Determine the empirical formulas for the following compounds:
caffeine, C8H10N4O2
fructose, C12H22O11
hydrogen peroxide, H2O2
glucose, C6H12O6
ascorbic acid (vitamin C), C6H8O6
The correct answer and explanation is :
To determine the empirical formula of a compound, we need to find the simplest whole-number ratio of the elements present in the compound. The empirical formula represents the smallest ratio of the atoms of each element in the compound.
1. Caffeine, C₈H₁₀N₄O₂
The molecular formula of caffeine is given as C₈H₁₀N₄O₂. To find the empirical formula, we divide each subscript by the greatest common divisor (GCD) of the subscripts.
- Carbon (C) = 8
- Hydrogen (H) = 10
- Nitrogen (N) = 4
- Oxygen (O) = 2
The greatest common divisor of 8, 10, 4, and 2 is 2. Dividing each by 2:
- C: 8 ÷ 2 = 4
- H: 10 ÷ 2 = 5
- N: 4 ÷ 2 = 2
- O: 2 ÷ 2 = 1
So, the empirical formula for caffeine is C₄H₅N₂O.
2. Fructose, C₁₂H₂₂O₁₁
The molecular formula of fructose is C₁₂H₂₂O₁₁. To find the empirical formula, we again divide each subscript by the GCD.
- Carbon (C) = 12
- Hydrogen (H) = 22
- Oxygen (O) = 11
The greatest common divisor of 12, 22, and 11 is 1, meaning the formula is already in its simplest form. Therefore, the empirical formula for fructose is C₁₂H₂₂O₁₁ (same as the molecular formula).
3. Hydrogen Peroxide, H₂O₂
The molecular formula of hydrogen peroxide is H₂O₂. The subscripts for hydrogen (H) and oxygen (O) are both 2.
Dividing both by 2:
- H: 2 ÷ 2 = 1
- O: 2 ÷ 2 = 1
Thus, the empirical formula for hydrogen peroxide is HO.
4. Glucose, C₆H₁₂O₆
The molecular formula of glucose is C₆H₁₂O₆. To find the empirical formula, we divide each subscript by the GCD of 6, 12, and 6.
- Carbon (C) = 6
- Hydrogen (H) = 12
- Oxygen (O) = 6
The greatest common divisor of 6, 12, and 6 is 6. Dividing each by 6:
- C: 6 ÷ 6 = 1
- H: 12 ÷ 6 = 2
- O: 6 ÷ 6 = 1
So, the empirical formula for glucose is CH₂O.
5. Ascorbic Acid (Vitamin C), C₆H₈O₆
The molecular formula of ascorbic acid is C₆H₈O₆. We divide each subscript by the GCD of 6, 8, and 6.
- Carbon (C) = 6
- Hydrogen (H) = 8
- Oxygen (O) = 6
The greatest common divisor of 6, 8, and 6 is 2. Dividing each by 2:
- C: 6 ÷ 2 = 3
- H: 8 ÷ 2 = 4
- O: 6 ÷ 2 = 3
Thus, the empirical formula for ascorbic acid is C₃H₄O₃.
Summary of Empirical Formulas:
- Caffeine: C₄H₅N₂O
- Fructose: C₁₂H₂₂O₁₁ (same as molecular formula)
- Hydrogen Peroxide: HO
- Glucose: CH₂O
- Ascorbic Acid: C₃H₄O₃
The empirical formula helps us understand the simplest ratio of elements in a compound, but it does not provide the actual number of atoms in the molecule as the molecular formula does.