The molar mass of the common antibiotic oxytetracycline is found to be 460 g mol-1 and a 2.000 g sample contains 1.1478 g of carbon, 0.10435 g of h, 0.62609 g of oxygen and the remainder being nitrogen. what is the molecular formula of the oxytetracycline

              C₂₂H₂₄O₉N₂

Solution:

Step 1: Calculate %age of Elements;

                         %C  =  1.1478 / 2 × 100 = 57.39%

                         %H  =  0.104035 / 2 × 100 = 5.20%

                         %O =  0.62609 / 2.00 × 100 = 31.30%

                         %N  =  100% -(57.39 + 5.20 + 31.30) = 6.11%

Step 2: Calculate Mass of Elements as;

                         C =  (57.39 / 100 ) × 460  =  263.99 g

                         H  =  (5.20 / 100 ) × 460  =  23.92 g

                         O =  (31.30 / 100 ) × 460  =  143.98 g

                         N =  (6.11 / 100 ) × 460  =  28.10 g

Step 3: Calculate Moles of Elements:

                         C =  263.99 / 12  =  21.99 mol

                         H =  23.92 / 1  =  23.92 mol

                         O =  143.98 / 16  =  8.99 mol

                         N  =  28.10 / 14  =  2.00 mol

Step 4: Calculate the simplest mole ratio as;

                C                         H                           O                          N

             21.99/2        :       23.92/2       :        8.99/2          :         2/2

                 10.99                     11.96                   4.49                       1

                  ≈ 11                         ≈ 12                     ≈ 4.5                    1

Multiply by 2 to get the whole number for oxygen

                    22                           24                      9                        2

                         Empirical Formula  =  C₂₂H₂₄O₉N₂

It is also the molecular formula because the mass of empirical formula is equal to molecular mass as,

                         = (12)₂₂ + (1)₂₄ + (16)₉ + (14)₂

                         = 264 + 24 + 144 + 28

                         = 460

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explanation: