Problem 97 - Chemistry The Central Science

Question

(a) In early studies it was observed that when the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) was placed in water, the electrical conductivity of a 0.05\(M\) solution changed from an initial value of 191 \(\mathrm{ohm}^{-1}\) to a final value of 374 \(\mathrm{ohm}^{-1}\) over a period of an hour or so. Suggest an explanation for the observed results.(See Exercise 23.69 for relevant comparison data.) (b) Write a balanced chemical equation to describe the reaction. (c) \(A 500\)-mL solution is made up by dissolving 3.87g of the complex. As soon as the solution is formed, and before any change in conductivity has occurred, a 25.00-mL portion of the solution is titrated with 0.0100 \(\mathrm{M} \mathrm{AgNO}_{3}\) solution. What volume of AgNO \(_{3}\) solution do you expect to be required to precipitate the free \(\operatorname{Br}^{-}(a q) ?(\mathbf{d})\) Based on the response you gave to part (b), what volume of \(\mathrm{AgNO}_{3}\) solution would be required to titrate a fresh 25.00 -mL sample of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right] \mathrm{Br}\) after all conductivity changes have occurred?

Step-by-Step Solution

Answer

The complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\) undergoes a reaction in water that releases \(\mathrm{Br}^-\) ions, increasing the conductivity over time: \[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br} (s) \rightarrow \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{H}_{2}\mathrm{O}\mathrm{Br}\right]^{+} (aq) + \mathrm{Br}^{-} (aq)\] Before any conductivity change, 0.125 L of 0.0100 M \(\mathrm{AgNO}_{3}\) solution is needed to titrate the free \(\mathrm{Br}^-\) ions in a 25.00 mL sample of the solution. After all conductivity changes have occurred, the same volume of \(\mathrm{AgNO}_{3}\) solution (0.125 L) is needed to titrate a fresh 25.00 mL sample of the complex.

Step 1: When the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\) is placed in water, initially, the complex dissolves and the conductivity increases due to the presence of \(\mathrm{Br}^-\) ions. Over time, the coordination sphere of cobalt(III) changes due to the replacement of one or more \(\mathrm{Br}^{-}\) ions by water molecules. This leads to an increase in conductivity as more \(\mathrm{Br}^{-}\) ions are released into the solution. The complex would undergo the reaction: \[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br} \rightarrow \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{H}_{2}\mathrm{O}\mathrm{Br}\right]^{+} + \mathrm{Br}^{-}\] #b) Write a balanced chemical equation to describe the reaction#

Based on the explanation for the change in conductivity, the balanced chemical equation for the reaction is: \[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br} (s) \rightarrow \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{H}_{2}\mathrm{O}\mathrm{Br}\right]^{+} (aq) + \mathrm{Br}^{-} (aq)\] #c) Calculate the volume of AgNO3 solution needed to precipitate the free Br-(aq)#

Step 2: To calculate the volume of \(\mathrm{AgNO}_{3}\) solution needed, first determine the moles of free \(\mathrm{Br}^-\) ions in the 25.00 mL aliquot: 1. Calculate the moles of the complex in 500 mL of the 0.05 M solution: \[\text{moles of complex} = \text{M} \times \text{volume} = 0.05 \ M \times 0.5\ \text{L} = 0.025\ \text{moles}\] 2. Calculate the moles of the complex in the 25.00 mL aliquot: \[\text{moles of complex} = \frac{0.025\ \text{moles}}{500\ \text{mL}} \times 25\ \text{mL} = 0.00125\ \text{moles}\] Since there is one mole of free \(\text{Br}^-\) per mole of complex, there are 0.00125 moles of free \(\text{Br}^-\) ions in the 25.00 mL aliquot. 3. Finally, calculate the volume of 0.0100 M \(\mathrm{AgNO}_{3}\) solution needed to precipitate the free \(\mathrm{Br}^-\) ions: \[\text{volume} = \frac{\text{moles of } \text{Br}^-}{\text{M}} = \frac{0.00125\ \text{moles}}{0.0100\ \text{M}} = 0.125\ \text{L}\] #d) Calculate the volume of AgNO3 solution needed after all conductivity changes have occurred#

After all conductivity changes have occurred, one mole of \(\text{Br}^-\) will be released per mole of the complex: \[\text{moles of total } \text{Br}^- = 0.00125\ \text{moles}\] Calculate the volume of 0.0100 M \(\mathrm{AgNO}_{3}\) solution needed to precipitate both the free and released \(\mathrm{Br}^-\) ions: \[\text{volume} = \frac{\text{moles of total } \text{Br}^-}{\text{M}} = \frac{0.00125\ \text{moles}}{0.0100\ \text{M}} = 0.125\ \text{L}\] After all conductivity changes have occurred, the same volume of \(\mathrm{AgNO}_{3}\) solution (0.125 L) is needed to titrate a fresh 25.00 mL sample of the complex.

