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# A cube of gold that is 1.00 cm on a side has a mass of ISBN: 9780321809247 1

## Solution for problem 89 Chapter 2

Chemistry: A Molecular Approach | 3rd Edition

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Problem 89

A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 amu. (a) How many gold atoms are in the cube? (b) From the information given, estimate the diameter in Å o ? f a single gold atom. (c) What assumptions did you make in arriving at your answer for part (b)?

Step-by-Step Solution:

Solution : Step 1 : Gold is a chemical element having symbol Au. It has an atomic number of 79. Here, in the problem given : Side of gold cube = 1.00cm. Mass of gold cube = 19.3g. Mass of gold atom = 197.0 amu. Step 2: (a) How many gold atoms are in the cube Number of gold atoms = Mass of Cube Mass of Atom Here, ass of gold atom is given in amu and ass of gold cube is given in grams. So, let’s convert amu to grams a nd proceed with further calculation. 1 amu = 1.6605 × 10 -24g Therefore, mass of gold atom in amu is: -22 197amu = 3.271 × 10 g. Hence, number of gold atoms : -22 = 5.90 × 10 atoms. Step 3: (b) From the information given, estimate the diameter in Å of a single gold atom. To find the diameter of one single gold atom, first we need to find how many atoms are there in one edge of the cube. Diameter is 2 times the radius. So, we find radius of the atom using the formula to find volume of the sphere as atom is spherical in shape. Formula for volume of sphere : V = r where, v = volume, r = radius and = 22/7 or 3.1415 3 To proceed with further calculation we need to find the volume of cube : Volume of cube = a . 3 Where, a = side We have given the side of gold cube. 3 3 Therefore, volume of cube is = (1.0cm) = 1.0cm . Now, let’s find volume of one atom. volume of cube Volume of one atom = Number of atoms = 1.694 × 10 -23cm / atom.

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##### ISBN: 9780321809247

Since the solution to 89 from 2 chapter was answered, more than 832 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 89 from chapter: 2 was answered by , our top Chemistry solution expert on 02/22/17, 04:35PM. This full solution covers the following key subjects: gold, Single, mass, Cube, atom. This expansive textbook survival guide covers 82 chapters, and 9454 solutions. This textbook survival guide was created for the textbook: Chemistry: A Molecular Approach, edition: 3. The answer to “A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 amu. (a) How many gold atoms are in the cube? (b) From the information given, estimate the diameter in Å o ? f a single gold atom. (c) What assumptions did you make in arriving at your answer for part (b)?” is broken down into a number of easy to follow steps, and 67 words. Chemistry: A Molecular Approach was written by and is associated to the ISBN: 9780321809247.

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