chemical analysis shows that citric acid contains 37.51% C, 420% H, and 58.29% O. What is the empirical formula for citric acid?
To determine the empirical formula of citric acid, we need to calculate the ratio of elements present in the compound.
1. Convert the percentages of each element to moles:
- Carbon (C): 37.51%
- Hydrogen (H): 4.20%
- Oxygen (O): 58.29%
To convert to moles, assume we have 100 grams of citric acid:
- Carbon (C) moles = 37.51 grams / 12.01 g/mol = 3.122 moles C
- Hydrogen (H) moles = 4.20 grams / 1.01 g/mol = 4.158 moles H
- Oxygen (O) moles = 58.29 grams / 16.00 g/mol = 3.643 moles O
2. Divide each molar quantity by the smallest value:
- Carbon (C) = 3.122 moles C / 3.122 moles C = 1
- Hydrogen (H) = 4.158 moles H / 3.122 moles C = 1.33 ≈ 4/3
- Oxygen (O) = 3.643 moles O / 3.122 moles C = 1.166 ≈ 5/3
This gives us the empirical formula C1H4/3O5/3.
3. Multiply the subscripts by a common factor to obtain whole numbers:
To achieve whole numbers, multiply all the subscripts by 3, which results in C3H4O5.
Therefore, the empirical formula for citric acid is C3H4O5.
To determine the empirical formula for citric acid, we need to convert the percentages of each element to the corresponding mole ratios.
Step 1: Convert the percentages to masses.
We assume a 100g sample of citric acid.
- C: 37.51% of 100g = 37.51g
- H: 4.20% of 100g = 4.20g
- O: 58.29% of 100g = 58.29g
Step 2: Convert the masses to moles.
Use the molar masses of each element (C: 12.01 g/mol, H: 1.01 g/mol, O: 16.00 g/mol) to calculate the number of moles.
- C: 37.51g / 12.01 g/mol = 3.121 moles
- H: 4.20g / 1.01 g/mol = 4.158 moles
- O: 58.29g / 16.00 g/mol = 3.643 moles
Step 3: Divide each mole value by the smallest mole value.
Dividing each mole value by the smallest mole value (in this case, 3.121 moles) gives us the mole ratios.
- C: 3.121 moles / 3.121 moles = 1
- H: 4.158 moles / 3.121 moles ≈ 1.33
- O: 3.643 moles / 3.121 moles ≈ 1.17
Step 4: Round the mole ratios to the nearest whole number.
The ratios indicate that the empirical formula for citric acid is approximately C1H1.33O1.17.
Step 5: Multiply the subscripts by a common factor to get whole numbers.
To obtain whole numbers, we multiply all the subscripts by a common factor. Let's multiply by 3 to eliminate decimals.
- C: 1 × 3 = 3
- H: 1.33 × 3 ≈ 4
- O: 1.17 × 3 ≈ 3.5
Rounding the values to the nearest whole number gives us the empirical formula for citric acid, which is C3H4O3.