Plan for Wed, 8 Oct 08

1. Plan for Wed, 8 Oct 08 • Mistake in Exam 1 key • Graphical LR problem: #13 in V1, #5 in V2 • Keys say the answer is B…the answer is really D • Bring your exam to me by Monday to get these points back • Lecture • Ideal gas law and gas density (5.3) • Gas stoichiometry (5.4) • Don’t forget about Friday’s quiz.

2. Standard T & P (STP) At STP, 1 mol of any ideal gas occupies 22.4 L T = 273 K (0oC) P = 1 atm = 101.325 kPa = 1.01325 bar (1 bar = 100 kPa) 22.4 L

3. 1 L 1 mol N2 1000 mL NA molcs N2 PV = nRT Example • What is the pressure exerted by 1.00 x 1020 molecules of N2 gas in a 305 mL flask at 175oC? P = ? V = 305 mL = 0.305 L n = 1.00 x 1020 molcs N2 = 0.000166 mol N2 R = 0.08206 L.atm/mol.K T = 175oC + 273 = 448 K

4. What is the pressure exerted by 1.00 x 1020 molecules of N2 gas in a 305 mL flask at 175oC? P = ? V = 0.305 L n = 0.000166 mol N2 R = 0.08206 L.atm/mol.K T = 448 K

5. PV = nRT Example A 50.0 L gas cylinder containing 21.5 atm of gas is connected to an odd shaped tank. After the gas in allowed to expand into the tank, the pressure on the cylinder reads 1.55 atom. What is the volume of the tank? Petrucci, pg. 182

6. Gas density • We can use PV = nRT to determine the density of gases. • What are the units of density? mass/volume • What does this suggest about gas density? It will depend strongly on T and P. • Contrast with liquids and solids, whose densities depend somewhat on T, but far less on P.

7. Gas Density Example • What is the density of O2 gas in g/L at 25oC and 0.850 atm? Calculate # moles in 1 L, use MM of O2 to get g, divide by V P = 0.850 atm V = 1 L n = ? R = 0.08206 L.atm/mol.K T = 25oC + 273 = 298 K

8. What is the density of O2 gas in g/L at 25oC and 0.850 atm? Calculate # moles in 1 L, use MM of O2 to get g, divide by V P = 0.850 atm V = 1 L n = ? R = 0.08206 L.atm/mol.K T = 298 K Note: A value for gas density is meaningful only if accompanied by the T and P at which it was measured.

9. Gas Density and Molar Mass • In our previous example, we calculated the density of O2(g). • How would our calculation change if we wanted the density of Cl2(g)? Or Br2(g)? • Did this calculation depend at all on the nature of O2(g)? • No! It only depends on the T, P, and V. • Remember Avogadro’s Law? Two equal volumes of an ideal gas at the same T and P will contain the same number of moles of gas, regardless of the identity of the gas. • So, a 1 L sample of either Cl2(g) or Br2(g) at 0.850 atm and 298 K will contain 0.0347 mol of gas particles.

10. Gas Density and Molar Mass • Density of 1 L of Cl2(g) at 0.850 atm and 298 K: • Density of 1 L of Br2(g) at 0.850 atm and 298 K: • Therefore, the density of an ideal gas depends on T, P, V, and Molar Mass

11. Gas Density and Molar Mass • We can develop an expression relating density and MM using PV = nRT. • Substituting: • We can use the density of a gas to determine its molar mass. Density!!

12. Gas Stoichiometry • Many chemical reactions involve gases. • Gases are often measured in terms of volume (given T and P) or pressure (given V and T) rather than mass. • If we assume that the gasses behave ideally, we can use the Ideal Gas Law to determine the number of moles of gas consumed or produced.

13. Gas Stoichiometry Example • What volume of N2, measured at 735 mmHg and 26oC, is produced when 70.0 g NaN3 is decomposed? 2 NaN3(s)  2 Na(l) + 3 N2(g) a) find moles of NaN3 b) use mole ratio to find moles of N2 c) use PV= nRT to find volume of N2