How to Make a Gallon of Water Evaporate Completely in a Sealed Container?

What is the minimum volume of a perfectly insulated and sealed container needed for a gallon of water at 25⁰C to evaporate completely?

a. 222.758 cu.ft

b. 125.846 cu.ft

c. 300.452 cu.ft

Answer:

The minimum cubic volume for the complete evaporation of a gallon of water at 25⁰C into a perfectly insulated and sealed container, is approximately 222.758 cu.ft. The side length of this cubic container would be approximately 6.08 feet.

Explanation: To determine the minimum volume required for a gallon of water to evaporate completely in a sealed container, we can apply Avogadro's law. This law states that the volume of a gas is directly proportional to the quantity of molecules present (in moles) at a constant temperature and pressure.

First, we need to convert a gallon of water to kilograms. 1 gallon is approximately 3.785 liters, and with a density of 0.998 g/cm3, we have about 3.785 kg of water. The molar mass of water is roughly 18.015 g/mol, which gives us approximately 210.1 moles of water.

At boiling point (100⁰C), 1 mole of water vapor occupies about 30.1 liters. Therefore, 210.1 moles of water would occupy 6321.01 liters. Converting this to cubic feet, we get approximately 222.758 cu.ft.

For a cubic container, the side length can be calculated by taking the cube root of the volume. The side length would be approximately 6.08 feet.

By following these calculations and considerations, you can create the perfect setup for evaporating a gallon of water in a sealed container!