help with HW question, ppb by vol of SO2?

Hi all,
This is a homework question, and I don't want an answer- but I'd sure like a 'point'(or two...) in the right direction. I am sorta floundering.

First off- I'm NOT a chem or chem eng. major- I'm a mechanical engineering major about to graduate and I have to take this environ. chem. class. I like it a lot, I'm learning some cool stuff, but chem. nomenclature/vocab is not at all second nature for me, though 90% of the problems I am able to solve by just reading the problems well, and by using analysis and basic knowledge or research.

 So: the question.

Natural sources add sulfur dioxide (SO2) to the atmosphere at a rate of about
1E8 tonnes (S)/yr. The background concentration of atmospheric SO2, measured
in remote areas where anthropogenic sources are not likely to have much influence,
is about 0.1 parts per billion, by volume. What is the residence time of
atmospheric SO2 in the remote regions (in days)?

The "hint" given is as follows:
Calculate number of moles of background SO2 in atmosphere by multiplying number of moles of air by the molar fraction SO2. Residence time equals mass SO2 in atmosphere divided by SO2 input rate.

the second 'hint' is that the mass of the atmosphere is 5.14 E21 grams.

 So, okay.

 I am unsure about a couple of things.

First of all, calculating moles of SO2 in atmosphere by finding # of moles of air- what, in the whole atmosphere? I can do that, if I can use the usual approx for air of 29 g/mol.

Second, the units of measurement are given as parts per billion by volume, ppbv. I have not used this measurement before, and I am not really sure how to proceed with it.

Third, to find moles of air in a specific volume, IIRC, I can use the ideal gas relation PV = nRT, but is that R(bar) or R(bar)/M, and take M = 29 kmol/kg approx for air? (I would have to look up M for SO2, but finding that's not a problem- I think it's around 64g/mol if I remember right).
But I'm given the mass of the atmosphere, so I shouldn't need to use PV= nRT, because I can find n from mass and M(air).


(it's been a while; I have used slightly similar stuff in gas dynamics but I'm a little stuck here.)

One of the difficulties is that this is an online class with minimal support, and a text with not many examples nor a well-laid-out form.


This is what I've done so far, if anyone would be willing to look at it.

First, 1 E8 tonnes = 100 E12 grams. So my units are the same.

Mass of atmosphere = 5.14 E21 g

moles in atmosphere = 5.14 E 21 g * (1 mol air / 29 g) = 177.2 E 18 moles air in atmosphere

NO2 is .1 ppbv- here's where I get confused. It seems I should be able to then do this:

177.2 E18 moles air * (.1 part SO2/ 1 E9 parts air) = 17.72 E9 moles SO2 in atmosphere

17.72 moles SO2 *(64 g SO2/1 mol SO2) = 1.134 E12 g SO2 in atmosphere

1.134 E12 g SO2 / (100 E12 grams SO2/year) = .01134 years

in days, .01134 years * (365 days / 1 year) = 4.037 days

but that's not right. I don't have the right answer- I just know that mine's wrong.

any help is appreciated!!

k wallace
.

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