select the correct answer.\nthe mineral benitoite is a gemstone for making jewelry. it has a molecular…

Explanation:

Step1: Calculate moles of each element assuming 100g sample

For Ba: Mass = 33.21g, molar - mass of Ba = 137.33g/mol. Moles of Ba $n_{Ba}=\frac{33.21g}{137.33g/mol}\approx0.242mol$. For Ti: Mass = 11.58g, molar - mass of Ti = 47.87g/mol. Moles of Ti $n_{Ti}=\frac{11.58g}{47.87g/mol}\approx0.242mol$. For Si: Mass = 20.38g, molar - mass of Si = 28.09g/mol. Moles of Si $n_{Si}=\frac{20.38g}{28.09g/mol}\approx0.725mol$. For O: Mass = 34.83g, molar - mass of O = 16.00g/mol. Moles of O $n_{O}=\frac{34.83g}{16.00g/mol}\approx2.177mol$.

Step2: Find the mole - ratio of elements

Divide each number of moles by the smallest number of moles (0.242mol). For Ba: $\frac{0.242mol}{0.242mol}=1$. For Ti: $\frac{0.242mol}{0.242mol}=1$. For Si: $\frac{0.725mol}{0.242mol}\approx3$. For O: $\frac{2.177mol}{0.242mol}\approx9$. The empirical formula is $BaTiSi_{3}O_{9}$. Since the molar mass of $BaTiSi_{3}O_{9}$: $M = 137.33g/mol+47.87g/mol + 3\times28.09g/mol+9\times16.00g/mol$ $=137.33 + 47.87+84.27 + 144.00=413.47g/mol\approx413.44g/mol$ (close enough due to rounding in calculations), the molecular formula is the same as the empirical formula.

Answer:

A. $BaTiSi_{3}O_{9}$