Question

you have a 100 - gram sample of each of the following metals. which sample has the largest volume? answer: a aluminum, d = 2.7 g/cm³ b gold, d = 19.32 g/cm³ c iron, d = 7.86 g/cm³ d magnesium, d = 1.74 g/cm³ e silver, d = 10.5 g/cm³

Explanation:

Step1: Recall density - volume formula

The density formula is $d=\frac{m}{V}$, where $d$ is density, $m$ is mass and $V$ is volume. We can re - arrange it to $V = \frac{m}{d}$. Given $m = 100$ g for all samples.

Step2: Calculate volume for each metal

For aluminum: $V_{Al}=\frac{100}{2.7}\text{ cm}^3\approx37.04\text{ cm}^3$.
For gold: $V_{Au}=\frac{100}{19.32}\text{ cm}^3\approx5.18\text{ cm}^3$.
For iron: $V_{Fe}=\frac{100}{7.86}\text{ cm}^3\approx12.72\text{ cm}^3$.
For magnesium: $V_{Mg}=\frac{100}{1.74}\text{ cm}^3\approx57.47\text{ cm}^3$.
For silver: $V_{Ag}=\frac{100}{10.5}\text{ cm}^3\approx9.52\text{ cm}^3$.

Step3: Compare volumes

We can see that magnesium has the largest volume among the given metals.

Answer:

D. magnesium, $d = 1.74\text{ g/cm}^3$