Question

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

Short answer

The empirical formula for valproic acid is C4H8O, and the molecular formula is C8H16O2.

Step-by-step solution

Calculate moles of carbon, hydrogen, and oxygen

From the combustion reaction, we will get water and carbon dioxide as products. Given that a 0.165 g sample of the compound produces 0.166 g of water and 0.403 g of carbon dioxide, we need to find how many moles of carbon, hydrogen, and oxygen are present in this sample. First, let's convert the mass of water and carbon dioxide to moles using their molar masses: For water: \(2\,H + 1\,O\) Molar mass of water (H2O) = \(2(1.008\,g/mol) + 15.999\,g/mol = 18.015\,g/mol\) Moles of water = \(\frac{0.166\,g}{18.015\,g/mol} = 0.009212\,mol\) For carbon dioxide: \(1\,C + 2\,O\) Molar mass of carbon dioxide (CO2) = \(12.01\,g/mol + 2(15.999\,g/mol)\) = \(44.009\,g/mol\) Moles of carbon dioxide = \(\frac{0.403\,g}{44.009\,g/mol} = 0.009158\,mol\) Now, we can find the moles of each element in the sample: Moles of carbon = Moles of carbon dioxide (each molecule of CO2 has 1 carbon atom) Moles of carbon = \(0.009158\,mol\) Moles of hydrogen = 2 * Moles of water (each molecule of H2O has 2 hydrogen atoms) Moles of hydrogen = \(2 \times 0.009212\,mol = 0.018424\,mol\) Lastly, we will find moles of oxygen. Since there is only carbon and hydrogen in water and carbon dioxide, the remaining mass of the sample must be oxygen. We know the mass of the sample (0.165 g) and the mass of carbon and hydrogen from the moles calculated above. Mass of carbon = Moles of carbon * Molar mass of carbon Mass of carbon = \(0.009158\,mol \times 12.01\,g/mol = 0.1099\,g\) Mass of hydrogen = Moles of hydrogen * Molar mass of hydrogen Mass of hydrogen = \(0.018424\,mol \times 1.008\,g/mol = 0.018571\,g\) Mass of oxygen = 0.165 g (sample mass) - 0.1099 g (carbon mass) - 0.018571 g (hydrogen mass) Mass of oxygen = 0.036529 g Moles of oxygen = \(\frac{0.036529\,g}{15.999\,g/mol} = 0.002285\,mol\)

Determine the empirical formula

Now we have moles of each element in the sample. To get the empirical formula, we will divide the moles of each element (C, H, and O) by the smallest mole value: Smallest mole value = 0.002285 mol (for oxygen) Mole ratio of carbon = \(\frac{0.009158}{0.002285} = 4\) Mole ratio of hydrogen = \(\frac{0.018424}{0.002285} = 8\) Mole ratio of oxygen = \(\frac{0.002285}{0.002285} = 1\) So, the empirical formula is C4H8O1, or simply C4H8O.

Determine the molecular formula

We're given the molar mass of valproic acid as 144 g/mol. First, we need to find the molar mass of the empirical formula: Molar mass of empirical formula (C4H8O) = \(4(12.01\,g/mol) + 8(1.008\,g/mol) + 15.999\,g/mol = 72\,g/mol\) Now we can find the ratio of the molar mass of the molecular formula to the molar mass of the empirical formula: Ratio = \(\frac{144\,g/mol}{72\,g/mol} = 2\) Therefore, the molecular formula is twice the empirical formula, which is C8H16O2.

Key concepts

Molar Mass: Understanding the Basics

Molar mass is an essential concept in chemistry that helps us understand the mass of one mole of a substance. It's expressed in grams per mole (g/mol) and is crucial for converting between mass and moles of a substance.

The molar mass of a compound is calculated by summing the molar masses of all the atoms in the molecular formula. For instance, water (H₂O) consists of two hydrogen atoms and one oxygen atom. The molar mass of hydrogen is approximately 1.008 g/mol, and that of oxygen is about 15.999 g/mol.

To determine the molar mass of water, we add these together as follows:

• Molar mass of hydrogen: 2 × 1.008 g/mol = 2.016 g/mol
• Molar mass of oxygen: 15.999 g/mol
• Total molar mass of H₂O: 2.016 g/mol + 15.999 g/mol = 18.015 g/mol

This calculation method applies to any compound. Just multiply the number of each type of atom by its atomic mass and sum the results to find the molar mass.

Combustion Reaction: Unveiling the Process

A combustion reaction involves a substance (typically a hydrocarbon) reacting with oxygen gas to produce carbon dioxide and water. This type of reaction is exothermic, meaning it releases heat energy.

In our example with valproic acid, the combustion reaction helps us determine the amounts of carbon and hydrogen present. By finding the amount of carbon dioxide and water produced from the burning of the acid, we can infer the quantities of carbon and hydrogen in the original compound.

Here's the general form of a hydrocarbon combustion reaction:

• Hydrocarbon + O₂ → CO₂ + H₂O

The individual products (CO₂ and H₂O) tell us the number of moles of carbon and hydrogen. Each molecule of CO₂ results in one atom of carbon, while each molecule of H₂O results in two atoms of hydrogen. By analyzing these products, we can deduce the composition of the original organic compound.

Molecular Formula: Relating Empirical and Molecular

The molecular formula of a compound reveals the total number of each type of atom present in a molecule, providing a complete picture of its composition.

An empirical formula, on the other hand, represents the simplest whole-number ratio of atoms in a compound. To find the molecular formula, you need both the empirical formula and the molar mass of the compound.

Here's how you relate them:

• Determine the molar mass of the empirical formula. In our case, C₄H₈O has a molar mass of 72 g/mol.
• Divide the given molar mass of the compound (144 g/mol for valproic acid) by the molar mass of the empirical formula: 144 g/mol ÷ 72 g/mol = 2.
• Multiply the empirical formula by this ratio to find the molecular formula. Thus, the molecular formula is C₈H₁₆O₂, which means that each molecule of valproic acid contains 8 carbon atoms, 16 hydrogen atoms, and 2 oxygen atoms.

This process ensures that the molecular formula accurately reflects the composition of the compound based on empirical data and its measured molar mass.