Problem 55 - Chemistry and Chemical Reactivity

Question

Mandelic acid is an organic acid composed of carbon \((63.15 \%),\) hydrogen \((5.30 \%),\) and oxygen \((31.55 \%) .\) Its molar mass is \(152.14 \mathrm{g} / \mathrm{mol}\). Determine the empirical and molecular formulas of the acid.

Step-by-Step Solution

Answer

Empirical and molecular formula: \(\text{C}_8\text{H}_8\text{O}_3\).

Step 1: Convert Percentages to Grams

Assume you have 100 g of mandelic acid. This makes the composition: 63.15 g of carbon, 5.30 g of hydrogen, and 31.55 g of oxygen.

Step 2: Convert Mass to Moles

Using molar masses (C: 12.01 g/mol, H: 1.008 g/mol, O: 16.00 g/mol), calculate the moles for each element. - Moles of carbon: \(\frac{63.15}{12.01} \approx 5.26\)- Moles of hydrogen: \(\frac{5.30}{1.008} \approx 5.26\)- Moles of oxygen: \(\frac{31.55}{16.00} \approx 1.97\)

Step 3: Find the Empirical Formula

Divide each mole value by the smallest value among them to find the simplest integer ratio. - Ratio for carbon: \(\frac{5.26}{1.97} \approx 2.67\)- Ratio for hydrogen: \(\frac{5.26}{1.97} \approx 2.67\)- Ratio for oxygen: \(\frac{1.97}{1.97} = 1\)To get whole numbers, multiply each by 3:- Carbon: \(2.67 \times 3 \approx 8\)- Hydrogen: \(2.67 \times 3 \approx 8\)- Oxygen: \(1 \times 3 = 3\)Thus, the empirical formula is \( \text{C}_8\text{H}_8\text{O}_3 \).

Step 4: Determine the Molecular Formula

First, calculate the molar mass of the empirical formula \(\text{C}_8\text{H}_8\text{O}_3 \). - Carbon: \(8 \times 12.01 = 96.08\)- Hydrogen: \(8 \times 1.008 = 8.064\)- Oxygen: \(3 \times 16.00 = 48.00\)- Total = 152.14 g/molThe empirical formula's molar mass is equal to the given molar mass of mandelic acid. Thus, the molecular formula is the same as the empirical formula: \( \text{C}_8\text{H}_8\text{O}_3 \).

Key Concepts

Molecular Formula

A molecular formula is a way of expressing the number of atoms of each element in a molecule of a compound. For instance, in the case of mandelic acid, the molecular formula is \( \text{C}_8\text{H}_8\text{O}_3 \). This indicates that each molecule consists of 8 carbon atoms, 8 hydrogen atoms, and 3 oxygen atoms. It provides the actual number of atoms found in one molecule of a substance.
This contrasts with the empirical formula, which shows the simplest whole-number ratio of the elements within the compound. Often, the molecular formula is a multiple of the empirical formula, but sometimes, as in the case of mandelic acid, they are the same. Knowing the molecular formula is essential in Organic Chemistry, especially for understanding the molecule’s composition and chemical behavior.

Molar Mass Calculation

Molar mass tells us about the mass of one mole of a given substance. It is expressed in grams per mole \( (\text{g/mol}) \) and is crucial for converting between the mass of a substance and the amount in moles. In the case of mandelic acid, its molar mass is determined to be \(152.14\text{ g/mol}\).
To calculate the molar mass of a compound, add up the molar masses of all the atoms in the molecular formula. For example, in \( \text{C}_8\text{H}_8\text{O}_3 \):

• Carbon: \(8 \times 12.01 = 96.08\)
• Hydrogen: \(8 \times 1.008 = 8.064\)
• Oxygen: \(3 \times 16.00 = 48.00\)

The total molar mass is \(96.08 + 8.064 + 48.00 = 152.14 \text{ g/mol}\). Understanding molar mass helps in stoichiometry for calculating how much of a chemical is needed or produced in a reaction.

Elemental Composition

Elemental composition refers to the percentage by mass of each element within a compound. This information is fundamental for determining empirical and molecular formulas. For mandelic acid, which is composed of 63.15% carbon, 5.30% hydrogen, and 31.55% oxygen:
1. Assume 100 grams total to simplify calculations
2. Convert the percentage of each element to grams:

• Carbon: 63.15 g
• Hydrogen: 5.30 g
• Oxygen: 31.55 g

3. Then, convert these masses to moles using each element's molar mass:

• Carbon: \(\frac{63.15}{12.01} \approx 5.26 \text{ moles}\)
• Hydrogen: \(\frac{5.30}{1.008} \approx 5.26 \text{ moles}\)
• Oxygen: \(\frac{31.55}{16.00} \approx 1.97 \text{ moles}\)

This step provides the basis for determining the empirical formula by finding the simplest ratio of moles of elements.

Organic Chemistry

Organic Chemistry is the branch of chemistry dealing with the study of carbon-containing compounds, their properties, reactions, and structures. It includes the study of compounds like mandelic acid which plays roles in various chemical, industrial, and biological processes.
Key concepts include:

• Structure: Understanding how carbon bonds with other atoms to form complex structures.
• Reactivity: Predicting how organic compounds will interact with other substances.
• Functional Groups: Identifying groups of atoms within molecules that have a specific chemical behavior, like -OH in acids like mandelic acid.

Organic Chemistry is essential for the development of pharmaceuticals, polymers, and numerous everyday chemicals, aiding in advancements in chemistry and technology.