Problem 125 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following compounds: I. DDT II. gammexane III. carbon tetrachloride IV. chlorobenzene The correct sequence of these compounds in the increasing order of percentage of chlorine in them is (a) I, II, III, IV (b) IV, I, II, III (c) IV, II, I, III (d) III, I, II, IV

Step-by-Step Solution

Answer

(c) IV, II, I, III

Step 1: Determine the chemical formulas

To find the percentage of chlorine in each compound, first determine their chemical formulas:- DDT: CCl\(_3\)C\(_6\)H\(_4\)Cl- Gammexane (also known as Lindane): C\(_6\)H\(_6\)Cl\(_6\)- Carbon tetrachloride: CCl\(_4\)- Chlorobenzene: C\(_6\)H\(_5\)Cl

Step 2: Calculate molar masses of compounds

Calculate the molar mass of each compound, as this will be used to find the percentage of chlorine:- CCl\(_3\)C\(_6\)H\(_4\)Cl: (12.01*14 + 1.01*4 + 35.45*4) = 354.49 g/mol- C\(_6\)H\(_6\)Cl\(_6\): (12.01*6 + 1.01*6 + 35.45*6) = 290.83 g/mol- CCl\(_4\): (12.01 + 35.45*4) = 153.81 g/mol- C\(_6\)H\(_5\)Cl: (12.01*6 + 1.01*5 + 35.45) = 112.56 g/mol

Step 3: Find total chlorine mass in each

Calculate the total mass of chlorine in each compound:- CCl\(_3\)C\(_6\)H\(_4\)Cl: 35.45*4 = 141.8 g- C\(_6\)H\(_6\)Cl\(_6\): 35.45*6 = 212.7 g- CCl\(_4\): 35.45*4 = 141.8 g- C\(_6\)H\(_5\)Cl: 35.45 g

Step 4: Calculate percentage of chlorine

Use the formula \(\frac{\text{Total mass of Cl}}{\text{Molar mass of compound}} \times 100\%\) for each compound:- CCl\(_3\)C\(_6\)H\(_4\)Cl: \(\frac{141.8}{354.49} \times 100 \approx 40.00\%\)- C\(_6\)H\(_6\)Cl\(_6\): \(\frac{212.7}{290.83} \times 100 \approx 73.11\%\)- CCl\(_4\): \(\frac{141.8}{153.81} \times 100 \approx 92.18\%\)- C\(_6\)H\(_5\)Cl: \(\frac{35.45}{112.56} \times 100 \approx 31.50\%\)

Step 5: Arrange in increasing order

Arrange the compounds in order of increasing chlorine percentage:- First: C\(_6\)H\(_5\)Cl (31.50\%)- Second: CCl\(_3\)C\(_6\)H\(_4\)Cl (40.00\%)- Third: C\(_6\)H\(_6\)Cl\(_6\) (73.11\%)- Fourth: CCl\(_4\) (92.18\%)The correct sequence is IV, I, II, III.

Key Concepts

Molecular Formula Determination

Determining the molecular formula of a compound is the first step in analyzing its chemical properties. This involves identifying the elements present in the molecule and the number of each type of atom. In the case of our compounds:

• DDT has the formula CCl3C6H4Cl, indicating it contains chlorine, carbon, and hydrogen.
• Gammexane (Lindane) has the formula C6H6Cl6, rich in chlorine.
• Carbon tetrachloride (CCl4) is composed entirely of carbon and chlorine.
• Chlorobenzene has the structure C6H5Cl, similar to benzene but with one hydrogen atom replaced by chlorine.

By determining the formula, we can understand the stoichiometry and calculate properties like molar mass.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental step in chemistry that allows us to convert between mass and moles. The molar mass is the total mass of all atoms in a molecule. Here's how we calculate it:

• Sum the product of atomic masses and their respective counts in the formula.
• For example, in DDT (CCl3C6H4Cl), calculate by adding the mass of each element: carbon, hydrogen, and chlorine. The atomic mass of chlorine, for instance, is 35.45 u.
• Reiterate this process for the other compounds to obtain their molar masses.

Knowing the molar mass assists in determining the percentage composition of each element.

Percentage Composition of Chlorine

Once we have the molar mass and chlorine mass for each compound, calculating the percentage of chlorine is a straightforward process. This tells us how much of the compound's mass is due to chlorine. Here's the calculation method:

• Compute the total mass of chlorine by multiplying its atomic mass by its count in the formula.
• Divide the total chlorine mass by the compound's molar mass.
• Multiply by 100 to convert this to a percentage.

For example, carbon tetrachloride (CCl4) shows a high chlorine content because all atoms except one are chlorine, leading to a large percentage. Such calculations help us order these compounds by their chlorine content.

Organic Compounds Analysis

Organic compounds often contain carbon and hydrogen, with elements like chlorine introducing additional properties. Analyzing these compounds involves understanding their composition and how it relates to their physical and chemical behavior:

• Determine how elements like chlorine affect the compound's reactivity and stability.
• Compare similarities and differences in related compounds, such as how chlorine's presence in DDT versus chlorobenzene affects their usage.
• Think about the compound's applications, as in how carbon tetrachloride was once widely used as a cleaning agent due to its high chlorine content.

Overall, a thorough analysis of organic compounds gives us insight into their roles in chemistry and industry.