Question

select the correct answer.
the mineral benitoite is a gemstone for making jewelry. it has a molecular weight of 413.44 grams/mole and a percent composition of 33.21% ba, 11.58% ti, 20.38% si, and 34.83% o. what is the molecular formula?
a. batisi₃o₉
b. ba₂tisi₂o₃
c. batisi₃o₆
d. batisi₆o₉

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. $BaTiSi_{3}O_{9}$