Reef Chemistry Question of the Day #61 Gas Exchange 2

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #61

Carbon dioxide in room air is a big source of carbon dioxide to a reef aquarium, and a primary reason that the pH of many reef aquariums is lower than the ocean. A primary source of carbon dioxide is the CO₂ that people exhale after metabolizing foods. It turns out that a doubling of the CO₂ level in the air (to 2x normal) will result in about a 0.3 pH unit drop in the pH of seawater that is equilibrated with it.

This question deals with how much carbon dioxide comes from human activities.

After a long afternoon of mowing the lawn on a hot summer day, you come into your living room (15' x 22' x 8'), pop open a 12-oz (~335 mL) Coca-Cola, and drink it while you watch your reef tank. Assuming that there is no other source of excess carbon dioxide in your living room, and that all of the carbon dioxide comes from the cola (both by carbonation and by your complete metabolism of the sugar in it), about how much would the CO₂ in your living room rise?

A. to between 1.0x and 1.2x normal
B. to ~1.5x normal
C. to ~3x normal
D. to ~5x normal
E. to ~8x normal
F. to more than 10x normal

Assume no gas exchange to outside the room or with the aquarium. 5x means the room has five times the normal amount of CO₂ in outdoor air. Also assume this Coke used real sugar, as opposed to high fructose corn syrup, although I doubt that makes a big difference.

Bonus question: which effect is the larger contributor to the room CO₂: the carbonation in the can, or your metabolism of the sugar?

Good luck!

 

[Cory]

This is a good question. Although I've got no idea! I'm going to use my super human ability and guess C.

 

[Randy Holmes-Farley]

Well, we'll see how good of a guesser you are.

FWIW, I doubt many people will try to calculate the actual answer, although I know many reefers who could. I posted this really for people to be able to appreciate the magnitude of the CO2 issue that a home might have (and that doesn't mean the answer is necessarily A or F ).

 

[Cory]

Haha I think your using your super human ability, how'd you know I was watching tv drinking a can of coke! But you guessed one part wrong, it was coke zero!

 

[H2O]

Good question I go with F I would like to know what makes more co2 in a small apt cooking diner on the stove for 30min a day or drinking a can of coke also if I was to start growing phyto plankton in a 5g bucket how much co2 will the plankton consume will the co2 drop at least 50% or house plants r the better way to keep co2 low

 

[saltyhog]

Hmmm I should make a guess. 15 people in my den will lower my pH about 0.6 but I'm sure there is plenty of air exchange.

 

[treemanone2003]

In my less than accurate math skills, I would make the decision that "D" is the most suitable answer, but for some reason my brain says "E" is correct.

For the bonus question I would be more inclined to say that this could be more tricky than the first question but my medical background goes with the metabolism answer as metabolism rates are much slower at rest than at play. I would lean to also argue with myself as well a bit because the contribution of the gas while releasing from the idle can and the exhaled breath/metabolism combined would increase the measurable amount more significantly than one or the other. I'll also say that I was looking for any consideration of houseplants as pointed out above.

 

[Randy Holmes-Farley]

I'll put a houseplant discussion/calculation into the discussion of the answer. But that effect is usually small unless you live in a greenhouse.

 

[beaslbob]

depends on what normal is. LOL

 

[Randy Holmes-Farley]

And the answer is...C. to ~3x normal

And, almost all of the CO2 comes from metabolism of the sugar.


Lost my calculations so I have to redo them...

The amount of CO2 in a can of coke is about 2.2 grams
http://chemistry.stackexchange.com/questions/9067/what-is-the-carbon-dioxide-content-of-a-soda-can-or-bottle

and there is 39 grams of sugar
How Much Sugar in Sodas and Beverages?

Let's convert that sugar into CO2:
Assuming it is pure sucrose, the formula is C12H22O11 with a molecular weight of 322 g/mole

The fraction of the sugar molecule that is carbon by weight is: 12 carbon atoms x 12 grams/mole/carbon atom /322 g/mole = 0.45
So the amount of carbon in the sugar is 39 grams x 0.45 = 17.4 grams of carbon.

Now we convert that to carbon dioxide...
carbon molecular weight = 12 g/mole
carbon dioxide molecular weight = 44 g/mole

So carbon comprises 12/44 = .27 of carbon dioxide by weight.

So that 17.4 grams of carbon becomes 17.4/0.27 = 64 grams of CO2.

So first, we can see that the sugar, producing 64 grams of CO2, added way more than the carbonation, at 2.2 g.

So 66 grams of CO2 added to the room.

How much did the CO2 rise in relation to normal levels?

The room is 15' x 22' x 8' = 2640 cubic feet

Normal air has about 350 ppm carbon dioxide.

The density of normal air is 1.225 kg/m3.

Converting that room in cubic feet to cubic meters we get:

1 cubic foot = 0.0283 cubic meters.

So the room contains 2640 x 0.0283 = 75 cubic meters of air

This is surprising to me, the air in that room weighs 75 m3 x 1.225 kg/m3 = 92 kilograms!

So, we added 66 grams of CO2 into 92 kilograms of air.

That's 66 grams/92,000 grams x 10^6 (to make the fraction into ppm) = 717 ppm

So that 717 ppm is just about double the normal CO2 level of 350 ppm, making the final value about triple the normal CO2 levels.

Glad that worked out a second time. Could have been embarrassing.

 

[Randy Holmes-Farley]

As to plants, a plant would need to add about that same weight of sugar (plus a bit more for the carbonation CO2) to its dry weight to compensate for the carbon dioxide produced.

That may not sound like a lot, but think about all the foods you and your family eat in a day. If all that metabolized food ended up in the house, then plants would have to add about as much weight each day as you ate in foods. That's really growing fast, unless you have a massive number of plants like a greenhouse.

 

[Cory]

Super cool Randy! No wonder they pay you so much. Why not get a bigger tank? Like a 500 gallon?

I knew my super human abilities would work

 

[Randy Holmes-Farley]

I knew my super human abilities would work

What else can you do?

 

[Cory]

Well mostly in really good at predicting the future but still haven't been able to lift mountains yet, or fly haha. I'm also pretty good at investigation, and have written a book, which you probably wouldn't have guessed due to my ability spell (not so super human). The book shows where most religions came from, or at least borrowed a particular symbol from.

 

[Randy Holmes-Farley]

Predicting the future would be among my top choices for a power. Maybe the top 1. Lucky you.

Congrats on the book. FWIW, I wrote a science fiction book, but it has only been rejected so far.

 

[Cory]

Wow that's nice you write a science fiction book! You can always publish it on create space. If you wrote a reef book, I'd buy it! Fwiw the information I discovered is scientific in a mathamatcal kind of way. The symbol incorporates the divine proportion (1.618033), Fibonacci numbers (0,1,1,2,5,8), and Pi, but the Egyptian version of Pi not the standard modern version.

 

[Cory]

I forgot the 3 in the Fibonacci sequece 0,1,1,2,3,5,8

Anyway thanks for the help Randy!