Question

Cobalt (III) ion forms many compounds with ammonia. To find the formula of one of these compounds, you t itrate the \(\mathrm{NH}_{3}\) in the compound with standardized acid. $$ \begin{aligned} &\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{\mathrm{x}} \mathrm{Cl}_{3}(\mathrm{aq})+{ }_{\mathrm{x}} \mathrm{HCl}(\mathrm{aq}) \rightarrow \\ &{ }_{\mathrm{x}} \mathrm{NH}_{4}{ }^{+}(\mathrm{aq})+\mathrm{Co}^{3+}(\mathrm{aq})+(\mathrm{x}+3) \mathrm{Cl}^{-}(\mathrm{aq}) \end{aligned} $$ Assume that \(23.63 \mathrm{~m} 1\) of \(1.500 \mathrm{M} \mathrm{HCl}\) is used to titrate \(1.580 \mathrm{~g}\) of \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{\mathrm{x}} \mathrm{Cl}_{3} .\) What is the value of \(X ?\) a. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\) b. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{cl}_{3}\) c. \(\left[\mathrm{Co}(\mathrm{NH})_{3} \mathrm{Cl}_{3}\right.\) d. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\)

Short answer

The correct formula is (a) \( \left[\text{Co}(\text{NH}_3)_6\right]\text{Cl}_3 \).

Step-by-step solution

Determine moles of HCl used

Calculate the moles of HCl used in the titration by using the formula \( ext{moles} = ext{molarity} \times ext{volume} \). The volume should be in liters. \( \text{moles of HCl} = 1.500 \, \text{M} \times 23.63 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.035445 \, \text{moles} \).

Relate moles of NH3 to moles of HCl

From the balanced equation, we see that \( x \) moles of HCl react with \( ext{Co}(\text{NH}_3)_x\text{Cl}_3 \) to release \( x \) moles of \( \text{NH}_3 \). Therefore, \( \text{moles of NH}_3 = \text{moles of HCl} = 0.035445 \, \text{moles} \).

Calculate moles of Co(NH3)xCl3

To find the moles of \( \text{Co}(\text{NH}_3)_x\text{Cl}_3 \), we divide the mass given by its molar mass. Let the molar mass be \( \text{Molar mass} = 58.93 + 14.01x + 3(35.45) \) and use its mass of \( 1.580 \, \text{g} \).

Calculate molar mass with assumption

Assume each possibility (a to d) and calculate its molar mass: \( a) \text{Molar mass} = 58.93 + 6\times14.01 + 3\times35.45 = 267.57 \, \text{g/mol} \); \( d) \text{Molar mass} = 58.93 + 4\times14.01 + 2\times35.45 + 35.45 = 273.41 \, \text{g/mol} \).

Verify moles for each assumption

For option (a), \( 1.580 \, \text{g} \div 267.57 \, \text{g/mol} = 0.005906 \, \text{moles} \). These moles should match \( 0.035445 \, \text{moles of NH}_3 \div 6 = 0.0059075 \, \text{moles} \), consistent with calculations.

Determine correct value of x

The moles calculated for option (a) are consistent with the given value of \( x = 6 \). Thus, \( x = 6 \) fits the given conditions and matches the calculations.

Key concepts

Complex Compounds

Complex compounds are fascinating structures in coordination chemistry. They consist of a central metal atom or ion bonded to a surrounding array of molecules or ions. These surrounding entities are called ligands. The nature of these compounds is characterized by the formation of coordination bonds between the central metal and the ligands. Unlike typical ionic or covalent bonds, coordination bonds involve the sharing of electron pairs.

• Central Metal Ion: Often a transition metal like cobalt, chromium, or iron. In our problem, cobalt is the central metal ion.
• Ligands: These can be molecules like water, ammonia, or ions such as chloride (Cl-). Ammonia serves as the ligand by bonding with the cobalt ion in the exercise.
• Coordination Number: This denotes the total number of coordination bonds the central metal makes with the ligands. It defines the structure and stability of the complex.

Understanding the nature of complex compounds helps in predicting their chemical behavior and reactivity, which is crucial for tasks like titration.

Titration

Titration is a key laboratory technique used to determine the concentration of a solution. The process involves adding a reagent, known as a titrant, to a solution until a reaction reaches its endpoint. In the context of our exercise, titration is used to find the amount of ammonia in a cobalt complex by reacting it with hydrochloric acid (HCl).
Important aspects of titration:

• Titrant: The solution of known concentration, in this exercise, it's the standardized HCl.
• Analyte: The substance whose concentration is being determined, here it's ammonia (NH3) in the cobalt complex.
• Equivalence Point: The point at which the mole ratio of titrant to analyte matches the required stoichiometric balance. This is reached when exactly enough acid has been added to react with all the ammonia present.

Using titration, we calculated the amount of ammonia, and thus determined the composition of the coordination complex.

Stoichiometry

Stoichiometry involves calculating the quantities of reactants and products in chemical reactions. It's crucial for converting experimental data into meaningful chemical information. Through stoichiometry, you can relate the amount of one chemical to another using a balanced chemical equation.
In the exercise, stoichiometry helps us in linking the moles of HCl used with the moles of ammonia released from the cobalt complex. The balanced reaction equation ensures that equal moles of HCl produce equal moles of NH3. This is key when solving for the value of \( x \) in the compound formula \( \text{Co}(\text{NH}_3)_x\text{Cl}_3 \).
Key calculations include:

• Determining moles of HCl: Using its molarity and the volume of the solution.
• Relating these moles to the moles of NH3 through the balanced equation.
• Comparing calculated moles of complex compound to determine the correct structure from options given.

By understanding stoichiometry, dissecting the chemical process into understandable data becomes achievable.

Cobalt Complexes

Cobalt complexes are an impressive subject in the study of coordination chemistry due to their interesting structures and diverse applications. Cobalt acts as a central metal ion, forming stable compounds with different ligands.
In our exercise, cobalt is in the +3 oxidation state, bonding with ammonia and chloride ions to form a complex. Coordination compounds of cobalt can exhibit various colors due to their electronic configurations and effects such as ligand field splitting.
Significant features of cobalt complexes include:

• Complex Structure: The cobalt ion can bond with multiple ligands, for example, 6 ammonia molecules in the complex \( [\text{Co}(\text{NH}_3)_6]\text{Cl}_3 \).
• Versatile Reactions: They are involved in numerous biochemical and industrial applications due to their range of reactivity.
• X-ray Crystallography: Advanced techniques like these can confirm the structure of such complexes.

Exploring these complexes not only enlightens students on chemical composition but also introduces them to the core principles and reactions within coordination chemistry.