# How does the volume of gas in a pop bottle change on opening the bottle?

When you open a bottle of soda does the air go in or out of the bottle and what is the volume of the air released or allowed in?
Mackenzie Altland

Stretching a balloon over the top of the bottle and popping off the cap under the balloon will reveal that gas leaves the bottle; the balloon most definitely expands. So gas will rush out of the bottle, but this gas is not air; it's mostly carbon dioxide saturated with water vapor, but other gases are present as well.

Computing the final volume of the gas after the top is removed requires additional information. The gas is released in two stages:

1. The gas originally trapped in the head space has higher than atmospheric pressure and will expand very quickly out of the bottle.
2. Gases dissolved in the soda will be released as well, but more slowly. Notice that these gases stay in the soda until the bottle is uncapped. You don't see bubbles until the cap is off. This is because the solubility of gas in the soda is proportional to the pressure of the gas in the head space (an assertion sometimes known as "Henry's Law"). The soda bottler adds high pressure CO2 to the head space to ensure that soda will dissolve more CO2. If the pressure in the head space drops when the cap is popped off, the solubility of the gas in the bottle also drops. The soda is now supersaturated with carbon dioxide, and the excess gas is released slowly over the next hour in streams of bubbles.

Let's just focus on the gas that is released quickly when the bottle is uncapped. To estimate the final volume of the gas, we need to have the following pieces of information:

• The pressure drop. The gases in the head space have a pressure of approximately 2 atm, and after uncapping, the pressure will fall to about 1 atm.
• The temperature drop. When the gas expands very quickly, it has to expend its own energy to push back the atmosphere. Additional energy will be required to overcome intermolecular attractions. Most real gas molecules weakly attract each other, and when the gas expands rapidly, additional energy is required to pull the molecules away from each other. The internal energy of the gas plummets, and so does its temperature. If the soda comes out of the fridge at 5°C, the temperature drop for the expansion of the headspace gases is about 40°C. He assumes that the expansion occurs so quickly that no heat flows between the gas and the surroundings. (Such expansions are referred to as adiabatic expansions).

One may then use the combined gas law for a quick and rather dirty estimate of the final volume:

V2/V1 = (P1/P2) × (T2/T1) = (2 atm/1 atm) × (248 K/ 278 K)
so just after the cap is popped the gases in the head space will leave the neck of the bottle, expanding to about 1.8 times their original volume. The volume of the original head space is required if you want to know the volume of gas that actually exits the bottle.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! How does the volume of gas in a pop bottle change on opening the bottle?