# 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.

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.