# Yeah, but why ARE nitrogen bubbles smaller?

**URL:** <https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545>\
**Category:** Factual Questions\
**Created:** [December 8, 2011, 7:26pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545 "2011-12-08T19:26:54Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\
**Post date:** [December 8, 2011, 7:26pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/1 "2011-12-08T19:26:54Z")

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Just re-reading The Master’s tome on Guinness stout and the inclusion of nitrogen bubbles, and wondering just why ARE nitrogen bubbles smaller than CO2 bubbles? I would think, from just hazy familiarity with general gas laws, that all gasses would produce bubbles of the same size, the pressure being the same within the liquid. Why would nitrogen bubbles be smaller? Are molecules of N2 actually smaller than molecules of CO2, and also therefore closer together? Where’s Avogadro when you really need him? And is he at all relevant in today’s world?

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**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\
**Post date:** [December 8, 2011, 8:26pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/2 "2011-12-08T20:26:03Z")

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> [@CC](#):
>
> Where’s Avogadro when you really need him?

Quaregna cemetery  
Vercelli  
Piemonte, Italy

I flailed around a while trying to answer the rest of your queries, but was only able to find solid info on that one point.

WAG: N[sub]2[/sub] is an appreciably smaller molecule than CO[sub]2[/sub]. Atomic weight 28 vs 44. That shouldn’t change the number of liters/mole but …

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**Author:** ![Baracus](https://avatars.discourse-cdn.com/v4/letter/b/2bfe46/32.png) [@Baracus](https://boards.straightdope.com/u/Baracus)\
**Post date:** [December 8, 2011, 9:20pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/3 "2011-12-08T21:20:36Z")

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There is an energetic penalty associated with the formation of an interface related to the associated surface tension which is proportional to the surface area. When a gas is supersaturated it is energetically favorable for the gas to form a bubble proportional to the volume of the bubble. The ratio of the surface area of a bubble to its volume decreases with radius. As such there is a minimum bubble radius below which the penalty of surface formation is greater than the bonus of gas phase formation and, hence, no stable bubble is formed.

Nitrogen, being less soluble than carbon dioxide, has a greater energy bonus for gas phase formation and can form smaller stable bubbles.

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**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\
**Post date:** [December 8, 2011, 10:01pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/4 "2011-12-08T22:01:08Z")

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> [@Baracus](#):
>
> There is an energetic penalty associated with the formation of an interface related to the associated surface tension which is proportional to the surface area. When a gas is supersaturated it is energetically favorable for the gas to form a bubble proportional to the volume of the bubble.

“a bubble proportional to the volume of the bubble”??? What could that possibly mean? How can a bubble be proportional to something?

> [@Baracus](#):
>
> The ratio of the surface area of a bubble to its volume decreases with radius

Are you saying that the relationship between the surface area of a sphere to its volume changes with the radius? How can that be? Isn’t everything in a sphere proportional regardless of size?

> [@Baracus](#):
>
> As such there is a minimum bubble radius below which the penalty of surface formation is greater than the bonus of gas phase formation and, hence, no stable bubble is formed.
> 
> Nitrogen, being less soluble than carbon dioxide, has a greater energy bonus for gas phase formation and can form smaller stable bubbles.

As of this point, I do not see your post as an answer. It may be that you are correct, but it hardly rises to the level of explanation. Can you/ will you try again? Thank you.

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**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\
**Post date:** [December 8, 2011, 10:25pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/5 "2011-12-08T22:25:34Z")

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> [@CC](#):
>
> Are you saying that the relationship between the surface area of a sphere to its volume changes with the radius? How can that be? Isn’t everything in a sphere proportional regardless of size?

Quick answer: Surface area increases by the square of the radius and volume increases by the cube of radius so volume increases at a faster rate than surface area.

Math answer: V/S = [(4/3) pi x r^3] / 4pi x r^2 = (1/3) r  
so the ratio of volume to surface area varies directly with the radius

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**Author:** ![Jas09](https://avatars.discourse-cdn.com/v4/letter/j/d07c76/32.png) [@Jas09](https://boards.straightdope.com/u/Jas09)\
**Post date:** [December 8, 2011, 10:27pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/6 "2011-12-08T22:27:25Z")

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> [@CC](#):
>
> “a bubble proportional to the volume of the bubble”??? What could that possibly mean? How can a bubble be proportional to something?

He is saying that the energy penalty for forming bubbles is proportional to the surface area of the bubble. Second, super-saturated gases are prone to form bubbles, and they do so proportionally with the volume of the bubble.

