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