Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

A complex compound of cobalt with the composition \(\mathrm{Co}=22.58 \%, \mathrm{H}=5.79 \%, \mathrm{~N}=32.2 \%, \mathrm{O}=12.20 \%\) and \(\mathrm{Cl}=27.17 \%\) on heating, looses ammonia to the extent of \(32.63 \%\) of its mass. The number of molecules of ammonia present in one molecule of the cobalt complex is (At. mass of \(\mathrm{Co}=58.9\) ) (a) 7 (b) 5 (c) 8 (d) 12

Step-by-Step Solution

Answer

The number of ammonia molecules is 5.

Step 1: Calculate the molecular mass of the entire compound

The given percentage composition of the compound can be construed as representing a total of 100 g of the compound. Hence, in 100 g of the compound: - Mass of Co = 22.58 g - Mass of H = 5.79 g - Mass of N = 32.2 g - Mass of O = 12.20 g - Mass of Cl = 27.17 g These amounts total to 100 g.

Step 2: Calculate the mass of ammonia lost

The compound loses 32.63% of its mass as ammonia when heated. Thus, the mass of ammonia in 100 g of the compound is:\[\text{Mass of } \text{NH}_3 = 32.63 \text{ g}\]

Step 3: Determine moles of ammonia

Use the molecular weight of ammonia (NH₃), which is 14 (N) + 3×1 (H) = 17 g/mol:\[\text{Moles of } \text{NH}_3 = \frac{32.63}{17} \approx 1.92 \text{ moles}\]

Step 4: Determine the stoichiometry of the molecules

To find how many molecules of ammonia correspond to one molecule of the cobalt compound, we use the ratio of the total moles of ammonia to the moles of the cobalt compound calculated from mass. For the cobalt mass in 100 g:\[\text{Moles of Co} = \frac{22.58}{58.9} \approx 0.383\]The ratio of ammonia moles to cobalt moles gives:\[\frac{1.92}{0.383} \approx 5.01\]This suggests there are approximately 5 ammonia molecules per cobalt complex molecule.

Key Concepts

Understanding Percentage Composition

In coordination chemistry, percentage composition is a way to describe the relative amounts of each element in a compound. These percentages help scientists understand the makeup of a compound quickly.
In the provided exercise, it's given that cobalt, hydrogen, nitrogen, oxygen, and chlorine make up 100% of the compound by mass.
To elaborate further, imagine each percentage as a part of a 100-gram sample of the compound. The given mass percentages translate directly to the mass of each element in grams, simplifying calculations.
For example:

• Cobalt (Co) is 22.58%, so in a 100g sample, there are 22.58g of cobalt.
• Hydrogen (H) is 5.79%, resulting in 5.79g of hydrogen.
• Nitrogen (N) is 32.2%, giving 32.2g of nitrogen.
• Oxygen (O) at 12.20% contributes 12.20g.
• Chlorine (Cl) forms 27.17%, making up 27.17g.

These calculated masses total exactly to 100g, showcasing that percentage composition is essential for determining how much of each element is present in a sample.

Molecular Mass Calculation Demystified

Calculating the molecular mass of a compound involves summing the atomic masses of all atoms present in the molecule. Accurate molecular mass calculations are critical for understanding the formula and structure of complex compounds.
In the exercise, we're considering a compound with known mass percentages for each element. To find the molecular mass, treat those percentages as gram masses in a 100g sample. Once masses are assigned:

• Add them up: - Co: 22.58g - H: 5.79g - N: 32.2g - O: 12.20g - Cl: 27.17g - Total = 100g

This total represents the compound's molecular mass in a theoretical 100g sample, and it matches the 100g starting mass assumed when using percentage composition.
Understanding this concept is crucial for stoichiometry and further chemical analysis.

Stoichiometry in Coordination Compounds

Stoichiometry allows chemists to understand the relative positions or amounts of constituents in a chemical reaction or compound, especially vital for coordination compounds.
In a coordination compound like the given cobalt complex, stoichiometry helps determine the number of ammonia molecules associated with the cobalt. The exercise involves heating the compound and losing ammonia as it decomposes.
Given that 32.63% of the compound's mass is lost as ammonia corresponds to 32.63g of ammonia in a 100g sample: Calculating the moles of ammonia is the next step:

• Ammonia (NH₃) has a molecular weight of 17g/mol.
• The moles of ammonia = 32.63g ÷ 17g/mol = 1.92 moles.

To establish how many ammonia molecules are in the cobalt complex, consider the stoichiometric ratio to cobalt itself:

• Moles of Cobalt (Co) = 22.58g ÷ 58.9g/mol = 0.383 moles.

Next, find the ratio of ammonia moles to cobalt moles:

• The ratio is 1.92/0.383 ≈ 5.01.

This means there are approximately 5 molecules of ammonia per molecule of the cobalt complex, highlighting stoichiometry's role in determining compound structure.