Water in this scenario = miraculously pure H2O. No atmospheric gas dissolved in it.
Assume maximum amount of gas is dissolved in the water
2-liter bottle of carbonated water (not gassing off–no bubbles)
2-liter bottle of water
Any difference in weight?
How about if we swap CO2 for Nitrogen?
CO[sub]2[/sub] dissolved in water forms carbonic acid, which has a density of 1.668 g/cm[sup]3[/sup], compared to 1 g/cm[sup]3[/sup] for pure water. So the bottle with CO[sub]2[/sub] will be heavier. You can look up the solubility at a certain temperature if you want to calculate how much heavier it would be.
Nitrogen is less soluble than CO[sub]2[/sub] so it would be lighter, but I’m not sure by how much.
Water mass plus dissolved gas mass = final mass. Density doesn’t factor in there. It does factor into buoyancy, which will affect what the balance reads, but that’s small in air.
Actually, only a small part of the CO[sub]2[/sub] will form carbonic acid; most will just remain dissolved in the water.
(Thanks for teaching me how to do subscripts!)
Except that the question specifies a 2-liter volume, not a given mass of water and a given mass of gas.
Whether you’re ending up with a gas+water final volume of 2L, or starting with 2L and adding the amount of gas that would saturate the water at a given temperature and pressure, you’ll have the same answer.
When one volume is made of only H20 with no dissolved gas, it would have a molecular mass of ~18g/mol.
When you make of a combination of H20 and CO2 you’ll have some (mostly) water at 18 g/mol and some CO2 which has a mass of ~44 g/mol. Whatever the ratios of the two, you’re adding something with a higher mass to water and you’ll end up with a final mass higher than that of pure water. The same goes for nitrogen gas with a mass of ~28g/mol.
You can do the math to get actual weights based on how much gas would dissolve, but it doesn’t really matter; if you’re adding any amount of something having a higher molecular mass than water to it, you have to end up with an overall higher mass per unit volume and therefore weight.
Of course it’s not very likely outside of a controlled lab that you’ll ever encounter water with zero dissolved gas; it’ll typically have a mixture of about 80% nitrogen and 20% oxygen (air) dissolved in it with of course tiny fractions of other gasses to minute to worry about. So a more real-world question would be the difference in weights between water+air, water+CO2, and water+N2.
The water+CO2 would still be heaviest, but since the molecular weight of air works out to be about 29g/mol, water+nitrogen would be slightly lighter than water+air.
Excellent answer, mmmiiikkkeee!
But by this logic, a 2L bottle of CO[sub]2[/sub] would weigh more than a 2L bottle of H[sub]2[/sub]O. You’re logic only works if both substances are liquid.
Yes, thank you! Assuming temperature matters for deciding how much gas can be dissolved at 1 atm, let’s say we’re talking about 21c. What kind of weight difference are we talking between water and water + CO2? A few grams? Lots more? Lots less?
No, I’m talking about masses of substances and their molecular weights with respect to each other, while your example is about a given volume of space with an unspecified mass of the substance in question within. A “2L bottle of water” doesn’t say anything about how much water you actually have, the amount of water is left to assumption.
A 2L bottle containing 2,000 grams of water will weigh more than a 2L bottle containing 100g of lead. That water could be in liquid form or solid form, the lead could be solid or molten…it’s the mass that matters.
Density most certainly is important. You’re making the assumption that dissolving something in water does not change the original volume of water, which isn’t true. You need to know the density of the resulting solution before you can say that the substance with a higher molecular weight solute will be the heaviest. You are correct that the CO[sub]2[/sub] mixture is heavier, but you can’t know that by solely comparing molecular weights.
True, but in this case it’s close enough. CO[sub]2[/sub] is a tad bit denser than water than the molecular weights would indicate, but not very much. And it wouldn’t be a mixture, it’s a solution, so the CO[sub]2[/sub] dissolved in the water will be in it’s liquid state of matter (this addresses Saint Cad’s comment)
I ran simulations, using the Sour PR (Peng Robinson) and Sour SRK (Soave Redlich Kwong) equations of state. (Standard simulations used by chemical engineers to predict CO2 and H2S removal)
Assumptions : Temperature is 75F and Pressure is 55 psig (Reference : Sowell, Jeff. Consumer Affairs Specialist. Coca-Cola Company. Letter. 31 May 2000. cite )
Water and CO2 are pure - No other gases present
Results (Under the assumed conditions and purity - and with numerical approx) :
Mole percent of CO2 dissolved = 0.0029
1> Density of Water = 62.95 lb/ft3 or 1008 g/l (So the 2l bottle contents weigh 2016 g)
2> Density of Water saturated with CO2 = 63.02 lb/ft3 (So the 2l bottle contents weigh 2018 g)
Swapping N2 for CO2 for the same conditions above
Mole percent of N2 dissolved : 0.0001
1> Density of Water = 62.9452 lb/ft3 or 1008.2872 g/l
2> Density of Water saturated with N2 = 62.9428 lb/ft3 or 1008.2491 g/l