Applying the ideal gas equation

1. Applying the ideal gas equation General Chemistry: Chapter 6

2. Using the Gas Laws General Chemistry: Chapter 6

3. 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

4. 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

5. Completion of “XO2 example” in class

6. 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?

7. 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 oCa 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.

8. 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.

9. Empirical Formula of CxHyFz • “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. Mass of C atoms Mass of H atoms Mass of F atoms Moles of C atoms Moles of H atoms Moles of F atoms

10. 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. General Chemistry: Chapter 6

11. 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.... General Chemistry: Chapter 6

12. The total pressure of a mixture of gases is the sum of the partial pressures of the components of the mixture. Dalton’s law of partial pressures illustrated Figure 6-12 General Chemistry: Chapter 6

13. na naRT/Ptot Va = = ntotRT/Ptot ntot Vtot na a Recall = ntot na Pa naRT/Vtot = = ntotRT/Vtot ntot Ptot Partial Pressure Ptot = Pa + Pb +… Va = naRT/Ptot and Vtot = Va + Vb+… General Chemistry: Chapter 6