1. 11 L of a stoichiometric mixture of methane, CH₄, dioxygen, O₂, and an unreactive diluent gas, D, at STP are sparked, and the products are returned to STP where their total volume now measures 9 L. What were the mole fractions of the original gas mixture? [HINT: H₂O is certainly not a gas at STP.]

2. The heat capacity at constant pressure, C_P, of dioxygen is 29.4 J/mol°C at standard conditions while that of methane is 35.3 J/mol°C. If you can't run it stoichiometrically, do you want to run an oxy-methane torch (super-Bunsen burner) a little rich or lean for the highest temperatures? Why? (Not a lot rich or lean, mind you, or you will change the combustion products!)

3. Methane and dioxygen at the same pressure and temperature in their respective tanks are leaking through identical sized holes into a vacuum chamber.
   1. What are the mole fractions of the two gases in the chamber? Is that rich or lean?

   2. If the dioxygen was at 25°C, at what temperature of the methane would that mole fraction be equal?


4. Methane is a greenhouse gas, but it burns fairly cleanly, producing another greenhouse gas in CO₂. Still, methane engines can be tuned easily to eliminate CO and unburnt hydrocarbon, so it is an attractive fossil fuel. And a whole lot more of it has recently been discovered!

   Just as CO₂ forms a hydrate at ocean floor pressures, so does methane! That pale blue flame arising from the white powder is methane slowly burning out of its water clathrate. Estimates of the earth's supply of methane hydrate exceed all other known hydrocarbon supplies! But there's a danger: methane is a Greenhouse gas; so "spills" don't mess up coastlines, they mess up climates.

   So if we want to tap this source, we need to know about its decomposition properties. Fortunately, the experiments have been done (figure at right). A MPa is, of course, 1000 kPa or 10 bar ~ 10 atm. Notice that the methane pressure is 1 MPa at about 240 K and 10 MPa at about 285 K. What is DH_sublimation of methane hydrate in this temperature range?

5. The primary destruction mechanism for methane in the troposphere starts with the following elementary radical reaction:
   ·OH + CH₄ ·CH₃ + H₂O     k = 1.60×10¹² e^{-15,000 J / RT} L mol^-1 s^-1

   The natural environment background concentration of methane in the atmosphere is about 700 ppb (parts per billion by volume), but Man's influence has raised that to 1780 ppb now. (You gotta worry when we more than double a component of the air.) And the average concentration of ·OH is 8.1×10⁵ molecules/cm³ assumed fixed.

   Estimate the half-life of methane in the 5°C troposphere at sea level. [HINT: Convert everything to M first so you don't go insane. And note that if ·OH really is fixed in concentration, that reaction can be reduced to a first-order one! Think about its effective first order rate constant. Clever?]

6. Lightning strokes last only 0.2 ms, but there may be 35 of them in a single flash which lasts about 0.25 s. So even during a flash, the lightning is spending most of its time thinking about the next stroke rather than discharging it.

   But during each stroke, the current averages about 40,000 amps at about 10 MV. Since the energy of the stroke is the charge in Coulombs multiplied by the voltage in volts, what's the work done by a single stroke in MJ? How about a flash of 35 such strokes?

   It's not hard to see how a lot of NO and O₃ can get produced thereby. In fact, since DH_f[NO] = 90 kJ/mol, how many moles of NO could a flash produce? (But it can't because there aren't that many moles of oxygen in the volume of the flash to get converted!)

7. The fundamental acid-base reaction,
   2 H₂O(liq) H₃O⁺(aq) + OH^-(aq)

   makes us worry briefly about reaction entropy, because the molar entropies of water, hydronium ion, and hydroxide ion are 70, 0, and -11 J/mol K^-1, respectively.

   Why is that jarring? And what resolves the paradox?


8. OK...enough "interesting" questions, right?

   To the right is the crystal structure of nickel arsenide.

   This mineral has an amazingly high specific gravity of 7.8 g/cc.

   What, then, is the volume of that unit cell (in ų)? [HINT: an Š= 100 pm]

    

    

9. A diver, seeking to avoid the bends, substitutes He for the N₂ in her scuba tank. If Henry's constant for helium at blood temperature is 2610 L atm/mol, what is the concentration (millimolar) of helium in her blood at the bottom of a 100 foot dive? [HINT: specific gravity of the water is 1 but that of mercury is 13.6. Oxygen is still 20% of the mixture in her tank; we don't want her to asphyxiate. We just want her to sound like Donald Duck.]

10. The cryoscopic constant (fancy name for the freezing point depression) of water is 1.86 °C kg/mol. If some solution exhibits a 1.00 m (of water) osmotic pressure at 25°C, what would its freezing point be? (See? Osmosis is much more sensitive.)

11. The addition of HCl to propene (CH₃CH=CH₂) to make 2-chloropropane (CH₃CHClCH₃) apparently proceeds through an HCl dimer and a propene-dimer complex as follows:
    2 HCl (HCl)₂     K₁   fast
    (HCl)₂ + propene complex     K₂   fast
    HCl + complex 2-chloropropane + 2 HCl     k   slow
    1. Show that this mechanism yields the correct overall reaction.
    2. What are the orders of the reactants in the overall rate expression?

    [HINT: Be sure to see the difference between capital K as an equilibrium constant and lowercase k as a rate constant.]

12. The reduction potentials for the zinc and silver from their normal ions are -0.76 and +0.80 volts, respectively. In a Galvanic cell properly constructed of these metals and their solutions, would diluting the silver ion increase or decrease the cell's potential? Why?

For those of you who have forgotten the way to lunch, the map overleaf has a star on 3208 Regent Place. You go up Waterview (north) from the University which turns into Independence. Go left (west) on 15th and right (north) on Silverwood (at the Baptist Church). The first right is the Regent Place cul-de-sac. Ours is the southernmost home.