The volume of a single molecule of water is 2.99 × 10^-23 mL. For a sample of gaseous water at 1.00 atm and 150 °C, what fraction of the container's volume is occupied by the molecules themselves?

Question

Quizplus · Accepted Answer

To find the fraction of the container's volume occupied by the molecules themselves, we need to calculate the volume of one mole of gaseous water at the given conditions and divide it by the total volume of the container.

First, we need to use the ideal gas law to find the molar volume of the gas:

PV = nRT

V = nRT/P

V = (1 mol)(0.08206 L·atm/K·mol)(423 K)/(1 atm)

V = 34.6 L/mol

Next, we need to convert this volume to mL/mol:

34.6 L/mol x 1000 mL/L = 34600 mL/mol

Finally, we can calculate the volume of a single molecule of water by dividing this molar volume by Avogadro's number:

34600 mL/mol ÷ 6.022 × 10^23 molecules/mol = 5.75 × 10^-20 mL/molecule

Now we can calculate the fraction of the container's volume that is occupied by the molecules themselves:

(2.99 × 10^-23 mL/molecule) / (5.75 × 10^-20 mL/molecule) = 5.2 × 10^-4

This fraction is equivalent to 5.2 × 10^-4 × 100% = 5.2 × 10^-2%, or about 0.0052%. Therefore, the best choice is C, 5.2 × 10^-4 or 5.2 × 10^-2%.

The Volume of a Single Molecule of Water Is 2