Problem 86 - A Complete Resource Book in Chemistry for JEE Main

Question

The percentage by weight of hydrogen in \(\mathrm{H}_{2} \mathrm{O}_{2}\) is (a) \(6.5\) (b) \(5.88\) (c) 25 (d) 50

Step-by-Step Solution

Answer

The percentage by weight of hydrogen in \(\mathrm{H}_2\mathrm{O}_2\) is (b) \(5.88\).

Step 1: Determine the molar mass of hydrogen peroxide

First, find the molecular formula of hydrogen peroxide, which is \( \text{H}_2 \text{O}_2 \). To calculate the molar mass, add the atomic masses of all the atoms present: Hydrogen (H) has an atomic mass of approximately 1 g/mol and Oxygen (O) has an atomic mass of approximately 16 g/mol. Therefore, the molar mass of hydrogen peroxide is: \[ 2 \times 1 + 2 \times 16 = 2 + 32 = 34 \text{ g/mol} \]

Step 2: Calculate the contribution of hydrogen to the molar mass

Since there are two hydrogen atoms in hydrogen peroxide and each has a mass of approximately 1 g/mol, the contribution of hydrogen to the total molar mass is: \[ 2 \times 1 = 2 \text{ g/mol} \]

Step 3: Find the percentage by weight of hydrogen

To find the percentage by weight, divide the total mass of hydrogen by the molar mass of the compound and multiply by 100: \[ \frac{2}{34} \times 100 \approx 5.88 \% \]

Step 4: Choose the correct option

The calculated percentage by weight of hydrogen in hydrogen peroxide is approximately 5.88%. Therefore, the correct option is (b) \(5.88\).

Key Concepts

Molar Mass Calculation

The molar mass of a substance is the mass of one mole of that substance in grams. It takes into account all the atoms that make up a molecule. To find it, you need to sum the atomic masses of each element in the compound. For instance, calculating the molar mass of hydrogen peroxide (H₂O₂) requires you to know the atomic masses of hydrogen (H) and oxygen (O).

• Hydrogen has an atomic mass of approximately 1 g/mol.
• Oxygen has an atomic mass of approximately 16 g/mol.

To find the total molar mass, add together the contribution of all atoms:\[ 2 \times (1 \text{ g/mol}) + 2 \times (16 \text{ g/mol}) = 34 \text{ g/mol} \]Understanding molar mass is crucial because it lets you determine how much of each element is present in a mole of the compound.

Atomic Mass

Atomic mass is the mass of a single atom of a chemical element, often expressed in atomic mass units (amu). Each element has a unique atomic mass, which is found on the periodic table. Atomic mass helps determine how much each element contributes to a compound's molar mass. For example, in hydrogen peroxide (H₂O₂):

• Hydrogen contributes approximately 1 g/mol for each atom.
• Oxygen contributes approximately 16 g/mol for each atom.

With this information, one can determine how each element's atomic mass contributes to the overall composition of the compound.

Molecular Formula

The molecular formula of a compound indicates the actual number of each type of atom present in a molecule. It provides critical information that allows you to calculate the molar mass. For hydrogen peroxide (H₂O₂), the formula reveals there are:

• 2 hydrogen atoms
• 2 oxygen atoms

This is fundamental because knowing the molecular formula helps in calculating percentages and understanding the compound's properties. Once you know the molecular formula, you can proceed to perform calculations such as finding the percentage by weight of elements in the compound.