Problem 97 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.189 \mathrm{gm}\) of an organic compound gives \(0.287 \mathrm{~g}\) of \(\mathrm{AgCl}\). The \(\%\) of \(\mathrm{Cl}\) in it is? (a) \(18.75 \%\) (b) \(37.56 \%\) (c) \(55.25\) (d) \(74 \%\)

Step-by-Step Solution

Answer

The percentage of Cl in the compound is approximately 37.53%, corresponding to option (b) 37.56%.

Step 1: Determine Molar Mass of AgCl

Start by finding the molar mass of silver chloride (AgCl). The molar mass is calculated by adding the atomic masses of silver (Ag, 107.87 g/mol) and chlorine (Cl, 35.45 g/mol). Therefore, the molar mass of AgCl is 143.32 g/mol.

Step 2: Calculate Moles of AgCl Produced

Use the mass of AgCl produced (0.287 g) to determine the number of moles of AgCl. Use the formula: \( \text{moles of AgCl} = \frac{\text{mass of AgCl}}{\text{molar mass of AgCl}} \). This gives: \( \frac{0.287}{143.32} \approx 0.002002 \) moles.

Step 3: Calculate Moles of Cl in AgCl

Since one mole of AgCl contains one mole of Cl, the moles of Cl are also 0.002002.

Step 4: Find Mass of Cl

Calculate the mass of chlorine using its molar mass (35.45 g/mol) and the moles of Cl calculated in the previous step: \( \text{mass of Cl} = 0.002002 \times 35.45 \approx 0.070951 \) g.

Step 5: Determine Percentage of Cl in Organic Compound

To find the percentage of Cl in the original organic compound, use the formula: \( \% \text{Cl} = \left(\frac{\text{mass of Cl}}{\text{mass of organic compound}}\right) \times 100 \). Substituting the given values gives: \( \frac{0.070951}{0.189} \times 100 \approx 37.53\% \).

Key Concepts

Determining percentage composition

Determining the percentage composition of an element in a compound involves calculating the proportion of that element relative to the entire compound. It provides insight into the compound's makeup and is essential for understanding its chemical properties.

To calculate the percentage of chlorine (Cl) in the compound, we first determine the mass of Cl within it. Once the mass is known, you divide the mass of Cl by the total mass of the compound. Finally, multiply the result by 100 to convert it into a percentage.

In this case, we already know the mass of chlorine is approximately 0.070951 g, and the total mass of the organic compound is 0.189 g. Using the formula:

• Percentage of Cl = \( \left(\frac{\text{mass of Cl}}{\text{mass of organic compound}}\right) \times 100 \)

This calculation results in around 37.53%, indicating the proportion of chlorine within the compound.

Molar mass calculation

Molar mass calculation is fundamental to understanding the composition and reactions of chemical compounds. The molar mass of a substance is the mass of one mole of its molecules or atoms expressed in grams per mole (g/mol).

To calculate the molar mass, add up the atomic masses of all the atoms in a molecule. For silver chloride (AgCl), it involves summing the atomic masses of silver (Ag) and chlorine (Cl). Silver has an atomic mass of approximately 107.87 g/mol, while chlorine's atomic mass is approximately 35.45 g/mol.

• Therefore, the molar mass of AgCl is calculated as: \( 107.87 + 35.45 = 143.32 \) g/mol.

This calculation is crucial for converting a given mass of a substance to a number of moles, which is the basis for further stoichiometric calculations.

Stoichiometry

Stoichiometry involves calculating the quantities of reactants and products in chemical reactions. It is based on the balanced chemical equation and the concept of the mole. This field of chemistry is crucial for predicting the results of reactions and the amounts needed or produced.

In the exercise, stoichiometry helps us determine how much chlorine (Cl) is present in the form of silver chloride (AgCl) given the mass of AgCl produced. By knowing the number of moles of AgCl (calculated from its mass and molar mass), we could infer the number of moles of Cl present, as it maintains a 1:1 ratio in the compound.

• The calculation is done as: \( \text{moles of AgCl} = \frac{0.287 \text{ g AgCl}}{143.32 \text{ g/mol}} \approx 0.002002 \text{ moles} \).
• Since AgCl contains one mole of Cl for each mole of AgCl, there are 0.002002 moles of Cl.

Navigating these calculations allows us to understand not just the quantity of reactants or products, but also the precise interactions within the reaction.