Problem 61 - A Complete Resource Book in Chemistry for JEE Main

Question

An organic compound is found to have the formula \(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{ONCl}\). The percentage of nitrogen present in it is (a) \(23.36 \%\) (b) \(10.3 \%\) (c) \(41.05 \%\) (d) \(5.06 \%\)

Step-by-Step Solution

Answer

The percentage of nitrogen present in the compound is (b) 10.3%.

Step 1: Determine Atomic Masses

To solve this problem, first list the atomic masses of each element in the compound: Carbon (C) is approximately 12 g/mol, Hydrogen (H) is 1 g/mol, Oxygen (O) is 16 g/mol, Nitrogen (N) is 14 g/mol, and Chlorine (Cl) is 35.5 g/mol.

Step 2: Calculate Molecular Mass

Calculate the compound's total molecular mass by multiplying each element's atomic mass by the number of its atoms in the formula, then summing them: \[ ext{Molecular mass} = (5 imes 12) + (10 imes 1) + (1 imes 16) + (1 imes 14) + (1 imes 35.5) \] Calculating gives: \[ 60 + 10 + 16 + 14 + 35.5 = 135.5 extrm{ g/mol} \]

Step 3: Calculate Nitrogen's Mass Percentage

The mass of nitrogen in the compound is 14 g (1 N atom). The percentage mass of nitrogen is calculated as:\[ \text{Percentage of N} = \left( \frac{\text{mass of N}}{\text{total molecular mass}} \right) \times 100 = \left( \frac{14}{135.5} \right) \times 100 \] Calculating this gives approximately 10.33\%.

Step 4: Select the Correct Answer

In the provided options, 10.3% is the closest value to our calculated percentage. Therefore, the correct answer is option (b) 10.3%.

Key Concepts

Molecular Mass Calculation

Calculating the molecular mass of a compound helps us understand its composition on a quantitative level. This is essential for determining the mass percentage of each element in a compound. To calculate the molecular mass:

• Identify the chemical formula of the compound, which indicates the number of each type of atom.
• Multiply the atomic mass of each element by the number of atoms of that element in the compound.
• Add these values together to obtain the total molecular mass.

For example, in the compound \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\), we sum the products of the atomic masses and their respective atom counts: \(5 \times 12 + 10 \times 1 + 1 \times 16 + 1 \times 14 + 1 \times 35.5\). This results in a molecular mass of \(135.5\, \text{g/mol}\).
By calculating this, we gain insight into the quantitative relationships of all atoms in the compound.

Organic Compounds

Organic compounds are primarily made of carbon and hydrogen atoms but may include other elements such as oxygen, nitrogen, halogens, etc. These compounds are fundamental to life and countless industrial applications. Organic molecules:

• Contain carbon-carbon bonds which form a variety of structures like chains, rings, and complex branches.
• Include functional groups that define their chemical properties and reactions.
• Have a vast array of configurations, making the study of their structural formulas crucial.

In the case of \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\), the compound features not only aliphatic partially saturated hydrocarbons but also incorporates nitrogen and oxygen, showing how structural variants can lead to diverse functionalities in organic chemistry.

Atomic Mass Determination

Atomic mass is a key concept that defines the mass of an atom, usually expressed in atomic mass units (u). To determine the atomic mass, we rely on:

• Measurements relative to the carbon-12 isotope, setting it as the standard of exactly 12 u.
• The average mass of all isotopes for an element, since most elements have multiple isotopes.
• Referencing established values from periodic tables or scientific data sources.

For example, nitrogen's atomic mass is roughly \(14\, \text{u}\) because it accounts for the weighted average of its stable isotopes. Knowing precise atomic masses allows us to solve problems involving molecular compositions, like calculating the mass percent of nitrogen in the compound in question.