Question

A plastic soda bottle is flexible enough that the pressure of the bottle can change even

without opening it. You have an empty soda bottle at room temperature (25.0 °C) and
standard pressure (100 kPa). What will the new temperature be if you put it in your
freezer and the bottle decreases its pressure to 702 mm Hg? Do not include units in your
answer.

Answer 1

To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:

P1V1/T1 = P2V2/T2

where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.

Since the bottle is sealed and the volume is constant, we can simplify the equation to:

P1/T1 = P2/T2

Rearranging and plugging in the given values, we get:

T2 = (P2 × T1) / P1

= (702 mmHg × 298 K) / 100 kPa

≈ 209.8 K

Converting to Celsius, we get:

T2 ≈ -63.3 °C

Therefore, if the bottle decreases its pressure to 702 mm Hg in the freezer, the new temperature will be approximately -63.3 °C.