.2 kPa is observed. Determine (a) the empirical formula of the compound and (b) the molecular formula of the compound. A Step at a Time? • One possible strategy is: • Step 1: Use mass % composition data to determine the empirical formula for CxHyFz. • Step 2: Use the ideal gas law equation to get (a) the number of moles of CxHyFz in 2.400g of compound and (b) the molar mass of CxHyFz. • Step 3: Combine the results to Step 1 and Step 2 to find the molecular formula of CxHyFz. Empirical Formula of CxHyFz • Mass of C atoms Mass of H atoms Mass of F atoms Moles of C atoms Moles of H atoms Moles of F atoms • “Knowing too much chemistry” one might be tempted to use 2.016 g.mol-1 for the molar mass of H. Why is this absolutely wrong? We’ll complete this problem in class. 6-5 Gases in Chemical Reactions •Stoichiometric factors relate gas quantities to quantities of other reactants or products. •Ideal gas equation relates the amount of a gas to volume, temperature and pressure. •Law of Combining Volumes can be developed using the gas law. Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 10 of 41 6-6 Mixtures of Gases •Partial pressure –Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone. • Gas laws apply to mixtures of gases. • Simplest approach is to use ntotal, but.... Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 11 of 41 The total pressure of a mixture of gases is the sum of the partial pressures of the components of the mixture. Figure 6-12 Dalton’s law of partial pressures illustrated Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 12 of 41 Partial Pressure Ptot = Pa + Pb +… Va = naRT/Ptot and Vtot = Va + Vb+… na naRT/Ptot Va = = ntotRT/Ptot ntot Vtot Pa Ptot Recall na = ntot a na naRT/Vtot = = ntotRT/Vtot ntot Copyright © 2011 Pearson Canada Inc. General Chemistry: Chapter 6 Slide 13 of 41