Residence time of SO2 in the atmosphere

[il27]

Homework Statement

1. Use the IPCC estimate of anthropogenic SO2 emissions of 55 ⋅ 109 kg/year and natural SO2 emissions of 15 ⋅ 109 kg/year to estimate the residence time of SO2 in the atmosphere.
2. Is the residence time consistent with SO2 emissions being able to travel from Ohio to Maine as part of a weather system before precipitating as acid rain?

Homework Equations

$$ \tau = \frac{M}{m'} $$
number of moles of air/in atmosphere = 1.77 x 10^20 mol using the equation
$$ n_{air} = \frac{m_{atm}}{\text{molecular weight}_{air}} $$

The Attempt at a Solution

I was unsure in this question if the anthropogenic SO2 emissions in units of kg/year could also be the removal rate? So then I could use an equation to find the number of moles of SO2. and then when finding the residence time I could use m' to be say 55 x 10^9 kg/year.
but i am not sure if it is right to assume that the anthro. SO2 emissions mean the removal rate?
Basically... I am stuck on how to begin this problem.

 

[scottdave]

Anthropogenic emissions means of human origin (basically from factories, etc). So you have two forms of emitting (producing) SO₂. But your problem statement does not give indication of how fast it precipitates, or how long the trip from Ohio to Maine will take in a weather system. There must be some more information to answer this question.

 

[haruspex]

But your problem statement does not give indication of how fast it precipitates

Quite so. The extra info I would expect would relate to the mean level in the atmosphere, either now or pre-industrially. But either way, there seems no need to be given both emission rates. Very odd.

 

[il27]

The SO2 emitted by the burning of fossil fuels is the primary source of acid rain in the northeastern U.S. The burning of coal in the midwest is said to be responsible for this (as well as the mercury found in the fish). The dissolution of carbon dioxide in cloud droplets makes natural rainwater slightly acidic with a pH of 5 - 5.6; the dissolving of SO2 can decrease the pH of rainwater to a value as low as 2, considerably lower than that of vinegar (pH = 2.8).

I am only given different pHs :/ so I am not sure how to go about this.

 

[haruspex]

I am only given different pHs

You did not mention pH in post #1. It is important that you provide the whole question as given to you. Have you now provided every detail?

 

[il27]

You did not mention pH in post #1. It is important that you provide the whole question as given to you. Have you now provided every detail?

Yes! Sorry about that earlier. This is part of the question as well:

The SO2 emitted by the burning of fossil fuels is the primary source of acid rain in the northeastern U.S. The burning of coal in the midwest is said to be responsible for this (as well as the mercury found in the fish). The dissolution of carbon dioxide in cloud droplets makes natural rainwater slightly acidic with a pH of 5 - 5.6; the dissolving of SO2 can decrease the pH of rainwater to a value as low as 2, considerably lower than that of vinegar (pH = 2.8).do i need the PHs to find the residence time? also how does the total amount of sulphur in the atmosphere affect the residence time?

 

[haruspex]

do i need the PHs to find the residence time?

I can't see that it helps.

how does the total amount of sulphur in the atmosphere affect the residence time?

It's the other way around. The removal rate is proportional to the quantity in the atmosphere and inversely proportional to the residence time. So if the emission rate increases then the level in the atmohere increases until the removal rate matches the new emission rate.
The residence time itself depends on the rainfall and the chemistry, not the level in the air.

 

[il27]

I can't see that it helps.

It's the other way around. The removal rate is proportional to the quantity in the atmosphere and inversely proportional to the residence time. So if the emission rate increases then the level in the atmohere increases until the removal rate matches the new emission rate.

okay, so it was okay to use the emission rate as m'? i added the two emission rates.

 

[haruspex]

okay, so it was okay to use the emission rate as m'? i added the two emission rates.

Adding the two emission rates to get the total emission rate is fine, but without knowing the ambient level in the atmosphere I do not see how you can calculate the residence time.

 

[il27]

Adding the two emission rates to get the total emission rate is fine, but without knowing the ambient level in the atmosphere I do not see how you can calculate the residence time.

what is the ambient level in the atmosphere?

because what i did was i fonud the total # of mols in the atmosphere. multiplied the number of moles in atm by the concentration of SO2 in the amtosphere. from a book it said 10 pptv - 1ppbv, so i used those two values.
so # of moles SO2 in atmosphere was calculated from # of moles of air times the parts per volume.
then the total mass was multiplied by the molecular weight of SO2 with the # of moles.
then the residence time was calculated from dividing the total mass by the total emission rate.

with 10 pptv, i got a residence time of .6 days. with a concentration of 1ppbv i got a res. time of 59 days.

i just don't understand the second part of the problem on whether the residence time is likely for SO2 emissions to travel from ohio to maine... also if we need to find the total amonut of sulphur in the atmosphere.

 

[haruspex]

a residence time of .6 days. with a concentration of 1ppbv i got a res. time of 59 days.

Online I see a figure of 1 day, so you are in the right ballpark.

whether the residence time is likely for SO2 emissions to travel from ohio to maine

Wind speeds?

 

[il27]

Online I see a figure of 1 day, so you are in the right ballpark.

Wind speeds?

do you have an idea how to use the wind speeds? i am just cnofused on the second part of hte question.

 

[haruspex]

do you have an idea how to use the wind speeds? i am just cnofused on the second part of hte question.

On second thoughts, it might be more a question of how fast weather fronts move. Do you understand the difference?
See https://www.livescience.com/39004-weather-fronts-definition-facts.html.
It's a bit complicated. If a weather front is so large that it spans Ohio to Maine then wind speed within the front may be what's crucial; if it is much smaller than that then the speed of the front is what matters (and this will generally be lower); in between, it's a combination of the two.

 

[il27]

On second thoughts, it might be more a question of how fast weather fronts move. Do you understand the difference?
See https://www.livescience.com/39004-weather-fronts-definition-facts.html.
It's a bit complicated. If a weather front is so large that it spans Ohio to Maine then wind speed within the front may be what's crucial; if it is much smaller than that then the speed of the front is what matters (and this will generally be lower); in between, it's a combination of the two.

oh okay thank you. i'll see what i can do.
however do you think my process for finidng the residence times is accurate for So2 in the atmosphere?

 

[haruspex]

oh okay thank you. i'll see what i can do.
however do you think my process for finidng the residence times is accurate for So2 in the atmosphere?

It is ok, but given the 100:1 ratio on the fraction of SO2 in the atmosphere it cannot be considered accurate.
I have no better suggestion.