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To my understanding the carbonated beverage loses its $\ce{CO2}$ content as gas bubbles which gives the drink its 'fizziness'. The loss of $\ce{CO2}$ occurs due to the low solubility of carbonic acid formed during carbonation resulting in an excess of unreacted $\ce{CO2(g)}$ which is trapped in the container when bottled and escapes when opened:

$$\ce{H2O(aq) + CO2(g) -> H2CO3(aq) + CO2(g)}$$

Temperature and volume of the solvent play a critical role in the solubility of matter.

Would the decrease in temperature and slight increase in solvent caused by the ice cube being added to a carbonated beverage exposed to air cause the solution to remain 'fizzy' for longer than the same solution at RT°C with no solvent increase?

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Let me lightly gloss over the issue of nucleation sites and ice. While one observes bubbles forming on ice in the glass, they continue to form on the glass as well.

Instead, one could well ask the impact of temperature on release of the carbon dioxide, and thermodynamically that does come down to the solubility of carbon dioxide in water. Since this is of great importance to the soda industry, the study goes back some ways. R. Wieb and V.L. Gaddy, "The solubility of carbon dioxide in water at various temperatures from 12 to 40 degress and at pressures to 500 atmospheres - Critical phenomena', Journal of the American Chemical Society 62 815-817 (1940) shows measured solubility curves close to the temperatures of interest. One should note the increase in solubility as the temperature is dropped from room temperature down towards zero C.

While the carbon dioxide is supersaturated in the soda water, the driving force relates to the difference of the supersaturation to the solubility limit. As the temperature decreases, the thermodynamics favor retention of more carbon dioxide, which will then come out in your (warmer) mouth, giving you that 'fizz'.

Further, ignoring nucleation sites on the ice being much better than on the glass, as the temperature is decreased, the kinetics of nucleation will be at least partially suppressed as well.

Plus, I like my soda (and beer) cold, not warm!

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    $\begingroup$ Lots of nucleation sites on a glass indicates a dirty glass. craftbeer.com/craft-beer-muses/… $\endgroup$ – MaxW Dec 22 '15 at 17:37
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    $\begingroup$ Yes, but I'm not quite ready to use a piranha clean at home! $\endgroup$ – Jon Custer Dec 22 '15 at 17:40
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    $\begingroup$ I worked in a bar. Having clean glassware was a matter of pride (and kept health inspector happy...). $\endgroup$ – MaxW Dec 22 '15 at 17:42
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    $\begingroup$ I guess there is a difference between the bubbles that stick to the side of the glass, and that one place where a steady stream of bubbles comes from - it is the second one that is a nucleation site. But even with a nucleation site, there is still the thermodynamic driving force as part of the kinetics... And, sometimes that site is an actual flaw in the glass (or that is what I tell myself). $\endgroup$ – Jon Custer Dec 22 '15 at 17:50
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    $\begingroup$ It absolutely does if you are using dry ice. I love dry ice in my drinks. $\endgroup$ – Broklynite Dec 24 '15 at 8:17
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Your analysis of the situation is wrong. Most of the carbon dioxide in the solution is present as dissolved gas, not carbonic acid. Remember that the beverage was under pressure when packaged. When the liquid is poured into a cup there is no longer any great carbon dioxide pressure and the drink (solution) becomes supersaturated with carbon dioxide. Adding ice cubes creates nucleation sites which promote the supersaturated dissolved gas to form bubbles and release carbon dioxide into the atmosphere. So adding ice causes the drink to go flat faster.

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    $\begingroup$ On the other hand, the decrease in temperature should really slow down the release of $\ce{CO2}$. It is not immediately clear to me what would be the overall effect. $\endgroup$ – Ivan Neretin Dec 22 '15 at 6:10
  • $\begingroup$ @Ivan Neretin , that's exactly what I meant about the temperature variable. I understand it is always going to release the CO2 likewise if the ice is added or not but does the drop in temp slow the rate it is released. If the sparkling mineral water was heated would the CO2 be released faster? $\endgroup$ – Technetium Dec 22 '15 at 9:58
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    $\begingroup$ @Joel - The nucleation sites are on the surface of the ice cube, not into the solution. Drop an ice cube from the freezer into a carbonated drink and watch it fizz. You can reduce the fizz by pretreating the ice cube. Put some ice cubes from the freezer into a glass. Fill glass with water to cover the cubes. Stir for a couple of seconds and let glass sit for about 30 seconds. Pour off water and use those cubes to cool the drink. You have less ice, but the surface is now much smoother and the ice is at 0 C not freezer temperature. This greatly reduces fizzing of drink. $\endgroup$ – MaxW Dec 22 '15 at 17:07
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    $\begingroup$ The other thing to reduce fizz is to start with soda that is already cold from the fridge. So pouring cold soda over pretreated ice cubes works much better than warm soda over cubes straight from the freezer. $\endgroup$ – MaxW Dec 22 '15 at 17:40
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    $\begingroup$ A pre chilled glass would be good also ... $\endgroup$ – Technetium Dec 25 '15 at 23:37

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