Question
The density of a quartz-magnetite rock with $30\%$ magnetite is around
The correct answer is
$3.3\text{ g/cc}$
Estimating Quartz-Magnetite Rock Density
The density of a rock composed of multiple minerals is a weighted average of the densities of its constituent minerals, based on their proportions.
Component Densities
| Mineral | Approximate Density (g/cc) |
| Quartz ($\text{SiO}_2$) | $2.65$ |
| Magnetite ($\text{Fe}_3\text{O}_4$) | $5.15$ |
Density Calculation
The rock contains $30\%$ magnetite and $70\%$ quartz. The weighted average density ($\rho_{\text{rock}}$) is calculated as follows:
$ \rho_{\text{rock}} = (\% \text{ magnetite} \times \rho_{\text{magnetite}}) + (\% \text{ quartz} \times \rho_{\text{quartz}}) $ Plugging in the values: $ \rho_{\text{rock}} = (0.30 \times 5.15 \text{ g/cc}) + (0.70 \times 2.65 \text{ g/cc}) $ $ \rho_{\text{rock}} = (1.545 \text{ g/cc}) + (1.855 \text{ g/cc}) $ $ \rho_{\text{rock}} = 3.40 \text{ g/cc} $Conclusion
The calculated density is $3.40 \text{ g/cc}$. Comparing this to the options, $3.3 \text{ g/cc}$ is the closest value.
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