Answer:
C₂H₄O₂
Step-by-step explanation:
To find the molecular formula of the organic acid, you need to (1) determine the mass of each element (from the given percents), then (2) convert grams of each element to moles (via atomic masses), then (3) find the empirical formula, and then (4) find the molecular formula.
(Step 1)
39.9% C -----> 39.9 g C
6.7% H -----> 6.7 g H
53.4% O -----> 53.4 g O
(Step 2)
Atomic Mass (C): 12.011 g/mol
Atomic Mass (H): 1.008 g/mol
Atomic Mass (O): 15.988 g/mol
39.9 grams C 1 mole
---------------------- x ---------------------- = 3.32 moles C
12.011 grams
6.7 grams H 1 mole
-------------------- x --------------------- = 6.65 moles H
1.008 grams
53.4 grams O 1 mole
---------------------- x ---------------------- = 3.34 moles O
15.998 grams
(Step 3)
The empirical formula is made up of the lowest possible amount of each element in the molecule. These amounts can be found by dividing the molar value of each element by the smallest molar value. In this case, the smallest molar value is 3.32 moles C. The calculated values make up the subscripts in the empirical formula.
3.32 moles C / 3.32 = 1 mole C
6.65 moles H / 3.32 = 2 moles H
3.34 moles O / 3.32 = 1 mole O
Empirical Formula: CH₂O
(Step 4)
To find the molecular formula, you first need to determine the molar mass of the empirical formula. Once you have this value, you need to determine how much you need to scale the formula up by. In this case, the molar mass of the empirical formula is half of the molar mass of the molecular formula. Therefore, you need to multiply the amount of each element in the molecule by 2.
Molar Mass (CH₂O): 12.011 g/mol + 2(1.008 g/mol) + 15.998 g/mol
Molar Mass (CH₂O): 30.025 g/mol
30.025 g/mol x 2 = 60.05 g/mol
CH₂O x 2 = C₂H₄O₂