Problem 113 - A Complete Resource Book in Chemistry for JEE Main

Question

In Carius method of estimation of halogens, \(250 \mathrm{mg}\) of an organic compound gave \(141 \mathrm{mg}\) of \(\mathrm{AgBr}\). The percentage of bromine in the compound is (At. mass \(\mathrm{Ag}=108 ; \mathrm{Br}=80\) ) (a) \(24 \%\) (b) \(36 \%\) (c) \(48 \%\) (d) \(60 \%\)

Step-by-Step Solution

Answer

The percentage of bromine in the compound is 24%.

Step 1: Determine Molar Mass of AgBr

Calculate the molar mass of \( \mathrm{AgBr} \). Using the atomic masses, \( \mathrm{Ag} = 108 \) and \( \mathrm{Br} = 80 \), the molar mass of \( \mathrm{AgBr} \) is: \[ \mathrm{Molar\,mass\,of\,AgBr} = 108 + 80 = 188\, \text{g/mol} \]

Step 2: Calculate the Moles of AgBr Formed

Convert the mass of \( \mathrm{AgBr} \) to moles using its molar mass: \[ \text{Moles of } \mathrm{AgBr} = \frac{141}{188} = 0.75\, \text{mol} \] Here, 141 mg is converted to grams (0.141 g) for the calculation.

Step 3: Determine the Mass of Bromine in AgBr

Find the mass of bromine in the \( \mathrm{AgBr} \) produced: Since the atomic mass of Br is 80, and there is 1 mole of Br per mole of \( \mathrm{AgBr} \), the mass of Br in 0.75 moles of \( \mathrm{AgBr} \) is: \[ \text{Mass of Br} = 0.75 \times 80 = 60\, \text{mg} \]

Step 4: Calculate the Percentage of Bromine

Now calculate the percentage of bromine in the original compound: \[ \text{Percentage of Br} = \left( \frac{60}{250} \right) \times 100 = 24\% \]

Key Concepts

Estimation of Halogens

Halogens, such as fluorine, chlorine, bromine, and iodine, are a group of elements often found in organic compounds. Determining the amount of these elements in a compound is important in chemical analysis. The Carius method is a well-known laboratory technique used to estimate the content of halogens, particularly bromine, in organic compounds.

This technique involves heating the compound with silver nitrate in a sealed tube. This reaction forms a precipitate of silver halide (such as AgBr). By measuring the amount of this precipitate, one can back-calculate how much halogen was originally present in the compound. The precision of the Carius method makes it a reliable choice for such analyses, even though it requires careful handling of dangerous chemicals at high temperatures.

Organic Compound Analysis

Organic compound analysis is all about identifying the elements present in a compound and quantifying their amounts. When dealing with organic compounds, it’s often crucial to know their elemental composition, which influences their properties and reactivity.

This analysis may involve breaking down the compound to determine the quantities of its elements.

• The combustion analysis might determine carbon and hydrogen content.
• The Dumas method might determine nitrogen content.
• The Carius method, as discussed, is effective for estimating halogen content.

Such analyses help chemists understand the molecular structure and functional groups within the compound, which are vital for determining both its chemical behavior and potential applications.

Molar Mass Calculation

Molar mass, or molecular weight, is the mass of a compound divided by its amount of substance. It is expressed in g/mol. To calculate molar mass, you add the atomic masses of all atoms in a molecule.

In this exercise, the molar mass of AgBr was calculated by summing the atomic masses of silver (Ag) and bromine (Br): 1. Silver has an atomic mass of 108 g/mol.2. Bromine has an atomic mass of 80 g/mol.3. Therefore, the molar mass of AgBr was found to be 188 g/mol.
Mathematically, this would be expressed as: \[ \text{Molar mass of } \mathrm{AgBr} = 108 + 80 = 188\, \text{g/mol} \]
Accurate molar mass determination is crucial in stoichiometric calculations to convert between mass and moles, further allowing chemists to explore reaction stoichiometries and yields.

Percentage Composition

Percentage composition refers to the relative mass of each element in a chemical compound. This tells us how much of each element is present in a given mass of the compound, expressed as a percentage of the total mass.

To determine the percentage composition of bromine in our compound, the mass of bromine obtained was compared to the initial mass of the compound.

The formula used is: \[ \text{Percentage of Br} = \left( \frac{\text{mass of Br}}{\text{mass of compound}} \right) \times 100 \]
Substituting the given values: \[ \text{Percentage of Br} = \left( \frac{60}{250} \right) \times 100 = 24\% \]
This calculation helps chemists understand the quantitative composition of a compound, facilitating the identification and confirmation of its structure and purity.