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The side of a cube of a face-centered cubic substance is 0.51 nm. If the molar mass of the pure substance is 97.9 g/mol, what is the density of the pure substance in g/cm³? (Give your answer to 2 decimal places.)

A. 10.42 g/cm³
B. 5.11 g/cm³
C. 1.96 g/cm³
D. 2.08 g/cm³

Answer :

Final answer:

The density of a face-centered cubic substance with a side length of 0.51 nm and a molar mass of 97.9 g/mol is calculated to be approximately 4.89 g/cm^3.

Explanation:

The question is asking for the density of a substance which has a crystalline structure of face-centered cubic and known side dimension (0.51 nm) and molar mass (97.9 g/mol). In a face-centered cubic unit cell, there are 4 atoms per unit cell. The volume of the unit cell can be calculated with the cube of the side length. After converting the side length to cm (0.51 nm = 0.51 x 10^-7 cm), the volume is (0.51 x 10^-7 cm)^3).

Then, to calculate the mass, the formula is: mass = number of atoms per cell * (molar mass / Avogadro's Number), where Avogadro's number is approximately 6.022 x 10^23 mol^-1. Finally, density is obtained by dividing mass by volume.

So the calculation would be as follows:

  • Volume of the cell = (0.51 x 10^-7 cm)^3 = 1.33 x 10^-21 cm^3
  • Mass of the cell = 4 * (97.9 g/mol / 6.022 x 10^23 mol^-1) = 6.50 x 10^-23 g
  • Density = Mass/Volume = 6.50 x 10^-23 g / 1.33 x 10^-21 cm^3 = 4.89 g/cm^3

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