Will that Pop Bottle Really Go Pop? An EquilibriumQuestion An article apppared in N ~ ~ ~ S c i e n l i srecentlg 11 3 t b ~ vrpl.,din.: t I:irlmmed hewrage bottles. T h r description of the pressure build.up in shaken hnttlrs srai pwAinr t u ur To quo1e;'Shaking a bottle .. .causes some carbon dioxide ta came out of salutian. If enough carbon dioxide leaves the liquid then the enclosed system approaches its equilibrium state when the pressure in the headspace can reach three or more times the pressure of the atmosphere." As this science newspaper is a prime source of scientific knowledge for a wide readership, we feel this ought to he challenged. The article is concerned withdangers of soda bottlesin the marketplace, and the author warns us notto disturb them unduly. The statement implies thnta closed bottle of carbonated beverage is not a t equilibrium, even after remaining undisturbed for indefinite periods. Alternatively, if the bottle is a t equilibrium, onemay ask where the free energycame from to increase the energy available asPVwork in the headspace. Does the shaking somehow add energy t o the system? This seems unlikely. A third possibility is that the statement is simply wrong. Practical experience does tell us that, if a hottle of soda is opened, then shaken with a thumh over the opening, a n increase in pressure occurs that can be put to good use. To test these various oossihilities. we have constructed a "barocolameter" (see fieure). - which permitsmeasurements of the headspace pressure in asoda hottle under various conditions. Our results can be summarized as follows: 1. If a bottle has been elosed for some time (a day or so may berequired), i t reaches an equilibrium pressure that is a function only of the temperature and Henry's law (the solubility of a gas in a liquid is proportional to the gas pressure). Carbon dioxide in water obeys Henry's law a t pressures up to 5 atm, and i t remains a good approximation up to 10 atm.2 Shaking has no effect on the pressure in the headsoace of a hottle that has came t o equilibrium, and we conclude that the sentence quoted above is misleadine a t best 2. when a bottle that has reached eauilihrium is first ooened. the head nressureimmediatelv falls t o one atmomhere. The contents of the hottle are no lonwr at equilibrium. and gas slowly leaves iulution untd ihe bewra+ 'err Itlnt". H ~ w e v e r , thr i ~ bottle isshaken, nuelentionsited in rhefo,rmufsmall buhhles are produced uhich prrmit rartwn diuxidpu, cmne out ul solution at a relativrly rapid rate. If a thumh ( w uur bsrocolameter) is stoppering thr bottle, the prrsaurr at room temperature rises to approximately three atmospheres, a t which point equilibrium is again reached. The nucleation effect is of considerable interest in itself. Bubbles do not form spontaneously in liquids. This follows from the Laplace equation, which states that the excess pressure inside a bubble (compared t o the liquid surroundings) is inversely proportional t o the radius r of the bubble: AP = 2-y/r, where y is the surface energy of the liquidlair interface. Therefore. under ideal conditions an infinite oressure would be reauired t o initiate the formation of a bubble when r = 0. Once a hubblr is formed, for instance by introducing nucleation s/tes with shaking, the exrejs pressure d e c r r n c ~ eas the bublrleexpands,nortsrateofrupnnsi~~ni~limitedonly hy the rateat whicbgascnn besupplied tothe h111Nefrom t h ~ s u r rounding liquid. This fact leads to an important caveat, which most of us have learned through hard experience. Although shaking does not increase the beadspace pressure of bottles a t equilibrium, recently shaken bottles still should not he opened immediately. The nucleation sites remain for awhile, and will increase the rate of approach t o equilibrium. As noted ahove, the resulting hubhles grow rapidly in volume, often emptying the bottle's contents. For the same reason, the carbonated beverage industry takes great care t o use ultraclean water in order to minimize potential nucleation sites. 3. The article is correct in noting that larger headsoaces are ootentiallv mare daneerous than smaller ones, but this is not related t o carhon r;aehea thd same ea;ilibrium o&ssure reeardless of the headsnace . dioxide oressuk ner , -seywhich ~~. ~ vdume. Imtrad, it folltru~from the fact that the potential energy ara~lnhlein any spnee under prrssure is s iunction of prewure X I r.lurne. In rmnpsring the relative danger of larger vs. smaller headspares nt the same pressure, the greater l more glass shards (i.e., a greater area of glass) if a bottle is energy available in a larger volume will ~ r o p e significantly dropped ~
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New Sei. 1986,21 Aug., 28. "L6sungsgleichgewichte (Gase in Fltissigkeiten)". In Taschenbueh fiir Cherniker und Physiker D'Ans.Lar, 3rd ed.; Springer Verlag: Berlin, 1967; Vol. 1, pp 1-1205. Davld W. Deamer and Benjamln K. Sellnger Ausnalian National University Canberra. ACT 2601, Australia
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