When 6.853 mg of a sex hormone was burned in a combustion
analysis, 19.73 mg of CO2 and 6.391 mg of H2O were
obtained. What is the empirical formula of the compound?
To determine the empirical formula of a compound, we need to calculate the ratio of the elements present in the compound. In this case, we have the masses of carbon dioxide (CO2) and water (H2O) obtained from the combustion analysis.
1. Start by calculating the number of moles for each compound.
- Moles of CO2 = mass of CO2 / molar mass of CO2
- Moles of H2O = mass of H2O / molar mass of H2O
The molar mass of CO2 is determined by the atomic masses of carbon (C) and oxygen (O):
Molar mass of CO2 = atomic mass of C + 2 * atomic mass of O
The molar mass of H2O is determined by the atomic masses of hydrogen (H) and oxygen (O):
Molar mass of H2O = 2 * atomic mass of H + atomic mass of O
2. Next, calculate the moles of carbon (C) and hydrogen (H) in the original compound.
- Moles of C = moles of CO2 * 1 (since there is 1 mole of carbon per mole of CO2)
- Moles of H = moles of H2O * 2 (since there are 2 moles of hydrogen per mole of H2O)
3. Finally, divide the moles of each element by the smallest number of moles obtained.
- Divide the moles of C and H by the smaller value obtained in step 2.
The resulting quotients will give you the subscripts for the empirical formula of the compound.
Let's work through the calculations:
1. Molar mass of CO2 = atomic mass of C + 2 atomic mass of O = 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol
- Moles of CO2 = 19.73 mg / 44.01 g/mol = 0.4482 mmol
2. Molar mass of H2O = 2 * atomic mass of H + atomic mass of O = 2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
- Moles of H2O = 6.391 mg / 18.02 g/mol = 0.3550 mmol
3. Moles of C = 0.4482 mmol * 1 = 0.4482 mmol
Moles of H = 0.3550 mmol * 2 = 0.7100 mmol
4. Divide the moles of C and H by the smallest value (0.3550) mmol:
- Moles of C = 0.4482 mmol / 0.3550 mmol ≈ 1.26
- Moles of H = 0.7100 mmol / 0.3550 mmol ≈ 2.00
Therefore, the empirical formula of the compound is CH2O (1.26C:2H:1O).