Key Concepts

Complex Ions

Complex ions are fascinating structures formed when central metal atoms or ions, like cobalt, are surrounded by several molecules or ions called ligands. In our exercise, the complex ion is \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\), which involves cobalt at its core. These ligands, which in this case include amine (\(\mathrm{NH}_3\)) molecules and bromide (\(\mathrm{Br}^-\)) ions, coordinate around the central metal through ionic or coordinate covalent bonds.

• Cobalt(III): Acts as the central metal providing positive charge.
• Ammonia ligands (\(\mathrm{NH}_3\)): Neutral ligands that donates electron pairs to the metal to form strong bonds.
• Bromide ions (\(\mathrm{Br}^-\)): Provides negative charge that balances the whole complex charge.

Coordination chemistry explores these interactions and the resulting structural dynamics, such as changes when certain ligands are replaced by others with a stronger affinity, as seen when water molecules replace \(\mathrm{Br}^-\) in this reaction.

Conductivity

Conductivity in solutions is an important property that reveals information about the ions present in the solution. In this exercise, the distinct change in conductivity when the complex \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\) is dissolved is due to dynamic release and replacement of the bromide ions. Initially, heavy conductivity is due to the release of \(\mathrm{Br}^-\), but it increases over time as more \(\mathrm{Br}^-\) ions are released upon replacement by water molecules.

• Conductivity indicates the presence and amount of ionic species in the solution.
• Higher conductivity means more ions are freely moving in the solution.
• Changes in conductivity can also signal chemical reactions or structural changes in complexes.

Understanding conductivity helps to deduce the reaction mechanisms happening in the solution without directly observing them.

Chemical Equations

Chemical equations offer a concise way to describe chemical reactions. In the context of this exercise, the balanced chemical equation represents the transformation the \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\) complex undergoes in solution:\[\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br} (s) \rightarrow \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{H}_{2}\mathrm{O}\mathrm{Br}\right]^{+} (aq) + \mathrm{Br}^{-} (aq)\]In this process, the equation captures several essential points:

• Substitution Reaction: Water replaces bromide ions in the complex.
• The physical state labels (s for solid and aq for aqueous) depict the initial solid complex and its subsequent ionization in solution.
• Ensures conservation of mass and charge through reactants and products.

Balancing chemical equations is vital in chemistry to maintain the law of conservation of mass, showing that the atoms are merely rearranged, not created or destroyed.

Titration

Titration is a method of analysis for determining the concentration of a solute in a solution. In this exercise, after creating a solution of the cobalt complex, a titration is performed using \(0.0100\ \mathrm{M} \ \mathrm{AgNO}_{3} \)to precipitate freely available bromide ions.

• The \(\mathrm{Ag}^+\) ions from \(\mathrm{AgNO}_3\) react with \(\mathrm{Br}^-\) ions, forming an insoluble product, silver bromide \(\mathrm{AgBr}\).
• The amount of \(\mathrm{AgNO}_3\) needed gives us a precise measure of \(\mathrm{Br}^-\) present.
• Ensure accurate measurement of volume and concentration for reliable results.

Titration is a cornerstone laboratory technique for quantifying chemical concentrations and reactions, helping to confirm theoretical predictions in practical scenarios.

Reaction Mechanisms

Reaction mechanisms explain the step-by-step transformation during a reaction. In complex ions like \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Br}_{2}\right]\mathrm{Br}\), understanding mechanisms helps visualize how ligands are exchanged in coordination complexes:

• The bromide ions initially coordinated with cobalt get replaced by water molecules.
• This substitution exposes more \(\mathrm{Br}^-\) ions to the solution, thus increasing conductivity.
• The mechanism involves transient stages where certain ligands detach and others attach to the metal center.

Studying these mechanisms gives insight into the kinetics and energetics of reactions, allowing scientists to tailor conditions or catalysts to control the reaction path and its efficiency.