*Asked and Answered 5.0*

*Asked and Answered 5.0*

I recently became a bitters-and-club-soda drinker. As I was to discover, club soda has the annoying habit of going flat before one finishes the bottle. To reduce waste, one can buy small bottles of national brands but they are much more expensive than the one-liter or two-liter bottles of store brands. What’s a club soda drinker to do? Glad you asked, and here’s your answer.

If club soda did not go flat, the choice would be clear. A six-pack of 10-ounce glass bottles of White Rock Club Soda costs $3.99 here — 33.25 cents per 5-ounce serving — while four one-liter bottles (135.3 ounces) of our store-brand club soda cost only $3.00 — 11.09 cents per serving. This means club soda in the 10-ounce bottles is three times more expensive… at least before any drinks are poured.

I tried a few one-liter bottles and was surprised to see how much club soda went to waste. (Soda without sparkle belongs in the drain, not the drink.) So I sat down to figure out whether the one-liter variety was a bargain or a boondoggle. The answer would involve Henry’s Law, the Ideal Gas Law, bottling industry data and a few simplifying assumptions. (Full details are provided in the Appendix.)

But let’s start with how club soda goes flat (Figure 1). The icon at far left represents the bottle as you buy it — filled to the neck with liquid and then topped off with high-pressure carbon dioxide (CO_{2}). Then, you open the bottle, pour a serving, and re-close the bottle. The headspace is now filled with air from your room. Over time, as the bottle rests in your refrigerator, CO_{2} escapes from the soda and collects in the headspace, until the pressure reaches an equilibrium (as determined by Henry’s solubility constant for carbon dioxide). This equilibrium CO_{2} pressure will be lower than the original pressure — as suggested by the lighter shades of blue in the diagram — due to the CO_{2} that escaped when you opened the bottle along with the CO_{2} that you poured into your drink.

The club soda gets flatter each time you open the bottle and pour a serving, until hardly any gas is left. At some point, you may as well water your plants with what remains.

The question is, for a given serving size and bottle size, how many servings can one pour before the contents become undrinkable? In my case, a serving is 5 oz (148 ml), I drink one serving a day, and I consider club soda too flat to drink if it has less than half of the original fizz (your mileage may vary). This is the case I will address first, comparing the 10-ounce bottles to the one-liter bottles.

Let’s assume we refrigerate the bottle at 4C (39F). Once a day, we take it out of the fridge, open it, pour the 5-oz serving, then close the bottle and return it to the fridge, all done as quickly as possible so that the contents do not get a chance to warm up. We repeat these steps every day until the bottle is empty or the soda is flat. The following chart (Figure 2) shows the resulting carbonation level for each serving, for both sizes of bottles:

We see that the 10-ounce bottle delivers two acceptable servings — the carbonation level of the second serving (57%) satisfies my 50% specification. But the real surprise is that the one-liter bottle yields just one more drinkable (61%) serving — the fourth serving has only 36% of the original fizz and the fifth 17%.

So, by my criterion, almost 56% of the one-liter bottle is undrinkable. This increases the effective cost-per-serving of a one-liter bottle from 11 cents to 25 cents. Even so, it is *still* less expensive than the 33 cents-per-serving cost of a 10-ounce bottle.

Pouring two servings at a time (1o ounces) makes the one-liter bottle an even better value, but not by much. The first two servings would be full strength of course, and the next two would have 72% of the original fizz. The final two servings, however, would drop to 34%. The effective cost-per-serving in this scenario would be 19 cents, and 41% of the contents would still be undrinkable.

To completely eliminate waste from a one-liter bottle, you would have to either (a) lower your fizz-level standards, or (b) belt down half the bottle (3-plus servings) each time that you open it. Only then will it cost you 11 cents per serving.

The bottom line is, a one-liter bottle of club soda at $0.75 is a better buy than a six-pack of glass bottles at $3.99, even if you have to share half of it with your houseplants. But if the one-liter bottle costs $1.00, it is a break-even proposition.

*Keep the Fizz Alive*

Want to get the most fizz for your club-soda buck? Research by Nestlé [1] suggests that soda in one-liter plastic (PET) bottles loses about 10% of its carbonation every 60 days when stored at room temperature. This is because CO_{2} gas diffuses through the walls of the bottle. (Bottlers compensate for the loss in shelf-life by adding extra carbonation to PET bottles.) There are three takeaways from this:

(1) *Buy your club soda from a busy supermarket.* This increases your chance of drinking recently-bottled higher-carbonation product.

(2) *Only buy as many bottles as you will use this week.* For the same reason.

(3) *Refrigerate your club soda. *This reduces the internal pressure — and thus the rate of CO_{2} loss due to diffusion — by about one-third compared to room-temperature storage. Not only that, cold liquid dissolves more CO_{2} so less gas is lost when you open the bottle.

Follow this advice and you will earn an A for effervescence. And don’t forget to recycle.

### Appendix

To estimate the carbonation in a bottle of club soda at each step of its product life, I made a number of reasonable simplifying assumptions:

- The bottle is completely rigid.
- The gases and liquids follow Henry’s Law and the Ideal Gas Law.
- When the bottle is filled, the headspace gas is assumed to be pure CO
_{2 }. - The carbonic acid formed by the reaction of CO
_{2}and water is insignificant. - The diffusion of CO
_{2}through the walls of the PET bottle is ignored. - Evaporation of the soda is insignificant.
- The liquid and gas are at equilibrium before the bottle is opened.
- Bubbles that escape from the soda just before it is poured are ignored.
- The contents of the bottle remain at 4C (39F) while the soda is poured.
- When the soda is poured, the gas in the headspace is replaced entirely by air.
- The amount of CO
_{2}and water vapor in the air can be ignored.

