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 in the compound is (b) \(10.3\%\).

Step 1: Understanding the Composition

To find the percentage of nitrogen in the compound, we first need to understand its composition based on the molecular formula \(\mathrm{C}_5\mathrm{H}_{10}\mathrm{ONCl}\).

Step 2: Calculate Molar Mass of the Compound

Calculate the molar mass by adding the atomic masses of all the atoms in \(\mathrm{C}_5\mathrm{H}_{10}\mathrm{ONCl}\). Atomic masses: \(\mathrm{C} = 12\ \text{g/mol}\), \(\mathrm{H} = 1\ \text{g/mol}\), \(\mathrm{O} = 16\ \text{g/mol}\), \(\mathrm{N} = 14\ \text{g/mol}\), \(\mathrm{Cl} = 35.5\ \text{g/mol}\).

Step 3: Calculate Total Molar Mass

The total molar mass is calculated as follows: \[5(12) + 10(1) + 1(16) + 1(14) + 1(35.5) = 60 + 10 + 16 + 14 + 35.5 = 135.5\ \text{g/mol}.\]

Step 4: Calculate Nitrogen's Contribution

Determine the mass contribution from nitrogen in the compound: - Nitrogen mass = \(14\ \text{g/mol}\).

Step 5: Calculate Nitrogen Percentage

The percentage of nitrogen is then calculated as follows: \[\left(\frac{14}{135.5}\right) \times 100\% = 10.33\%.\]

Step 6: Match with Given Options

Comparing the calculated percentage with the options provided, \(10.3\%\) correlates closest to option (b), hence the percentage of nitrogen is approximately \(10.3\%\).

Key Concepts

Understanding the Molecular Formula

One of the fundamental concepts in organic chemistry is the molecular formula. It's a representation of the types and numbers of atoms in a molecule. For instance, the compound \[ \text{C}_5\text{H}_{10}\text{ONCl} \] is made up of 5 carbon atoms, 10 hydrogen atoms, 1 oxygen atom, 1 nitrogen atom, and 1 chlorine atom.

• The molecular formula tells us not just the count but also the kind of atoms present in the compound.
• This information is crucial when it comes to determining properties such as mass and chemical reactivity.

Knowing the molecular formula is the first step to calculating other characteristics of the compound, such as its molar mass, which is critical in determining the percentage composition of each element.

Molar Mass Calculation

The molar mass of a compound is the mass in grams of one mole of the substance. It is calculated by summing the atomic masses of all the atoms present in the molecular formula. This is expressed in grams per mole (\text{g/mol} ). To calculate the molar mass of our compound, \text{C}_{5} \text{H}_{10} \text{ONCl}, let's examine the atomic masses:

• Carbon (\text{C}): 12 g/mol, and there are 5 Carbon atoms.
• Hydrogen (\text{H}): 1 g/mol, with 10 Hydrogen atoms.
• Oxygen (\text{O}): 16 g/mol, and 1 Oxygen atom.
• Nitrogen (\text{N}): 14 g/mol, with 1 Nitrogen atom.
• Chlorine (\text{Cl}): 35.5 g/mol, and 1 Chlorine atom.

Adding these gives\[5 \times 12 + 10 \times 1 + 16 + 14 + 35.5 = \text{135.5 g/mol}\] It's essential to perform these calculations accurately as any mistake can lead to errors in understanding the composition of the compound.

Percentage Composition

The percentage composition describes the proportion of each element's mass in the compound. It is calculated by dividing the mass of each element by the total molar mass of the compound, then multiplying by 100. This percentage shows how much each element contributes to the overall mass of the compound. Finding the percentage composition is vital because:

• It informs us on how the compound is constituted by its elements.
• Provides insight into the compound's chemical reactivity and properties.

Using our compound as an example, the process is used to find the nitrogen percentage as a demonstration, determining its proportion relative to the entire compound.

Importance of Nitrogen Content

Nitrogen content is a specific focus because nitrogen atoms can greatly influence the properties and behavior of organic compounds. Calculating the nitrogen percentage offers insight into several characteristics:

• Nitrogen presence often indicates potential reactive sites in the molecule.
• Particularly in pharmaceuticals and dyes, nitrogen can denote important functional groups.
• Knowing the nitrogen percentage helps predict how the compound might interact with other chemicals or environments.

The calculation for this involves using the atomic mass of nitrogen and its contribution relative to the entire compound's molar mass. For our case, the nitrogen percentage was calculated as:\[\left( \frac{14}{135.5} \right) \times 100\% = 10.33\%.\]This systematic approach allows chemists to compare different compounds or assess the quality of synthesized chemicals accurately.