Citric acid, the compound responsible for the sour taste of lemons, has the following elemental composition: C, 37.51%; H, 4.20%; O, 58.29%. Calculate the empirical formula of citric acid. (Type your answer using the format CO2 for CO2.)
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The answer should actually be C6H8O7. The other user should have multiplied by 2.
To determine the empirical formula of citric acid, we need to find the simplest whole number ratio of the elements present.
1. Convert the percentages to grams:
Assume we have 100 grams of citric acid.
- Carbon (C): 37.51 grams
- Hydrogen (H): 4.20 grams
- Oxygen (O): 58.29 grams
2. Convert the grams to moles:
- Carbon (C): Moles = grams/molar mass = 37.51 g / 12.01 g/mol = 3.121 moles
- Hydrogen (H): Moles = grams/molar mass = 4.20 g / 1.008 g/mol = 4.167 moles
- Oxygen (O): Moles = grams/molar mass = 58.29 g / 16.00 g/mol = 3.643 moles
3. Divide each mole value by the smallest number of moles to obtain the simplest ratio:
For citric acid, the smallest number of moles is approximately 3.121.
- Carbon (C): 3.121 moles / 3.121 = 1 mole
- Hydrogen (H): 4.167 moles / 3.121 ≈ 1.333 moles (rounded to the nearest whole number, which is 4)
- Oxygen (O): 3.643 moles / 3.121 ≈ 1.167 moles (rounded to the nearest whole number, which is 3)
The empirical formula of citric acid is CH4O3.
To calculate the empirical formula of citric acid, we need to determine the simplest whole-number ratio of atoms present in the compound based on the given percentage composition of each element.
We can assume we have 100 g of citric acid, which means we have:
- 37.51 g of carbon (C)
- 4.20 g of hydrogen (H)
- 58.29 g of oxygen (O)
Next, we need to convert the mass of each element into moles by dividing it by the molar mass of that element.
The molar mass of carbon (C) is 12.01 g/mol.
The molar mass of hydrogen (H) is 1.01 g/mol.
The molar mass of oxygen (O) is 16.00 g/mol.
Now, let's calculate the number of moles for each element:
- Moles of carbon (C) = 37.51 g / 12.01 g/mol ≈ 3.12 mol
- Moles of hydrogen (H) = 4.20 g / 1.01 g/mol ≈ 4.16 mol
- Moles of oxygen (O) = 58.29 g / 16.00 g/mol ≈ 3.64 mol
Next, we want to find the simplest whole-number ratio of these moles. We can do this by dividing each number of moles by the smallest number of moles (in this case, 3.12 mol):
- Simplified moles of carbon (C) = 3.12 mol / 3.12 mol = 1
- Simplified moles of hydrogen (H) = 4.16 mol / 3.12 mol ≈ 1.33
- Simplified moles of oxygen (O) = 3.64 mol / 3.12 mol ≈ 1.17
Since we need to find the simplest whole-number ratio, we'll round the moles of hydrogen (H) and oxygen (O) to the nearest whole number:
- Simplified moles of carbon (C) = 1
- Simplified moles of hydrogen (H) = 1
- Simplified moles of oxygen (O) = 1
Finally, we write the empirical formula using the simplified moles as the subscripts:
- Empirical formula of citric acid = CH2O
So, the empirical formula of citric acid is CH2O.
First convert each percentage to grams.
37.51g C x (1 mol C/12.01g C)= 3.123 mol C
4.20g H x (1 mol H/1.008 g H)= 4.17 mol H
58.29 O x (1 mol O/16.00 g O)= 3.643 mol O
Since C has the lowest moles divide each mole by the moles of Carbon.
C= 1 mole
H= 1.34 moles
O= 1.167 moles
Then multiple each mole by 3.
The empirical formula is C3H4O3.