Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

\(9.9 \mathrm{~g}\) of an amide with molecular formula \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{\mathrm{x}} \mathrm{O}_{\mathrm{z}}\) on heating with alkali liberated \(1.7 \mathrm{~g}\) of ammonia. If the percentage of oxygen is \(32.33 \%\), then the ratio of \(\mathrm{N}\) and \(\mathrm{O}\) atoms in the compound is (a) \(2: 1\) (b) \(1: 2\) (c) \(2: 5\) (d) \(2: 3\)

Step-by-Step Solution

Answer

(b) 1:2

Step 1: Determine Oxygen Content

The total mass of the compound is given as \( 9.9 \text{ g} \). Given that the percentage of oxygen is 32.33%, calculate the mass of oxygen in the compound using the formula:\[ \text{Mass of Oxygen} = \frac{32.33}{100} \times 9.9 \text{ g} = 3.2 \text{ g} \]

Step 2: Calculate Number of Oxygen Atoms

The number of moles of oxygen can be calculated by dividing the mass of oxygen by its molar mass (16 g/mol):\[ \text{Moles of Oxygen} = \frac{3.2}{16} = 0.2 \text{ moles} \]

Step 3: Determine Number of Nitrogen Atoms From Ammonia

From the reaction, 1.7 g of ammonia (NH₃) is released. Calculate the moles of ammonia by dividing by its molar mass (17 g/mol):\[ \text{Moles of Ammonia} = \frac{1.7}{17} = 0.1 \text{ moles} \]Ammonia has one nitrogen atom per molecule, so the moles of nitrogen in ammonia is 0.1 moles, corresponding to 0.1 moles of nitrogen atoms.

Step 4: Find the Atom Ratio of Nitrogen to Oxygen

The moles of nitrogen atoms in ammonia is 0.1, and the moles of oxygen atoms in the compound is 0.2. The ratio of nitrogen to oxygen atoms in the compound is given by:\[ \text{N:O} = \frac{0.1}{0.2} = 1:2 \]

Step 5: Conclusion

The ratio of the nitrogen and oxygen atoms, based on provided data and calculations, is \(1:2\). The correct answer is option (b).

Key Concepts

Molecular Formula Calculation

Understanding the molecular formula is crucial in chemistry. Here, we have the amide compound with the formula \(\text{C}_4\text{H}_5\text{N}_{x}\text{O}_{z}\). This formula informs us about the number of each type of atom in a molecule of the compound. With this formula, we need to determine the unknowns \(x\) and \(z\) for nitrogen and oxygen, respectively. The exercise reveals how these unknowns relate by weighing the amide and measuring the released ammonia upon heating.When given a percentage composition and experimental data, this formula allows us to calculate how much of each element is in the compound. For instance, by knowing the oxygen percentage, we can find out the mass of oxygen relative to the entire compound. This helps ensure that the components of the molecular formula balance correctly and makes further calculations possible.

Ammonia Liberation

Ammonia liberation is a common reaction when heating amides with alkali. Here, 1.7 g of ammonia is released. When amides are heated, the nitrogen present in the amide is converted into ammonia (\(\text{NH}_3\)). Ammonia only contains nitrogen and hydrogen, so by calculating the mass of ammonia released, we can directly find the amount of nitrogen that was in the amide. The molar mass of ammonia is 17 g/mol, and using this, we calculate the moles of ammonia released. Consequently, this calculation gives the moles of nitrogen atoms involved, as one molecule of ammonia contains one nitrogen atom.These steps help us bridge the molecular formula to the chemical changes during heating, allowing us to quantify element composition in a compound.

Oxygen Percentage

Calculating the percentage of an element in a compound is key to understanding its composition. In this exercise, the percentage of oxygen is given as 32.33%. This information tells us that oxygen makes up one-third of the total weight of the compound. To translate this percentage into a usable form for calculations, convert it to the mass of oxygen present by multiplying by the total mass of the compound. Once you have the mass of oxygen, determine the moles of oxygen by dividing by the molar mass of oxygen (16 g/mol). Knowing the moles of oxygen as well as other components allows the determination of atom ratios.

Atom Ratio Determination

Determining the atom ratio in a compound is crucial to understanding its identity and properties. In the given problem, the atom ratio of nitrogen to oxygen is calculated based on their moles. We found that 0.1 moles of nitrogen were present from the ammonia, while there were 0.2 moles of oxygen. The ratio is simply this comparison of moles: \(\text{N:O} = \frac{0.1}{0.2} = 1:2\).This ratio helps in concluding the structural arrangement and stoichiometry of the compound. Knowing the atom ratio allows for a deeper comprehension of the compound's behavior and interaction in chemical reactions. These ratios are vital in predicting the outcomes and products of various chemical processes.