The antibiotic doxycycline is used to treat Lyme disease. A 100 mg dose of the antibiotic consists of 59.5 mg of C, 5.40 mg of H, 6.30 mg of N and 28.8 mg of O by mass. What is the empirical formula of doxycycline

C₁₁H₁₂NO₄

Explanation:

In order to determine the empirical formula of doxycycline, we need to follow a series of steps.

Step 1: Determine the centesimal composition

C: 59.5 mg/100 mg × 100% = 59.5%

H: 5.40 mg/100 mg × 100% = 5.40%

N: 6.30 mg/100 mg × 100% = 6.30%

O: 28.8 mg/100 mg × 100% = 28.8%

Step 2: Divide each percentage by the atomic mass of the element

C: 59.5 /12.0 = 4.96

H: 5.40/1.00 = 5.40

N: 6.30/14.0 = 0.450

O: 28.8/16.0 = 1.80

Step 3: Divide all the numbers by the smallest one

C: 4.96/0.450 = 11

H: 5.40/0.450 = 12

N: 0.450/0.450 = 1

O: 1.80/0.450 = 4

The empirical formula of doxycycline is C₁₁H₁₂NO₄