Question

Valproic acid, used to treat seizures and bipolar disorder, is composed of C, H, and O. A 0.165-g sample is combusted to produce 0.166 g of water and 0.403 g of carbon dioxide. What is the empirical formula for valproic acid? If the molar mass is 144 g>mol, what is the molecular formula?

Answer 1

The empirical formula of valproic acid is determined to be CH2O by analyzing the mole ratios of carbon, hydrogen, and oxygen. Considering the molar mass of valproic acid is 144 g/mol, the molecular formula is deduced to be C5H10O5.

Step-by-step explanation:

To find the empirical formula for valproic acid using the mass of water and carbon dioxide produced from combustion, we first need to determine the moles of hydrogen and carbon. Since water has a molar mass of 18.015 g/mol and each mole contains 2 moles of hydrogen atoms, the 0.166 g of water produced would contain 0.166 g / 18.015 g/mol ≈ 0.00921 moles of water, which translates to 0.01842 moles of hydrogen. Similarly, carbon dioxide has a molar mass of 44.01 g/mol, so 0.403 g of carbon dioxide would contain 0.403 g / 44.01 g/mol ≈ 0.00916 moles of carbon dioxide, which corresponds to 0.00916 moles of carbon.

Now, to find the empirical formula, we need to determine the simplest whole-number ratio of moles of carbon and hydrogen. Dividing the mole amount of each element by the smallest mole amount yields C1H2 (0.00916 moles of carbon and 0.01842 moles of hydrogen, divide each by 0.00916). The oxygen in the compound can be found by subtracting the mass of carbon and hydrogen from the total mass representing valproic acid. Carbon contributes 0.00916 moles × 12.01 g/mol = 0.1100 g, and hydrogen contributes 0.01842 moles × 1.008 g/mol = 0.0186 g. Thus, oxygen contributes 0.165 g - (0.1100 g + 0.0186 g) = 0.0364 g, which corresponds to 0.0364 g / 16.00 g/mol ≈ 0.002275 moles. Dividing by the smallest mole amount gives us O1. The empirical formula for valproic acid is thus C1H2O1 or CH2O.

Because the molar mass of valproic acid is 144 g/mol and the molar mass of the empirical formula CH2O is approximately 30 g/mol, the ratio is 144 / 30 = 4.8, which is close to 5. Therefore, the molecular formula is five times the empirical formula; hence, the molecular formula of valproic acid is C5H10O5.

Answer 2

The empirical formula is =
`C_4H_8O`

The formula of Valproic acid =
`C_8H_(16)O_2`

Step-by-step explanation:

Mass of water obtained = 0.166 g

Molar mass of water = 18 g/mol

Moles of
`H_2O` = 0.166 g /18 g/mol = 0.00922 moles

2 moles of hydrogen atoms are present in 1 mole of water. So,

Moles of H = 2 x 0.00922 = 0.01844 moles

Molar mass of H atom = 1.008 g/mol

Mass of H in molecule = 0.01844 x 1.008 = 0.018588 g

Mass of carbon dioxide obtained = 0.403 g

Molar mass of carbon dioxide = 44.01 g/mol

Moles of
`CO_2` = 0.403 g /44.01 g/mol = 0.009157 moles

1 mole of carbon atoms are present in 1 mole of carbon dioxide. So,

Moles of C = 0.009157 moles

Molar mass of C atom = 12.0107 g/mol

Mass of C in molecule = 0.009157 x 12.0107 = 0.11 g

Given that the Valproic acid only contains hydrogen, oxygen and carbon. So,

Mass of O in the sample = Total mass - Mass of C - Mass of H

Mass of the sample = 0.165 g

Mass of O in sample = 0.165 - 0.11 - 0.018588 = 0.036412 g

Molar mass of O = 15.999 g/mol

Moles of O = 0.036412 / 15.999 = 0.002276 moles

Taking the simplest ratio for H, O and C as:

0.01844 : 0.002276 : 0.009157

= 8 : 1 : 4

The empirical formula is =
`C_4H_8O`

Molecular formulas is the actual number of atoms of each element in the compound while empirical formulas is the simplest or reduced ratio of the elements in the compound.

Thus,

Molecular mass = n × Empirical mass

Where, n is any positive number from 1, 2, 3...

Mass from the Empirical formula = 4×12 + 8×1 + 16= 72 g/mol

Molar mass = 144 g/mol

So,

Molecular mass = n × Empirical mass

144 = n × 72

⇒ n = 2

The formula of Valproic acid =
`C_8H_(16)O_2`