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

Short answer

This solution doesn't match the provided options; there might be more unlisted steps, or additional needed information to reach the expected result.

Step-by-step solution

Determine the Molecular Formula Mass

First, calculate the total molecular formula mass using the percentage composition and their atomic masses: - Co (Cobalt): 22.58% with atomic mass 58.9 - H (Hydrogen): 5.79% with atomic mass 1 - N (Nitrogen): 32.2% with atomic mass 14 - O (Oxygen): 12.20% with atomic mass 16 - Cl (Chlorine): 27.17% with atomic mass 35.5

Key concepts

Percentage Composition

Percentage composition tells us how much of each element is present in a compound relative to the entire compound's mass. It's an essential concept in chemistry because it helps to determine what elements make up a compound and their proportions.

To determine the percentage composition, we calculate how much of each element is contained in 100 parts of the compound's total mass. For example, in the cobalt complex compound in the exercise, the composition is given as:

• Cobalt (Co): 22.58%
  
• Hydrogen (H): 5.79%
  
• Nitrogen (N): 32.2%
  
• Oxygen (O): 12.20%
  
• Chlorine (Cl): 27.17%
  

This information is vital for calculating the molecular formula mass, which we will explore in the next section. Always remember, the total percentage of all elements in a compound should add up to 100%.

Molecular Formula Mass

The molecular formula mass is crucial because it gives us the total mass of a single molecule of a compound. This is determined by adding up the masses of all the elements present in the compound, multiplied by their respective counts in the formula.

For the cobalt complex, the percentage composition, along with each element's atomic mass, allows us to calculate its molecular formula mass. Here's how it works:

• Cobalt (Co): 22.58% of the mass, with an atomic mass of 58.9
  
• Hydrogen (H): 5.79% of the mass, with an atomic mass of 1
  
• Nitrogen (N): 32.2% of the mass, with an atomic mass of 14
  
• Oxygen (O): 12.20% of the mass, with an atomic mass of 16
  
• Chlorine (Cl): 27.17% of the mass, with an atomic mass of 35.5
  

We multiply the atomic mass by the respective percentage of the element divided by 100. By summing these contributions, you obtain the whole compound's molecular formula mass. The calculations provide a deeper understanding of the compound's composition.

Atomic Mass Calculation

Atomic mass plays a pivotal role in understanding the properties of a compound. It is defined as the mass of an individual atom, typically measured in unified atomic mass units (u). The idea here is to identify how much each atom contributes to the overall molecular formula mass of the compound.

For the cobalt complex, each element's atomic mass is given as:

• Cobalt (Co): 58.9 u
  
• Hydrogen (H): 1 u
  
• Nitrogen (N): 14 u
  
• Oxygen (O): 16 u
  
• Chlorine (Cl): 35.5 u
  

By knowing these atomic masses, we can compute the relative masses of the elements in the compound. This helps deduce not only the molecular formula but also assists in determining the number of additional molecules, such as ammonia, attached to the complex, which we cover next.

Ammonia Molecule Determination

Determining the number of ammonia molecules in a cobalt complex involves understanding the relationship between ammonia's mass percentage and its contribution to the total mass.

In the given exercise, the complex loses 32.63% of its mass as ammonia when heated. Ammonia (N\(_2\)H\(_4\)) has a molecular mass of 17 u, calculated as 2(14)+4(1).

To determine how many molecules of ammonia are present, follow the steps below:

• Calculate the mass corresponding to 32.63% in terms of ammonia molecules.
  
• Divide this mass by the molecular mass of ammonia (17 u).
  

This calculation gives the number of ammonia molecules present in the cobalt complex. It’s essential to fit the number of ammonia molecules to one of the choices given in the problem, ensuring the theoretical mass loss aligns with the calculated value of 32.63%.