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Chapter 11: Problem 8

You and your friend are each drinking cola from separate 2-L bottles. Both colas are equally carbonated. You are able to drink 1 L of cola, but your friend can drink only about half a liter. You each close the bottles and place them in the refrigerator. The next day when you each go to get the colas, whose will be more carbonated and why?

Short Answer

Expert verified
The bottle with 1 L of cola left (your bottle) will have more carbonation compared to the bottle with 1.5 L left (your friend's bottle), because the larger headspace in your bottle allows for a slower loss of carbonation. This is due to the pressure difference created by the CO2, which remains in the liquid, keeping it more carbonated than your friend's bottle with a smaller headspace.

Step by step solution

01

Understand the factors affecting carbonation retention

Carbonation is a process in which carbon dioxide (CO2) is dissolved in a liquid. In this case, it's the cola. The CO2 is maintained in the bottle as long as it remains sealed. Once the bottle is opened, the CO2 starts to escape from the liquid and into the air. The rate at which carbonation is lost depends on the pressure inside the bottle, the surface area of the liquid exposed to air, and the temperature of the cola when it was sealed.
02

Compare the situations of both bottles

Now that we know the factors that affect the carbonation retention, let's compare the situations of both bottles. The first person drank 1 L of cola, leaving 1 L in the bottle; the second person drank 0.5 L, leaving 1.5 L in the bottle. The surface areas of the cola exposed to the air are equal between both bottles because they are identical. The pressure created in the space above the liquid will be different because the space that the CO2 escapes into differs. The remaining CO2 has more volume to fill in the bottle with 1 L left.
03

Relate the factors to the carbonation retention

The more space there is between the liquid and the closed top, the more room for the CO2 that would escape from the cola has to fill. As a result, less pressure is created in the headspace of the bottle, so the CO2 remains in the liquid, keeping the liquid carbonated. In the bottle with 1.5 L of cola remaining, the headspace is smaller, which means there is less space for the CO2 to occupy when it escapes from the liquid. This would create more pressure, causing the CO2 to leave the liquid and enter the headspace, leading to a decrease in the carbonation of the remaining liquid.
04

Make a conclusion

Considering the factors that affect carbonation retention, the bottle with 1 L of cola left (your bottle) will have more carbonation compared to the bottle with 1.5 L left (your friend's bottle). This is because the larger headspace in your bottle allows for a slower loss of carbonation. Take note that this is a simplified explanation, and other factors like temperature and agitation (not mentioned in the exercise) could also play a role in carbonation retention.

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