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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