Problem 65 - A Complete Resource Book in Chemistry for JEE Main

Question

Sorbic acid consists of \(\mathrm{C}=64.3 \%, \mathrm{H}=7.2 \%\) and \(28.5 \%\) oxygen. Find the empirical formula. (a) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\) (b) \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{2}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\) (d) \(\mathrm{CH}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The empirical formula is \( \text{C}_3 \text{H}_4 \text{O} \), so the answer is (c).

Step 1: Determine Mass in 100g Sample

Assume you have 100 grams of sorbic acid. Then, the mass of each element is equivalent to their percentage composition. Thus, carbon contributes 64.3 g, hydrogen contributes 7.2 g, and oxygen contributes 28.5 g.

Step 2: Calculate Moles of Each Element

Convert the mass of each element to moles by dividing by their atomic masses: - For carbon: \( \frac{64.3}{12.01} = 5.35 \) moles- For hydrogen: \( \frac{7.2}{1.008} = 7.14 \) moles- For oxygen: \( \frac{28.5}{16.00} = 1.78 \) moles.

Step 3: Determine the Simplest Whole Number Ratio

Divide the number of moles of each element by the smallest number of moles calculated: - For carbon: \( \frac{5.35}{1.78} \approx 3.01 \)- For hydrogen: \( \frac{7.14}{1.78} \approx 4.01 \)- For oxygen: \( \frac{1.78}{1.78} = 1 \).Therefore, the ratio is approximately 3:4:1.

Step 4: Construct the Empirical Formula

Use the calculated ratios to write the empirical formula. The elements are in the ratio \( \text{C}_3 \text{H}_4 \text{O}_1 \), so the empirical formula is \( \text{C}_3 \text{H}_4 \text{O} \).

Key Concepts

Percentage Composition in Chemistry

Percentage composition in chemistry is like breaking down a recipe to know exactly what ingredients are needed and in what quantities. It tells us the relative amount of each element in a compound in terms of mass. For example, if you take a compound like water (H₂O), percentage composition would tell you how much of it is hydrogen and how much is oxygen by weight.

To find the percentage composition, you must first have the chemical formula of the compound. You calculate this by dividing the mass of each element in the formula by the molar mass of the entire compound, and then multiplying by 100.

• Percentage of an element = \( \left( \frac{\text{Mass of the element in one mole of the compound}}{\text{Molar mass of the compound}} \right) \times 100 \% \)

In the case of sorbic acid, we started with the given percentages:

• Carbon = 64.3%
• Hydrogen = 7.2%
• Oxygen = 28.5%

This breakdown was the key to determining which formula best matched their relative amounts.

Mole Concept

The mole concept is a fundamental idea in chemistry, serving as a bridge between the atomic world and the real-world quantities we can see and measure. It allows chemists to count particles like atoms, molecules, or ions in a given mass of substance by converting the mass to moles.

In our exercise with sorbic acid, the mass of each element was known from the percentage composition, assuming a 100-gram sample. To find the number of moles, you simply divide the mass by the atomic weight (molar mass) of the element. This is because one mole of any substance contains Avogadro's number of entities, approximately \(6.022 \times 10^{23}\) particles per mole, linking mass to individual atoms.

For example, when converting 64.3 grams of Carbon to moles, you use its atomic weight of 12.01 g/mol:

• Carbon: \( \frac{64.3}{12.01} = 5.35 \) moles
• Hydrogen: \( \frac{7.2}{1.008} = 7.14 \) moles
• Oxygen: \( \frac{28.5}{16.00} = 1.78 \) moles

These calculations set the stage for finding the simplest whole-number ratio, essential for deriving the empirical formula.

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. It uses the relationships between the quantities of reactants and products involved in reactions to predict how much of each substance is consumed and produced. In the context of determining an empirical formula, stoichiometry helps us convert moles of elements into a fixed ratio to form the compound.

After calculating the number of moles of each element in sorbic acid, stoichiometry comes into play by helping us find the simplest ratio of these moles. You divide the number of moles of each element by the smallest number calculated, making the ratio a simple whole number because the empirical formula needs the simplest ratio:

• Carbon: \( \frac{5.35}{1.78} \approx 3.01 \rightarrow 3 \)
• Hydrogen: \( \frac{7.14}{1.78} \approx 4.01 \rightarrow 4 \)
• Oxygen: \( \frac{1.78}{1.78} = 1 \)

This means the empirical formula for sorbic acid is \( \text{C}_3 \text{H}_4 \text{O} \), representing the simplest whole-number ratio of the constituent elements. Stoichiometry ensures you can derive this empirical formula accurately by standardizing these ratios.