Chapter 3, Problem 69A

Interpretation Introduction

Interpretation : The bar of metal is pure gold or not to be determined?

Concept Introduction : The connectivity between mass and volume is density. The formula of density is given as

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 69A

Since the experimental density and actual density do not match, the metal bar is not pure gold.

Explanation of Solution

Given information:

The volume is $4.7{\text{cm}}^3$ .

The mass of metal is $57.3\text{g}$ .

Density is defined as the ratio of mass to volume. It gives the connectivity between mass and volume.

The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

To calculate the density, substitute the values in the above equation.

  $\begin{array}{c}\text{Density =}\frac{\text{mass}}{\text{volume}}\\ =\frac{57.3\text{g}}{4.7{\text{cm}}^3}\\ =11.76{\text{g/cm}}^3\end{array}$

The density of the metal according to the given mass and volume is $11.76{\text{g/cm}}^3$ .

But the actual density of gold is $19{\text{g/cm}}^3$ .

Since the experimental density and actual density do not match, the metal bar is not pure gold.