# Analysis of citric acid shows that contains 37.51% C, 4.20% H, and 58.29% O. What is the...

## Question:

Analysis of citric acid shows that contains 37.51% C, 4.20% H, and 58.29% O. What is the empirical formula?

## Empirical Formula:

The empirical formula of a chemical is the simplest whole number ratio of the different elements in a molecule. To calculate the empirical formula, we first convert percentages to masses, and the mass to moles. Then we divide by the smallest number of moles to get a ratio. Then finally, convert that to whole numbers.

## Answer and Explanation:

The empirical formula for citric acid is C6H8O7.

To get this we first convert all of the percentages to grams based on 100 grams of the substance:

37.51% C = 37.51g C

4.20% H = 4.20g H

58.29% O = 58.29g O

Now, we can use the molar mass from the periodic table to convert the grams of each element to moles.

37.51g C (1mol / 12.0g C) = 3.12mol C

4.20% H (1mol / 1.008g H) = 4.16mol H

58.29% O (1mol / 16.0g O) = 3.64mol O

Now, we can divide by the smallest number of moles (carbon) to get a ratio:

3.12mol C / 3.12 = 1mol C

4.16mol H /3.12 = 1.33mol H

3.64mol O / 3.12 = 1.17mol O

Now, we have a ratio 1:1.33:1.17 but the numbers are not whole. Now we must find a multiplier that gets each of the numbers to whole numbers. Some trial and error gives us 6 as the smallest whole number that converts each of the numbers in the ratio to whole numbers. Multiplying each number by 6 gives us the empirical formula C6H8O7.

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