Question

magnesium (mg) and iron (fe) are metals commonly used in engineering and construction applications. based on their average atomic weights, how much more dense would you expect iron to be compared to magnesium? to answer this problem you will need to assume that magnesium and iron atoms pack together in the metal structures in such a way that the same number of atoms of each would occupy exactly the same volume (this isnt actually true, but lets make this assumption for the purpose of this question). o iron will be more dense by a factor of 1.30 o iron will be more dense by a factor of 1.95 o iron will be more dense by a factor of 2.30 o iron will be more dense by a factor of 2.95

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$. Given same - volume $V$ and same number of atoms $n$. Let the atomic weight of magnesium be $M_{Mg} = 24.305$ and of iron be $M_{Fe}=55.845$. Mass $m = n\times M$ (where $M$ is the atomic weight).

Step2: Calculate density ratio

Since $V$ is the same and $n$ is the same, the ratio of densities $\frac{
ho_{Fe}}{
ho_{Mg}}=\frac{M_{Fe}}{M_{Mg}}$. Substitute $M_{Fe} = 55.845$ and $M_{Mg}=24.305$. Then $\frac{
ho_{Fe}}{
ho_{Mg}}=\frac{55.845}{24.305}\approx2.3$.

Answer:

Iron will be more dense by a factor of 2.30