So you have to forces - the difficulty of supporting a bubble (related to it’s surface tension and thus its surface area) and the propensity for a super-saturated gas to form bubbles (related to the volume of the bubble formed).

> [@](#):
>
> Are you saying that the relationship between the surface area of a sphere to its volume changes with the radius? How can that be? Isn’t everything in a sphere proportional regardless of size?

Volume of a sphere = (4_pi_r^3) / 3  
Surface area of a sphere = 4 \* pi \* r^2  
Ratio between the two = r / 3  
As the radius increases, so does the ratio of volume to surface area.

This part all leads to his first conclusion - there is a minimum radius bubble that can be supported and it is inversely related to the energy bonus for gas-phase transition.

Nitrogen has a greater gas-phase bonus so it can support smaller bubbles.

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**Author:** ![Kevbo](https://avatars.discourse-cdn.com/v4/letter/k/e47774/32.png) [@Kevbo](https://boards.straightdope.com/u/Kevbo)\
**Post date:** [December 8, 2011, 10:27pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/7 "2011-12-08T22:27:41Z")

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> [@CC](#):
>
> Are you saying that the relationship between the surface area of a sphere to its volume changes with the radius? How can that be? Isn’t everything in a sphere proportional regardless of size?

Surface area scales as the square of radius, volume as the cube. True of most solids…like cubes, from which we get the terms I have just used.

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**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\
**Post date:** [December 8, 2011, 10:33pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/8 "2011-12-08T22:33:39Z")

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> [@CC](#):
>
> “a bubble proportional to the volume of the bubble”??? What could that possibly mean? How can a bubble be proportional to something?

The energy cost of forming a bubble is proportional to the surface area. The energy benefit of forming a bubble is proportional to the volume.

(This is not my own knowledge - I am merely explaining the point Baracus made).

> [@](#):
>
> Are you saying that the relationship between the surface area of a sphere to its volume changes with the radius? How can that be? Isn’t everything in a sphere proportional regardless of size?

He is correctly saying that the ratio between the area and volume of a sphere is proportional to the radius. In a tiny bubble, (volume/area) is less than in a large bubble.

> [@](#):
>
> As of this point, I do not see your post as an answer. It may be that you are correct, but it hardly rises to the level of explanation. Can you/ will you try again? Thank you.

I thought it was a good explanation, and very concisely stated.

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**Author:** ![Baracus](https://avatars.discourse-cdn.com/v4/letter/b/2bfe46/32.png) [@Baracus](https://boards.straightdope.com/u/Baracus)\
**Post date:** [December 8, 2011, 10:50pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/9 "2011-12-08T22:50:08Z")

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In order for a bubble to form the change in Gibbs free energy on formation of the bubble must be less than zero.

The Gibbs free energy associated with the formation of the surface between the gas inside the bubble and the liquid outside is positive and proportional to the surface area of the bubble. Let’s call the constant of proportionality S, so that the Gibbs free energy of the surface = S_4_pi\*r^2 \<- the surface area of a sphere of radius r.

The Gibbs free energy associated with the gas molecules moving from the liquid phase to the gas phase is negative and proportional to the number of molecules. Under ideal gas law conditions this will be proportional to the volume of the bubble. Let’s call the constant of proportionality V, so that the Gibbs free energy associated with the phase change = - V\*(4/3)_pi_r^3 \<-volume of the bubble.

So the total change in Gibbs free energy on bubble formation, deltaG = S_4_pi_r^2 - V_(4/3)_pi_r^3

We can factor out some stuff and get  
deltaG = 4_pi_r^2 \* (S - V\*r/3)

Now as mentioned **deltaG** needs to be less than 0 for the bubble to be stable and we can solve for **r** to find the minimum stable bubble size.

4_pi_r\_min^2\*(S-V\*r\_min/3) = 0

becomes

r\_min = 3\*S/V

So we can see that the greater the value of **V** the smaller the bubbles can be and still be stable. The value of **V** is related to the solubility of the gas. The greater the solubility the smaller **V** is. Since carbon dioxide is much more soluble than nitrogen, its **V** is much smaller. The **S** values are similar, so that the **r\_min** of carbon dioxide is larger than that of nitrogen.

Better?

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**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\
**Post date:** [December 8, 2011, 10:50pm UTC](https://boards.straightdope.com/t/yeah-but-why-are-nitrogen-bubbles-smaller/605545/10 "2011-12-08T22:50:14Z")

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My geometrical ignorance aside, does it then follow that the size of a bubble that forms in a liquid is directly related to its solubility?