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Chemistry / Chemistry 11 / Chapter 3 / Problem 150P

Chemistry | 11th Edition | ISBN: 9780073402680 | Authors: Raymond Chang

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Solved: Suppose you are given a cube made of magnesium

Chapter 3, Problem 150P

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QUESTION:

Suppose you are given a cube made of magnesium (Mg) metal of edge length 1.0 cm.

(a) Calculate the number of Mg atoms in the cube.

(b) Atoms are spherical in shape. Therefore, the Mg atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Mg atoms, calculate the radius in picometers of a Mg atom. (The density of Mg is \(1.74 \mathrm{~g} / \mathrm{cm}^{3}\) and the volume of a sphere of radius r is \(\frac{4}{3} \pi r^{3}\).)

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QUESTION:

Suppose you are given a cube made of magnesium (Mg) metal of edge length 1.0 cm.

(a) Calculate the number of Mg atoms in the cube.

(b) Atoms are spherical in shape. Therefore, the Mg atoms in the cube cannot fill all of the available space. If only 74 percent of the space inside the cube is taken up by Mg atoms, calculate the radius in picometers of a Mg atom. (The density of Mg is \(1.74 \mathrm{~g} / \mathrm{cm}^{3}\) and the volume of a sphere of radius r is \(\frac{4}{3} \pi r^{3}\).)

ANSWER:

Step 1 of 4

Given:

Edge length of Mg metal cube = 1.0 .

(a) Here, we are asked to calculate the number of Mg atoms in the cube:

Mass of Mg = 1.74 g.

Molar mass of Mg = 24.305

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