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Chapter 3: Problem 26

All of the following minerals are semiprecious or precious stones. Determine the mass percent of the indicated element. (a) \(\mathrm{Zr}\) in zircon, \(\mathrm{ZrSiO}_{4}\) (b) Be in beryl (emerald), \(\mathrm{Be}_{3} \mathrm{Al}_{2} \mathrm{Si}_{6} \mathrm{O}_{18}\) (c) Fe in almandine (garnet), \(\mathrm{Fe}_{3} \mathrm{Al}_{2} \mathrm{Si}_{3} \mathrm{O}_{12}\) (d) S in lazurite (lapis lazuli), \(\mathrm{Na}_{4} \mathrm{SSi}_{3} \mathrm{Al}_{3} \mathrm{O}_{12}\)

Short Answer

Expert verified
The mass percent of each element in the mineral is calculated by the relation of its molar mass in the compound over the total molar mass of the compound. The solutions are obtained by applying this formula to each case.

Step by step solution

01

Molar mass calculation

For every mineral, calculate the molar mass which is the sum of the atomic masses of every atom in a single molecule of that substance. The atomic mass of each element can be found on a standard periodic table. Also calculate the molar mass for the specific element in question.
02

Calculation for Zircon

For zircon, \(\mathrm{ZrSiO}_{4}\), use the atomic masses to calculate the molar mass: \( \text{Molar Mass of ZrSiO}_{4} = 1* \text{Molar mass of Zr} + 1 * \text{Molar mass of Si} + 4 * \text{Molar mass of O}\). The percent of Zr in Zircon is then the molar mass of Zr divided by the molar mass of ZrSiO4, times 100.
03

Calculation for Beryl (Emerald)

The process for calculating the percent of Be in beryl (\(\mathrm{Be}_{3} \mathrm{Al}_{2} \mathrm{Si}_{6}\mathrm{O}_{18}\)) is the same as for zircon, but with different elements and quantities involved. Similarly, calculate the molar mass and then use it to find the percentage.
04

Calculation for Almandine (Garnet)

Follow similar steps to calculate for almandine (\(\mathrm{Fe}_{3} \mathrm{Al}_{2} \mathrm{Si}_{3}\mathrm{O}_{12}\)), evaluating the percent of Fe (iron).
05

Calculation for Lazurite (Lapis Lazuli)

Finally, for lazurite (\(\mathrm{Na}_{4} \mathrm{SSi}_{3} \mathrm{Al}_{3} \mathrm{O}_{12}\)), calculate the molar mass for the whole mineral and then isolate for S (sulfur) to find the mass percent.

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