CHEM HELP: electrochemistry?

Question

A digital watch battery draws 0.20 milliamperes of current, which is provided by a mercury battery whose net reaction is:

HgO(s) + Zn(s) --> ZnO(s) + Hg(l)

If a partially used battery contains 0.70 g of each of these four substances, for how many hours will the watch continue to run?

Answer 1

http://answers.yahoo.com/question/index;_ylt=AscW9c9bDJZgck4UKC84xt3sy6IX;_ylv=3?qid=20071118195511AA2u9DB&show=7#profile-info-GMBKWRVYaa

Answer 2

Bookkeeping.

First, as always when comparing different materials, convert grams to moles. You will quickly see which one is the limiting reagent.

Each mole of limiting reagent can generate, in this case, 2 faradays of electricity, because it is a two-electron reaction. That tells you how many coulombs you can still get out of the battery.

Finally, amps x time (s) = : coulombs (definition)

Answer 3

I really like these sorts of problems. They're idealized but they actually show you how nuts-'n'-bolts chemical knowledge can be practically useful.

Electricity is... electrons (duh)! In the reaction you've got drawn, the electrons come from Zn(0), which loses two electrons and goes to Zn(2+):

Zn(0) ----> Zn(II) + 2e-

the electrons travel along wires from where the Zn(s) is turning into ZnO, power the watch, travel along more wires to where the CuO is turning into Cu(s), and there get soaked up by copper going from +2 to 0. There's your chemical battery.

So... each mole of Zn(s) is going to give you two moles of electrons. Easy so far?

Two parts: first, figure how fast the watch is going to use up electrons. Second, figure how many electrons the zinc can provide.

Ampere, A, is defined as coulombs/s, so

1A=1C/1s

Also, 1 coulomb has been calculated as being equal to 6.24E18 electron charges, which are produced by 6.24E18 electrons. You could say that

1A = 6.24E18 electrons / s

The watch draws 0.0002A of current. That's engineering terminology. Chemically, you want to know how many electrons per second this current represents:

0.0002*1A is 0.0002*6.24E18 electrons / s

or

1.25E15 electrons / s

That's how many electrons per second the watch needs. Now, how many moles of electrons can this battery give you? it can give you twice as many electrons as there are moles of Zn(s) present. Zn has a FW of 65.4, so 0.7g of Zn(s) is about 0.01 moles of Zn(s), which will produce 0.02 moles of electrons. How many electrons are in this many moles of electrons?

6.022 electrons / 1 mole of electrons * 0.02 moles of electrons = 1.2E22 electrons

And that is how many electrons 700mg of Zn(0) can give.

So if ALL of the zinc oxidizes and ALL of those electrons go to powering the watch and none are lost to resistance in the wires (yeah, right), how long will the watch last if it is using 1.25E18 of the electrons up each second?

You know you want your answer to have units of seconds, so you can tell to divide the numbers so that seconds ends up being in the numerator:

1.2E22 electrons / 1.25E18 electrons/s = 9600s

How many minutes is that, at 60 seconds per minute?

9600s / 60s/min = 160 minutes, or 2 hours and 40 minutes

Your limiting number of significant figures in all of this comes from the 0.7g of zinc. That's one sigfig, so really you can only say 10000s is about 200 minutes or about 3 hours. I prefer to assume the 0.7g is meant to say 0.70g, because that lets me talk about hours and minutes in the answer. But as the problem is written, the final answer will have to be 3 hours.

I think that's how this would go. Does that make sense?