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

               Option-A (BaTiSi₃O₉)

Step 1: Calculate Moles of each Element;

                      Moles of Ba  =  %Ba ÷ At.Mass of Ba

                      Moles of Ba  = 33.21 ÷ 137.33

                      Moles of Ba  =  0.241 mol

                      Moles of Ti  =  %Ti ÷ At.Mass of Ti

                      Moles of Ti  = 11.58 ÷ 47.88

                      Moles of Ti  =   0.241 mol

                      Moles of Si  =  %Si ÷ At.Mass of Si

                      Moles of Si  = 20.38 ÷ 28.09

                      Moles of Si  =  0.725 mol

                      Moles of O  =  %O ÷ At.Mass of O

                      Moles of O  = 34.83 ÷ 16.0

                      Moles of O  =  2.176 mol

Step 2: Find out mole ratio and simplify it;

       Ba                            Ti                                Si                          O

     0.241                       0.241                          0.725                    2.176

 0.241/0.241           0.241/0.241                0.725/0.241            2.176/0.241

         1                             1                                    3                           9 

Hence,  Empirical Formula  =  BaTiSi₃O₉

Step 3: Calculating Molecular Formula:

Molecular formula is calculated by using following formula,

                    Molecular Formula  =  n × Empirical Formula   (1)

Also, n is given as,

                     n  =  Molecular Weight / Empirical Formula Weight

Molecular Weight  =  413.44 g.mol⁻¹

Empirical Formula Weight  =  137.33 (Ba) + 47.88(Ti) + 28.09 (Si₃) + 16 (O₉)  =  413.48 g.mol⁻¹

So,

                     n  =  413.44 g.mol⁻¹ ÷ 413.48 g.mol⁻¹

                     n  =  1

Putting Empirical Formula and value of "n" in equation 1,

                    Molecular Formula  = 1 × BaTiSi₃O₉

                   Molecular Formula  =  BaTiSi₃O₉

A.  

BaTiSi3O9

Explanation:

the molecular formula for the mineral benitoite is  BaTiSi3O9

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