Question #fde10

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Question #fde10

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Answer 1 · 2017-12-04T15:31:07

$221.30 g m o l^{- 1}$ $221.30 gmol^(-1)$

Explanation:

1. Calculate the volume of the unit cell

Convert pm to cm
1 pm = $1 \cdot 10^{- 10} c m$ $1 * 10^(-10) cm$
419 pm = $4.19 \cdot 10^{- 8} c m$ $4.19 * 10^(-8) cm$

Volume of unit cell = ${(4.19 \cdot 10^{- 8} c m)}^{3}$ $(4.19 * 10^(-8) cm)^3$
Volume of unit cell = $7.36 \cdot 10^{- 23} c m^{3}$ $7.36 * 10^(-23) cm^3$

2. Determine the mass of the metal in the unit cell
Mass of metal in unit cell = $20 g c m^{- 3} \times 7.36 \cdot 10^{- 23} c m^{3}$ $20 gcm^(-3) xx 7.36 * 10^(-23) cm^3$
Mass of metal in unit cell = $1.47 \cdot 10^{- 21} g$ $1.47 * 10^(-21) g$

3. Determine number of atoms per unit cell

We have face-centered unit cell:

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Lattice points on the corner count for an 1/8 because they are shared with 8 other unit cells. Lattice points on the face count for 1/2 as they are shared with one other unit cell.

1/8 x 8 corners = 1 lattice point
1/2 x 6 faces = 3 lattice points
Total number of lattice points (atoms) per unit cell = 4

4. Calculate molar mass of unknown metal

Mass per atom = Total mass of metal in unit cell / number of atoms in unit cell
Mass per atom = $\frac{1.47 \cdot 10^{- 21} g}{4}$ $(1.47 * 10^(-21) g) / 4$
Mass per atom = $3.68 \cdot 10^{- 22} g$ $3.68 * 10^(-22)g$

Use mass to determine molar mass by multiplying by Avogadro's number:

molar mass = $3.68 \cdot 10^{- 22} g \times 6.022 \cdot 10^{2} m o l^{- 1}$ $3.68 * 10^(-22)g xx 6.022 * 10^2 mol^(-1)$

molar mass = $221.30 g m o l^{- 1}$ $221.30 gmol^(-1)$

Looking at the periodic table, this molar mass is the closest to radon.

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