Problem 115 - Chemistry and Chemical Reactivity

Question

You wish to determine the weight percent of copper in a copper-containing alloy. After dissolving a 0.251 -g sample of the alloy in acid, an excess of KI is added, and the \(\mathrm{Cu}^{2+}\) and \(\hat{\mathrm{I}}^{-}\) ions undergo the reaction $$ 2 \mathrm{Cu}^{2+}(\mathrm{aq})+5 \mathrm{I}^{-}(\mathrm{aq}) \longrightarrow 2 \mathrm{CuI}(\mathrm{s})+\mathrm{I}_{3}^{-}(\mathrm{aq}) $$ The liberated \(I_{3}^{-}\) is titrated with sodium thiosulfate according to the equation \(\mathrm{I}_{3}^{-}(\mathrm{aq})+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq})\) (a) Designate the oxidizing and reducing agents in the two reactions above. (b) If 26.32 mL. of \(0.101 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) is required for titration to the equivalence point, what is the weight percent of Cu in \(0.251-\mathrm{g}\) sample of the alloy?

Step-by-Step Solution

Answer

The weight percent of copper in the alloy is 67.32%.

Step 1: Identify the Oxidizing and Reducing Agents

In the reaction \(2 \mathrm{Cu}^{2+}(\mathrm{aq})+5 \mathrm{I}^{-}(\mathrm{aq}) \longrightarrow 2 \mathrm{CuI}(\mathrm{s})+\mathrm{I}_{3}^{-}(\mathrm{aq})\), the oxidizing agent is \(\mathrm{Cu}^{2+}\) because it gains electrons to form \(\mathrm{CuI}\), and \(\mathrm{I}^{-}\) is the reducing agent because it loses electrons to form \(\mathrm{I}_{3}^{-}\). For the second reaction \(\mathrm{I}_{3}^{-}(\mathrm{aq})+2 \mathrm{S}_{2}\mathrm{O}_{3}^{2-}(\mathrm{aq}) \longrightarrow \mathrm{S}_{4}\mathrm{O}_{6}^{2-}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq})\), \(\mathrm{I}_{3}^{-}\) is the oxidizing agent and \(\mathrm{S}_{2}\mathrm{O}_{3}^{2-}\) is the reducing agent.

Step 2: Titration Calculation

First calculate the moles of \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) used in the titration. Use the formula: \[ \text{Moles of } \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} = \text{Concentration} \times \text{Volume (in L)} \]\[ = 0.101 \, \text{mol/L} \times 0.02632 \, \text{L} = 0.00265972 \, \text{mol} \]

Step 3: Moles of \(I_3^-") and Copper

From the titration reaction, \(\mathrm{I}_{3}^{-}\) reacts with \(\mathrm{S}_{2}\mathrm{O}_{3}^{2-}\) in a 1:2 mole ratio. Therefore, moles of \(\mathrm{I}_{3}^{-}\) are half the moles of \(\mathrm{S}_{2}\mathrm{O}_{3}^{2-}\):\[ \text{Moles of } \mathrm{I}_{3}^{-} = \frac{0.00265972}{2} = 0.00132986 \, \text{mol} \]The reaction between \(\mathrm{Cu}^{2+}\) and \(\mathrm{I}^{-}\) shows that \(2\; \mathrm{Cu}^{2+}\) ions produce \(\mathrm{I}_{3}^{-}\). Thus, moles of \(\mathrm{Cu}^{2+}\) are twice the moles of \(\mathrm{I}_{3}^{-}\):\[ \text{Moles of } \mathrm{Cu}^{2+} = 2 \times 0.00132986 = 0.00265972 \, \text{mol} \]

Step 4: Calculate Mass of Copper

Calculate the mass of copper using its molar mass (63.55 g/mol):\[ \text{Mass of Cu} = 0.00265972 \; \text{mol} \times 63.55 \; \text{g/mol} = 0.16893 \; \text{g} \]

Step 5: Determine Weight Percent of Copper

Calculate the weight percent of copper in the alloy:\[ \text{Weight percent of Cu} = \left( \frac{0.16893}{0.251} \right) \times 100 = 67.32\% \]

Key Concepts

Titration

Titration is an analytical technique used to determine the concentration of a dissolved substance. In this method, a solution of known concentration, called the titrant, is added to a solution of unknown concentration until the reaction between them is complete. This completion is typically indicated by a color change due to an indicator or an end-point determined by instrumentation.

In the given exercise, titration is used to measure the amount of copper in an alloy. The reaction involves sodium thiosulfate as the titrant, which reacts with triiodide (\( \mathrm{I}_{3}^{-} \)) produced from the initial reaction with copper ions. As the titrant is added, it reacts with the \( \mathrm{I}_{3}^{-} \), reducing it back to iodide ions, and thus marking the end-point when no \( \mathrm{I}_{3}^{-} \) remains. By measuring how much titrant is used, we can calculate the amount of copper present.

Oxidizing and Reducing Agents

Understanding oxidizing and reducing agents is crucial in redox reactions. An oxidizing agent gains electrons and is reduced itself, while a reducing agent loses electrons and is oxidized. In this exercise, these roles are determined for each step of the reaction.

In the first reaction with copper and iodide ions, \( \mathrm{Cu}^{2+} \) acts as the oxidizing agent because it gains electrons from iodide ions to form \( \mathrm{CuI} \). The iodide \( \mathrm{I}^{-} \) is the reducing agent as it loses electrons to form \( \mathrm{I}_{3}^{-} \).

In the subsequent titration reaction with sodium thiosulfate, \( \mathrm{I}_{3}^{-} \) serves as the oxidizing agent, and \( \mathrm{S}_{2} \mathrm{O}_{3}^{2-} \) is the reducing agent. The triiodide ion is reduced to iodide, while the thiosulfate is oxidized to tetrathionate. Recognizing the roles of these agents helps in understanding how electrons are transferred and facilitates the calculation of reactant quantities.

Weight Percent Calculation

Weight percent calculation is used to express the concentration of an element within a mixture or an alloy. It provides the proportion of a component relative to the total mass of the sample, multiplied by 100 to express it as a percentage.

For the copper-containing alloy, the weight percent of copper is determined through the reactions with iodide and thiosulfate. First, the moles of \( \mathrm{I}_{3}^{-} \) produced are calculated from the volume and concentration of sodium thiosulfate used in titration.

The stoichiometry of the reaction tells us that two moles of \( \mathrm{Cu}^{2+} \) produce one mole of \( \mathrm{I}_{3}^{-} \), allowing us to calculate the moles of copper in the sample. With the moles of copper and its molar mass (63.55 g/mol), we find the mass of copper in the sample. Using the formula: \[ \text{Weight percent of Cu} = \left( \frac{\text{Mass of Cu}}{\text{Total Mass}} \right) \times 100 \], we determine the weight percent of copper, providing a clear picture of its concentration in the alloy.