Dalton’s Law The total pressure of a mixture of gases equals the sum of the pressures

1. Dalton’s Law • The total pressure of a mixture of gases equals the sum of the pressures • each gas would exert independently • Ptotal = P1+ P2 + … • Partial pressures is the pressure a gas in a mixture • would exert if it were alone in the container • Particularly useful for determining the pressure a dry gas • collected over water: Ptotal = Pwet gas = Pgas + Pwater • 4. Pwater vapor depends on the temperature, look up in table • Combining Dalton’s Law and Ideal Gases • We can assume each gas will behave ideally in the mixture • It’s the total number of particles present that is important • The volume of the individual particle is very small • The forces among particles are very small

2. Problems • Example: 46L He and 12L O2 at 25 oC and 1atm are pumped into a 5.0L tank. What are the partial and total pressures? • Calculate the number of moles of each gas from the ideal gas law • Calculate partial pressures of each gas from new conditions • Add partial pressures: 9.3atm + 2.4atm = Ptot = 11.7atm • Mole fraction = c1 = moles of molecule 1 divided by moles total

3. 3. Example: Find cO2 if PO2 = 156torr in air at PT = 743torr. • cO2 = PO2/PT = 156torr/743torr = 0.210 • 21% of the air molecules are oxygen • 4. Example: Calculate PN2 if cN2 is 0.7808 when PT = 760torr. • PN2 = cN2 x PT = (0.7808)(760torr) = 593torr • Example: 0.650L of gas at 22 oC is collected over water in the decomposition reaction of KClO3. Calculate PO2 in this gas and the amount of KClO3 in the reaction. PH2O= 21torr at 22 oC. PT = 754 torr • 2KClO3(s) -------> 2KCl(s) + 3O2(g) • Find PO2 from Daltons Law: PO2 = PT – PH2O = 754-21 = 733torr • Use ideal gas law to find moles O2 • Calculate moles KClO3 needed to make this O2.

4. The Kinetic Molecular Theory of Gases • Empirical Laws • Gas Laws we have just studied • Describe how gases behave, but don’t explain why they behave that way • Theory or Model • Explains why gases behave as they do • Describing an Ideal Gas with the Kinetic Molecular Theory (KMT) • Gas particles very small compared to distance between them (assume gas molecules have no volume) • Molecules constantly and rapidly move in a straight line until they bump into each other or the wall (this causes pressure) • Assume that the gas molecules’ attraction for each other is negligible • Average kinetic energy is proportional to the temperature (K) • Real gas molecules do have volumes, do attract each other • Test: can the theory predict the experimental observations of PV = nRT? • Pressure is inversely proportional to Volume (Boyle’s Law) • KMT: Decrease in Volume means particles hits wall more often • This results in an increase in Pressure

5. Pressure is directly proportional to Temperature • KMT: As temperature increases, gas speed increase • Pressure increases as the collisions with the wall are harder • Volume is directly proportional to Temperature (Charles’s Law) • KMT: As temperature increases, gas speed increase • If pressure is to remain the same, the volume must increase • Volume is directly proportional to number of moles (Avogadro’s Law) • KMT: As moles increases, more collisions with the walls occur • If pressure is to remain the same, the volume must increase

6. Mixtures of Gases (Dalton’s Law) • KMT: Identity of the gas molecule doesn’t change (ideal) properties • Adding another gas increases pressure same as adding first gas • Ideal Gas Law—Derivation from KMT • Physics (NA = Avogadro’s number, m = mass of particle, m = velocity) • KMT: average KE is directly proportional to T(K) • The Meaning of Temperature • KMT: average KE is directly proportional to T(K)

7. Root Mean Square Velocity • Root mean square velocity = mrms • Deriving an expression for mrms • a. • b. • c. • 3. Example: Calculate mrms for He at 25 oC.

8. Range of velocities of a gas sample • Mean free path = avg. dist. between collisions ~ 1 x 10-7 m at STP • Many collisions produce large range of velocities • 500 m/s ~ mrms at STP, but velocities are widely ranging • Temperature greatly effects the distribution (KMT) • Effusion and Diffusion • Effusion = movement of gas into vacuum through a small opening • Example: Find ratio of effusion rate for H2 and UF6. • Graham’s Law:

9. KMT: effusion depends on average velocity of the gas particles • Diffusion = mixing of gases • NH3(g) + HCl(g) -------> NH4Cl(s) • Expected speed of mixing would allow estimation of distances: • Multiple collisions with air gases complicate the model of diffusion • The ratio of distance traveled is < 1.5; mixing time is several minutes

10. H. Real Gases • No gas is ideal, although most are close at low P and high T • Where does the KMT fail in describing Real Gases? • For an ideal gas, PV/nRT = 1 at all pressures and temperatures • Modifying the Ideal Gas Law • Real gas molecules have volume, which reduces the Volume available • An empirical constant b for each gas is determined 203 K

11. Real gas molecules attract each other, making Pobs < P’ • The higher the concentration of particles, the larger the effect • The number of interacting pairs depends on (concentration)2 • N particles has N-1 partners • Divide by 2 to eliminate counting each pair twice • The correction for V and P combine in van der Waalsequation • a and b are varied until the best fit of observation is found • Low pressure = large volume, where volume of particles is negligible • High temperature = fast motion, where attractions are negligible

12. Atmospheric Chemistry • Components: N2 = 78%, O2 = 21%, Ar, CO2, less than 1%, H2O is variable • Smog Production in the lower atmosphere • Burning fossil fuels produces NOx = NO and NO2 • NO2 + light -------> NO + O • O + O2 -------> O3 ------> O2 + O* (high energy O atom) • O* + H2O -------> 2OH radicals • OH + NO2 -------> HNO3 (nitric acid) • OH + hydrocarbons -------> photochemical smog • Prevalent in urban areas; harmful to respiratory system • Combated by public transportation, cleaner burning fuels • Acid Rain • 1. S(in coal) + O2 -------> SO2 • 2. 2SO2 + O2 -------> SO3 • SO3 + H2O -------> H2SO4 (sulfuric acid) • Harmful to buildings and organisms • Need to remove sulfur from coal (Scrubbing) • a. CaCO3 -------> CaO + CO2 • b. CaO + SO2 -------> CaSO3 (solid calcium sulfite)