Question

1. use the table above. if the volume of the sample of pyrite equals the volume of the sample of gold, how many times greater is the mass of the gold sample than the mass of the pyrite sample? a. 3.7 times greater b. 0.27 times greater c. 24.5 times greater d. 14.1 times greater

Explanation:

Step1: Recall the density - mass - volume relationship

Density ($
ho$) = $\frac{m}{V}$, where $m$ is mass and $V$ is volume. Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Here we can assume the reference substance is the same for both, so we can use specific gravity as a measure of relative density. Let the volume of pyrite and gold be $V$. Mass of pyrite $m_{pyrite}=
ho_{pyrite}V$, and mass of gold $m_{gold}=
ho_{gold}V$.

Step2: Find the ratio of the mass of gold to the mass of pyrite

The ratio $\frac{m_{gold}}{m_{pyrite}}=\frac{
ho_{gold}V}{
ho_{pyrite}V}$. The $V$ terms cancel out. From the table, $
ho_{gold} = 19.3$ (specific - gravity of gold) and $
ho_{pyrite}=5.2$ (specific - gravity of pyrite). So $\frac{m_{gold}}{m_{pyrite}}=\frac{19.3}{5.2}\approx3.7$.

Answer:

a. 3.7 times greater