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

8

Step 1: Assess the Given Composition

The compound consists of elements with the following percentage composition: Cobalt (Co) is 22.58%, Hydrogen (H) is 5.79%, Nitrogen (N) is 32.2%, Oxygen (O) is 12.20%, and Chlorine (Cl) is 27.17%. The compound loses 32.63% of its mass as ammonia when heated.

Step 2: Determine Molecular Masses

Use the atomic masses: Co = 58.9, H = 1, N = 14, O = 16, Cl = 35.5. Calculate the total relative mass of the compound considering each element's percentage.

Step 3: Calculate Ammonia Content

Since ammonia (NH₃) contributes 32.63% of the compound's mass, find the actual mass of the compound associated with this percentage. The molar mass of ammonia (NH₃) is 17 (since N = 14, H = 1 each, thus 14 + 3*1 = 17).

Step 4: Calculate Moles of Ammonia

From the percentage composition, calculate the mass of ammonia in a hypothetical 100 grams of compound, which is 32.63 grams. Use the formula: moles of NH₃ = \(\frac{32.63}{17} \approx 1.92\) moles.

Step 5: Determine the Number of Ammonia Molecules

Now that we calculated approximate 1.92 moles of NH₃ are present in a 100-gram sample of the compound, approximate this number down to the closest whole number, which would be the number of ammonia molecules in one molecule of the cobalt complex.

Key Concepts

Molecular Mass Calculation

Molecular mass is an essential aspect of understanding and analyzing the composition of chemicals, particularly in coordination compounds. It refers to the mass of a single molecule of a chemical substance and is calculated by summing up the atomic masses of all the atoms present in the molecule. When it comes to the cobalt complex, knowing the atomic masses of individual elements such as Cobalt (Co = 58.9 u), Hydrogen (H = 1 u), Nitrogen (N = 14 u), Oxygen (O = 16 u), and Chlorine (Cl = 35.5 u) is crucial.

To find the molecular mass of the cobalt complex, the next step is to consider the percentage composition of each component. Each element's contribution to the molecular mass is determined by its percentage in the compound. This aids in accurately estimating the total molecular mass, a necessary factor for further steps, such as percentage composition analysis.

Percentage Composition Analysis

Percentage composition analysis gives insight into the proportionate contribution of each element to the entire complex. In the cobalt complex, the given percentage compositions are: Cobalt (22.58%), Hydrogen (5.79%), Nitrogen (32.2%), Oxygen (12.20%), and Chlorine (27.17%). These percentages tell us how much each element contributes by mass to 100 grams of the compound.

This analysis is very informative. It allows chemists to identify the dominant elements and deduce sub-component details of the compound. In conjunction with the calculated molecular mass, this information is vital for the following steps, such as determining how much of the compound's mass is attributed to substructures, like ammonia (NH₃) in this scenario.

Ammonia in Coordination Compounds

Coordination compounds often contain ammonia as a ligand, playing a critical role in their structure and reactivity. Ammonia is particularly relevant here, as it makes up part of the cobalt complex and contributes 32.63% of the total mass of the compound.

Considering NH₃'s molar mass is 17, we can calculate the number of moles of ammonia in a hypothetical 100 grams of the compound. With 32.63 grams of that being ammonia, the moles are calculated by dividing this mass by the molar mass of ammonia: \[\text{moles of NH}_3 = \frac{32.63}{17} \approx 1.92\]
This value indicates that around 1.92 moles of ammonia are present, rounding to 2. This is foundational in concluding the number of ammonia molecules bound in one molecule of the cobalt complex. It's through such analysis that the integration of ammonia into coordination chemistry fully unveils itself to students and professionals alike.