We begin by writing down the initial conditions in each bottle (Figure 3). I will use liters as the unit of volume, atmospheres as the unit of pressure, and moles for the mass of CO_{2}. (One atmosphere is essentially sea-level pressure, and one mole of CO_{2} is about 44 grams.)

A few notes on these facts and figures. I measured the total volume of each bottle in my kitchen by filling them to the brim with water. I assumed that the actual amount of soda in each bottle was exactly what the label claimed (bottling equipment is very accurate). The initial headspace is the difference between those numbers.

According to Steen and Ashurst [2], bottle-filling is usually performed at 14C (about 57F) and the carbonation pressure for club soda is about 60 psi, or just over 4 atmospheres [3]. Assuming that all the gas in the headspace is carbon dioxide, we can use the Ideal Gas Law and Henry’s constant to calculate the amount of CO_{2} in the gas and liquid as bottled.

Initial moles CO_{2} in headspace (*n*_{0}) from the Ideal Gas Law [4]:

`\text{(1)}\hspace{5em}n_0 = p_0V_0 / RT_0 `

where *p*_{0} is the CO_{2} pressure (4.083 atm), *V*_{0} is the initial headspace volume (0.010 liters or 0.85 liters depending on bottle size), *R* is the gas constant (0.08206 liter-atm/mol-deg) and *T*_{0} is the filling temperature in degrees Kelvin (14C + 273.15 ≈ 287K).

Initial concentration of CO_{2} in liquid (*c*_{0}) from Henry’s Law [5]:

`\text{(2)}\hspace{5em}c_0 = p_0H_{14\text{C}} `

where *H*_{14c} is Henry’s constant at 14C (refer to above table).

We now know the total moles (*m*_{0}) of CO_{2} in the bottle:

`\text{(3)}\hspace{5em} m_0 = n_0 + c_0L_0`

where *L*_{0} is the initial liquid volume (0.296 or 1.000 liters depending on bottle size).

Chilling the bottle to 4C does not change the moles of CO_{2} in the bottle but it does affect the CO_{2} liquid-to-gas ratio. We find the new liquid concentration (*c*_{1}) at 4C by combining the Ideal Gas Law and Henry’s Law, then substituting for pressure *p*_{1} and rearranging:

`\text{(4)}\hspace{5em} n_1 = p_1V_1/RT_1 = m_1 - c_1L_1\;,`

`\text{(5)}\hspace{5em} p_1 = c_1/H_{4\text{C}}\;,\hspace{.75em}\text{and so...}`

`\text{(6)}\hspace{5em} c_1 = m_1H_{4\text{C}}/(L_1H_{4\text{C}}+V_1/RT_1)`

where *m*_{1} = *m*_{0 }, *L*_{1} = *L*_{0} and *V*_{1} = *V*_{0} (since nothing has been removed from the bottle). Knowing *c*_{i} lets us back-calculate *n*_{1} and *p*_{1} from Equations (4) and (5).

We now pour the first serving of soda, whose volume is *L*_{S }. The pour reduces the liquid in the bottle to *L*_{2} = *L*_{1} – *L*_{S }and the total moles of CO_{2} to *m*_{2} = *m*_{1} – *n*_{1} – *c*_{1 }*L*_{S }, as we assume all CO_{2} in the headspace is lost. The headspace volume is now *V*_{2} = *V*_{1} + *L*_{S }. We quickly close the bottle and return it to the refrigerator, so that *T*_{2} = *T*_{1 }. While the bottle rests, the CO_{2} concentration of the liquid gradually decreases from *c*_{1} to *c*_{2 }and the CO_{2} gas pressure in the headspace rises to *p*_{2 }. The values of *c*_{2 } and *p*_{2} are unknown, but we can solve for them using Equations (5) and (6) with new subscripts:

`\text{(5')}\hspace{5em} p_2 = c_2/H_{4\text{C}}\;,\hspace{.75em}\text{and...}`

`\text{(6')}\hspace{5em} c_2 = m_2H_{4\text{C}}/(L_2H_{4\text{C}}+V_2/RT_2) `

This is the procedure I used to generate the CO_{2} concentration results in this article.

### References

[1] Profaizer, Mauro. “Shelf life of PET bottles estimated via a finite elements method simulation of carbon dioxide and oxygen permeability.” *Italian Food and Beverage Technology*, vol. 48, 2007.

[2] Steen, David P., and Ashurst, Philip R. (editors). *Carbonated soft drinks: formulation and manufacture*. Oxford Ames, Iowa: Blackwell Publishers, 2006.

[3] Spangenberg, Craig. “Exploding Bottles.*” * *Ohio State Law Journal*, vol. 24, 1963, p. 513.

[4] Khan Academy (khanacademy.org) is one of thousands of sites with info on the Ideal Gas Law. The Ideal Gas Law (*pV*=*nRT*) is to chemistry what Newton’s Second Law (*F*=*ma*) is to physics.

[5] Choose your own reference: Henry’s Law on Wikipedia or Henry’s Sparkling Water on ice.