What is the pressure in the bottle now? What will happen if it is opened?

Question

You start out from Alaska, where it is -30 degrees C, and where there is exactly 1 ATM of atmospheric pressure, with an empty, 2 liter pop bottle that you have just tightly sealed in your trunk. You get to Mexico two days later where it is 40 deg. C. Your bottle still has the same shape and volume and the same number of gas molecules inside. What is the pressure in the bottle now? What will happen if it is opened?

Answer 1

P1 = initial pressure = 1 atm

T1 = initial temp in Kelvin = -30 + 273 = 243K

P2 = final pressure = ?

T2 = final temp in Kelvin = 40 + 273 = 313K

using Gay-lussac’s law …

P1 / T1 = P2 / T2 and solving for P2 we get …

P2 = P1T2 / T1 = (1 atm)(313K) / (243K)

P2 = 1.29 atm ( 3 sf) = 1.3 atm (2 sf).

In the problem it is stated that the original pressure of 1 atm was EXACT, so I see nothing inherently wrong with reporting you answer to 2 sig figs even though the given temps of -30 and + 40 degrees have only 1 sig fig.

Answer 2

Because the volume is not changing, we can use the Charles law for the isochoric prosses in a form

p₁ / T₁ = p₂ / T₂

From here for the final pressure we will have

p₂ = p₁T₂ / T₁

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Now we will plug in the numbers and get the answer.

Please do not forget that in this formula T - is absolute temperature. It means that to your temperature measured in degrees Celsius, you need to add up 273!