Question

Consider a perfectly insulated and sealed container. Determine the minimum volume of a container such that a gallon of water at will evaporate completely. If the container is a cube, determine the dimensions in feet. Assume the density of water is$\mathbf{0}\mathbf{.}\mathbf{998}\mathbf{g}\mathbf{/}{\mathbf{cm}}^3$.

Short answer

The length of the cube is 17.95 feet.

Step-by-step solution

Determine the moles of water

It is given that the $density of water=0.998g/ml$.

$number of moles=\frac{\rho \times V}{\text{atomic amss}}$

$$\begin{gathered} =\frac{0.998g/ml\times 3785.4ml}{18.02g/mol} \\ =209.646mol \end{gathered}$$

The volume of gas

We have the gas law:$pV=nRT$

$$\begin{gathered} V_{gas}=\frac{209.646\times 52.36Ltorr/molK\times \left(273+25\right)K}{23.8torr}\times 0.353146667feet/L \\ =5780.8\text{cubic feet} \end{gathered}$$

 Step 3: The length of the cube.

The length of the cube:

$$\begin{gathered} a=\sqrt[3]{V_{gas}} \\ =\sqrt[3]{5780.8\text{cubic feet}} \\ =17.95feet \end{gathered}$$