Problem 131 - A Complete Resource Book in Chemistry for JEE Main

Question

The maximum percentage of available chlorine on the basis of \(\mathrm{CaOCl}_{2} \cdot \mathrm{H}_{2} \mathrm{O}\) formula is (a) 40 (b) 35 (c) 49 (d) 45

Step-by-Step Solution

Answer

The maximum percentage of available chlorine is (d) 45%.

Step 1: Determine the Molar Mass of Ca(OCl)_2 · H_2O

To find the molar mass, we must add together the atomic masses of each element in the compound. The formula is \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \). The atomic masses are approximately: Ca = 40 g/mol, O = 16 g/mol, Cl = 35.5 g/mol, and H = 1 g/mol. Thus, the molar mass is \[ 40 + (16 \times 2 + 35.5 \times 2) + (2 + 16) = 40 + 103 + 18 = 161 \text{ g/mol}. \]

Step 2: Calculate the Mass of Available Chlorine

The mass of available chlorine in \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \) comes from the two \( \mathrm{Cl} \) atoms, each with a mass of 35.5 g/mol. Therefore, the total mass of chlorine is \[ 35.5 \times 2 = 71 \text{ g/mol}. \]

Step 3: Calculate the Percentage of Available Chlorine

To find the percentage of available chlorine, we divide the mass of chlorine by the molar mass of the entire compound and multiply by 100 to convert it to a percentage. Therefore, the percentage is \[ \left(\frac{71}{161}\right) \times 100 \approx 44.1\%. \]

Step 4: Choose the Closest Answer

Based on our calculation, the closest answer to 44.1% is 45%. So the maximum percentage of available chlorine in \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \) is (d) 45.

Key Concepts

Molar Mass Calculation

In chemistry, the molar mass of a compound is an essential concept that helps you determine how much one mole of that compound weighs. It's the sum of the atomic masses of all the atoms in a molecule. Let's break it down using our compound, calcium hypochlorite hydrate, \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \), as an example. First, we find the individual atomic masses of each element involved:

• Calcium (Ca) has an atomic mass of around 40 g/mol.
• Oxygen (O) has an atomic mass of around 16 g/mol.
• Chlorine (Cl) has an atomic mass of approximately 35.5 g/mol.
• Hydrogen (H) has the smallest atomic mass, about 1 g/mol.

To calculate the molar mass of our compound, we need to account for every atom:

• 1 Ca: 40 g/mol
• 2 OCl groups: for each group, there are 16 g/mol (O) + 35.5 g/mol (Cl), totaling 51.5 g/mol, and twice gives us 103 g/mol.
• 1 water molecule, which is 2 H (2 g/mol) + 1 O (16 g/mol), equals 18 g/mol.

Adding these all together, the molar mass is \( 40 + 103 + 18 = 161 \text{ g/mol} \). Understanding molar mass is vital for many aspects of chemistry, especially in reactions and stoichiometry.

Chemical Formula Interpretation

Interpreting chemical formulas is like understanding a recipe, where each element and number is an ingredient or step. The chemical formula \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \), for instance, tells you not just which elements are present but also how they are combined.Let's break down this formula step-by-step:

• Ca stands for calcium, a single atom contributing to the compound's framework.
• (OCl)_2 indicates that within the molecule, you have two OCl groups. Each OCl is made up of one oxygen and one chlorine atom, so there are two oxygens and two chlorines total.
• H_2O is a familiar molecule: water. However, here it exists as a part of the compound, forming what is known as a hydrate. It's attached to the calcium hypochlorite and contributes to its complete structure.

Reading and understanding chemical formulas is crucial for interpreting chemical reactions and properties. Knowing how elements are organized within a compound helps predict how they might interact in different scenarios, like mixing in a reaction.

Percentage Composition

Percentage composition answers how much of each element makes up a compound. This is particularly useful when you want to understand the proportion of a specific element in a compound. In our case, we're interested in the percentage of chlorine in calcium hypochlorite hydrate.Here's how we calculate it:1. **Total mass of chlorine:** We know from the formula \( \mathrm{Ca(OCl)_2} \cdot \mathrm{H}_2O \) that there are two chlorine atoms, each weighing about 35.5 g/mol. So, chlorine's total mass is \( 2 \times 35.5 = 71 \text{ g/mol} \).2. **Molar mass of the compound:** From our previous calculation, the total molar mass of the compound is 161 g/mol.3. **Percentage calculation:** To find out what percentage of the compound's mass chlorine constitutes, we use the formula: \[ \text{Percentage of Chlorine} = \left(\frac{71}{161}\right) \times 100 \approx 44.1\% \]This simple calculation gives us the idea of how much of the compound's weight is due to chlorine.Calculating percentage composition helps chemists determine how much of a substance they need to achieve the desired chemical reactions. It serves as a valuable tool for analyzing purity and for quantitative chemical analysis.