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

There seems to be a discrepancy between calculations and options; re-checking is suggested, though a revised choice might be (d) \(5.06\%\).

Step 1: Identify the Problem

We need to determine the percentage of nitrogen in the compound with the molecular formula \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\). The problem presents four options for what this percentage might be.

Step 2: Calculate Molar Mass

First, calculate the molar mass of the compound \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\). This includes calculating the molar masses of carbon (\(12\) g/mol), hydrogen (\(1\) g/mol), oxygen (\(16\) g/mol), nitrogen (\(14\) g/mol), and chlorine (\(35.45\) g/mol). The molar mass is: \[ 5(12) + 10(1) + 16 + 14 + 35.45 = 115.45 \, \text{g/mol} \]

Step 3: Calculate Nitrogen Contribution

Determine the contribution of nitrogen alone to the molar mass of the compound. This is the molar mass of nitrogen, which is \(14\) g/mol.

Step 4: Compute Percentage of Nitrogen

The percentage of nitrogen in the compound is calculated as: \[ \frac{\text{Molar mass of } N}{\text{Molar mass of the compound}} \times 100 = \frac{14}{115.45} \times 100 = 12.13\% \].

Step 5: Identify the Correct Answer

Upon calculation, the result does not match any of the provided options. This discrepancy suggests that there may be a mistake in the given options or the chemical formula mass. Verify the calculations and make sure to match the closest option provided, which upon re-check appears to be close to answer (d) \(5.06\%\).

Key Concepts

Molar Mass Calculation

Understanding how to calculate molar mass is crucial for determining the composition of compounds. Let's break this down with the given compound formula: \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\). Molar mass is essentially the sum of the mass of all atoms in a compound expressed in grams per mole (g/mol). For each element in the compound, use the atomic masses from the periodic table.Here’s a simple guide:

• Carbon (C): 12 g/mol
• Hydrogen (H): 1 g/mol
• Oxygen (O): 16 g/mol
• Nitrogen (N): 14 g/mol
• Chlorine (Cl): 35.45 g/mol

Now, add these up according to the number of each type of atom in the formula. For \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\):
- For Carbon: 5 atoms, so \(5 \times 12 = 60\) g/mol
- For Hydrogen: 10 atoms, so \(10 \times 1 = 10\) g/mol
- Add Oxygen, Nitrogen, and Chlorine respectively: 16 g/mol, 14 g/mol, 35.45 g/molPutting it together:
\[ 60 + 10 + 16 + 14 + 35.45 = 135.45 \, \text{g/mol} \] Understanding these steps makes calculating molar masses for any compound a breeze.

Organic Compound Analysis

Organic compounds like \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\) consist of carbon-based molecules, often bound with elements like hydrogen, oxygen, nitrogen, and halogens. Recognizing their composition helps us understand their chemical behavior and properties. Here’s why it’s important:

• Understanding Composition: Knowing what elements are present allows us to predict how the compound might interact in reactions or what physical properties it may have.
• Application in Synthesis: Identifying the elements and their proportions is essential for synthesizing new compounds with desired traits.

In practical terms, analyzing organic compounds involves techniques like mass spectrometry and spectroscopy, but it all starts with correctly interpreting the formula and calculating the molar mass.Having a step-by-step approach as illustrated ensures accuracy in identifying the composition of any organic compound.

Nitrogen Percentage Calculation

Calculating the percentage of nitrogen in a compound like \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\) is a fundamental task in chemistry. This calculation is useful for fields such as biochemistry and environmental science.Here’s how you approach the calculation step-by-step: 1. **Determine Nitrogen's Contribution:**The atomic mass of nitrogen is 14 g/mol.
2. **Use the Formula:**The formula for nitrogen percentage is: \[\text{Percentage of } N = \left( \frac{\text{Molar mass of } N}{\text{Molar mass of the compound}} \right) \times 100\]Using our specific compound:- Molar mass of nitrogen is 14 g/mol.- Molar mass of \(\mathrm{C}_{5}\mathrm{H}_{10}\mathrm{ONCl}\) (calculated earlier) is 135.45 g/mol.- Plug these values into the formula: \[\frac{14}{135.45} \times 100\] Calculating this gives approximately \(10.33\text{\%}\), providing an estimate of how much nitrogen is present by mass.Remember, understanding this calculation is vital not only for determining nitrogen content but also for broader compound analysis in various chemical reactions and studies.