Solution Found!
A pure copper cube has an edge length of 1.42 cm. How many copper atoms does it contain?
Chapter 6, Problem 103P(choose chapter or problem)
A pure copper cube has an edge length of 1.42 cm. How many copper atoms does it contain? (volume of a cube = \(\text { (edge length) }^{3}\) ; density of copper = \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\))
Questions & Answers
QUESTION:
A pure copper cube has an edge length of 1.42 cm. How many copper atoms does it contain? (volume of a cube = \(\text { (edge length) }^{3}\) ; density of copper = \(8.96 \mathrm{~g} / \mathrm{cm}^{3}\))
ANSWER:Step 1 of 2
Given :
Edge length of Cu cube = 1.42 cm
\(\text { Volume of a cube }(\mathrm{V})=(\text { edge length })^{3}=(1.42 \mathrm{~cm})^{3}=2.86 \mathrm{~cm}^{3}\)
\(\text { Density of } \operatorname{copper}(\rho)=8.96 \mathrm{~g} / \mathrm{cm}^{3}\)
Number of copper atoms the cube contains = ?
We are given the density and volume, let’s calculate the mass of the copper using the density formula :
\(\begin{aligned}\rho&=\frac{m}{V}\\ \Rightarrow m&=\rho V\\ \Rightarrow\mathrm{m}&=8.96\frac{\mathrm{g}}{\mathrm{cm}^2}\times2.86\mathrm{~cm}^2\\ \mathrm{~m}&=25.62\mathrm{~g}\end{aligned}\)
Therefore the mass of the copper in the copper cube is 25.62 g.