객관식
What is the volume, in cm^3, of an object that has a mass of 455.6 g and a density of 19.3 g/cm^3?
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1. Intro to General Chemistry
Density
객관식
Given that FeO crystallizes in the rock salt (NaCl) structure, which of the following is closest to its density in g/cm^3? (Atomic masses: Fe = 55.85 g/mol, O = 16.00 g/mol; Avogadro's number = 6.022 × 10^{23} mol^{-1}; edge length of unit cell = 4.30 Å)
A
4.30 g/cm^3
B
5.70 g/cm^3
C
7.00 g/cm^3
D
5.45 g/cm^3
검증된 단계별 안내1
Identify the type of crystal structure: FeO crystallizes in the rock salt (NaCl) structure, which is a face-centered cubic (FCC) lattice with a basis of two atoms (Fe and O). In this structure, there are 4 formula units of FeO per unit cell.
Calculate the mass of the unit cell by finding the molar mass of FeO and then converting it to the mass of 4 formula units. The molar mass of FeO is the sum of the atomic masses of Fe and O: \(M_{FeO} = 55.85 + 16.00\) g/mol. Then, multiply by 4 (number of formula units per unit cell) and divide by Avogadro's number \(N_A = 6.022 \times 10^{23}\) mol\(^{-1}\) to get the mass of one unit cell.
Convert the edge length of the unit cell from angstroms to centimeters: \(1 \text{ Å} = 1 \times 10^{-8}\) cm, so \(a = 4.30 \times 10^{-8}\) cm. Then calculate the volume of the cubic unit cell using \(V = a^3\).
Calculate the density using the formula \(\rho = \frac{\text{mass of unit cell}}{\text{volume of unit cell}}\). Use the mass from step 2 and the volume from step 3.
Compare the calculated density value to the given options to determine which is closest to the actual density of FeO.
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