Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

The empirical formula of a compound is \(\mathrm{CH}_{2}\). One mole of the compound has a mass of \(42 \mathrm{~g}\), its molecular formula is (a) \(\mathrm{C}_{2} \mathrm{H}_{2}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{8}\) (d) \(\mathrm{C}_{4} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

The molecular formula is \(\mathrm{C}_3\mathrm{H}_6\), not listed in given options.

Step 1: Determine molar mass of the empirical formula

The empirical formula is \(\mathrm{CH}_2\). The molar mass of carbon \(\mathrm{C}\) is \(12\, \text{g/mol}\), and the molar mass of hydrogen \(\mathrm{H}\) is \(1\, \text{g/mol}\). Calculate the molar mass of \(\mathrm{CH}_2\): \(12 + 2 \times 1 = 14\, \text{g/mol}\).

Step 2: Determine the ratio of molar masses

The molar mass of one mole of the compound is \(42\, \text{g/mol}\). Divide the molar mass of the compound by the molar mass of the empirical formula: \(\frac{42}{14} = 3\).

Step 3: Calculate the molecular formula

The ratio found is \(3\), which means the molecular formula is \(3\) times the empirical formula \(\mathrm{CH}_2\). Multiply each element in the empirical formula by \(3\): \(\mathrm{C}_3\mathrm{H}_6\).

Step 4: Match the molecular formula with the options provided

The compound \(\mathrm{C}_3\mathrm{H}_6\) matches none of the options precisely, indicating that the problem may contain a typographical error, or reevaluate the compound's properties with this empirical formula.

Key Concepts

Empirical Formula

In chemistry, an empirical formula represents the simplest whole-number ratio of atoms in a compound. For instance, if the empirical formula is \( \mathrm{CH}_2 \), it indicates that for every carbon atom, there are two hydrogen atoms. However, it does not provide information about the actual number of atoms in a molecule of the compound. This formula is determined through experimental data, where percentages of elements present are converted into moles and divided by the smallest number of moles found.

Empirical formulas are extremely useful when you want to get a basic understanding of the composition of a compound, especially if you lack details about its structure. But remember, they don’t show all the intricate details of the molecular architecture, which is where the molecular formula becomes necessary.

Molecular Formula Calculation

After understanding the empirical formula, calculating the molecular formula is the next step. The molecular formula tells you the exact number of each kind of atom in a molecule of a compound. To find the molecular formula, you first need to determine the molar mass of the empirical formula.

Take, for example, the empirical formula \( \mathrm{CH}_2 \). Calculate its molar mass by adding the molar masses of carbon (\(12\, \text{g/mol}\)) and hydrogen (\(1\, \text{g/mol}\)), leading to \(14\, \text{g/mol}\). Once you have this, use the given molar mass of the compound (e.g., \(42\, \text{g/mol}\) in this exercise) and divide it by the empirical formula's molar mass to ascertain a multiplication factor.

Finally, multiply each subscript in the empirical formula by this factor to achieve the molecular formula. In our case, dividing \(42\, \text{g/mol}\) by \(14\, \text{g/mol}\) gives us \(3\), which makes the molecular formula \( \mathrm{C}_3\mathrm{H}_6 \). This step is crucial in determining how the compound actually exists chemically.

Molar Mass Determination

Understanding molar mass is integral to both empirical and molecular formula calculations. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (\(\text{g/mol}\)). To find the molar mass of a compound, you need to sum the atomic masses of all atoms in its chemical formula. Use the periodic table to find atomic masses and multiply them by their respective quantities in the formula.

For example, in the empirical formula \(\mathrm{CH}_2\), the molar mass is calculated as follows: \(12\) from carbon and \(2 \times 1\) from the hydrogen atoms, which equals \(14\, \text{g/mol}\). This precise determination allows chemists to bridge empirical data with molecular structures effectively.

• Always start by identifying each element’s atomic mass.
• Multiply each by the number of times the element appears in the formula.
• Add them together for the total molar mass.

Accurate molar mass determination is essential for all kinds of formula calculations in chemistry.