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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 \(\mathrm{I}^{-}\) ions undergo the reaction $$2 \mathrm{Cu}^{2+}(\mathrm{aq})+5 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{CuI}(\mathrm{s})+\mathrm{I}_{3}^{-}(\mathrm{aq})$$ The liberated \(\mathrm{I}_{3}^{-}\) is titrated with sodium thiosulfate according to the equation $$\mathrm{I}_{3}^{-}(\mathrm{aq})+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \rightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq})$$ (a) Designate the oxidizing and reducing agents in the two reactions above. (b) If \(26.32 \mathrm{mL}\) 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 the alloy?

Step by step solution

01

Determine Oxidizing and Reducing Agents

In the first reaction, \( \mathrm{Cu}^{2+} \) is reduced to \( \mathrm{CuI} \), thus acting as the oxidizing agent. \( \mathrm{I}^{-} \) is oxidized to \( \mathrm{I}_{3}^{-} \), so it is the reducing agent. In the second reaction, \( \mathrm{I}_{3}^{-} \) is reduced back to \( \mathrm{I}^{-} \) and \( \mathrm{S}_{2}\mathrm{O}_{3}^{2-} \) is oxidized to \( \mathrm{S}_{4}\mathrm{O}_{6}^{2-} \). Hence, \( \mathrm{I}_{3}^{-} \) is the oxidizing agent and \( \mathrm{S}_{2}\mathrm{O}_{3}^{2-} \) is the reducing agent.

02

Calculate Moles of \( \mathrm{Na}_{2} \mathrm{S}_{2}\mathrm{O}_{3} \) Used

We have 26.32 mL of \( 0.101 \mathrm{M} \mathrm{Na}_{2}\mathrm{S}_{2}\mathrm{O}_{3} \). First, convert the volume from mL to L: \( 26.32\, \text{mL} = 0.02632\, \text{L} \). Calculate the moles: \(\text{Moles } = 0.101\, \text{mol/L} \times 0.02632\, \text{L} = 0.00265932\, \text{mol}.\)

03

Determine Moles of \( \mathrm{I}_{3}^{-} \)

From the titration equation, \( \mathrm{I}_{3}^{-} + 2\mathrm{S}_{2}\mathrm{O}_{3}^{2-} \rightarrow \mathrm{S}_{4}\mathrm{O}_{6}^{2-} + 3\mathrm{I}^{-} \), 1 mole of \( \mathrm{I}_{3}^{-} \) reacts with 2 moles of \( \mathrm{S}_{2}\mathrm{O}_{3}^{2-} \).So, the moles of \( \mathrm{I}_{3}^{-} \) = \( 0.00265932 \div 2 = 0.00132966 \) moles.

04

Find Moles of Copper

In the first reaction, \( 2 \mathrm{Cu}^{2+} + 5 \mathrm{I}^{-} \rightarrow 2\mathrm{CuI} + \mathrm{I}_{3}^{-} \), 2 moles of \( \mathrm{Cu}^{2+} \) correspond to 1 mole of \( \mathrm{I}_{3}^{-} \). Therefore, moles of \( \mathrm{Cu} = 0.00132966 \times 2 = 0.00265932 \) moles.

05

Calculate Mass of Copper

The atomic weight of copper is \( 63.55 \text{ g/mol} \). Therefore, the mass of copper is \(0.00265932 \text{ mol} \times 63.55 \text{ g/mol} = 0.16895 \text{ g}.\)

06

Determine Weight Percent of Copper

The weight percent of copper in the alloy is \[\text{Weight percent of Cu} = \left( \frac{0.16895 \text{ g}}{0.251 \text{ g}} \right) \times 100\%\]\(= 67.33\%.\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Redox Reactions

Redox reactions are fundamental in chemistry, involving the transfer of electrons between species. In these reactions, one substance is oxidized (loses electrons) and another is reduced (gains electrons). Oxidizing agents gain electrons and are reduced in the process, while reducing agents lose electrons and are oxidized.

In the given copper alloy problem, the first reaction is:
\[ 2 \text{Cu}^{2+} + 5 \text{I}^{-} \rightarrow 2 \text{CuI} + \text{I}_{3}^{-} \]

• Here, \( \text{Cu}^{2+} \) ions are the oxidizing agents because they gain electrons to become solid \( \text{CuI} \).
• The \( \text{I}^{-} \) ions are reducing agents as they lose electrons, forming \( \text{I}_{3}^{-} \).

The second reaction details the titration with sodium thiosulfate:
\[ \text{I}_{3}^{-} + 2 \text{S}_{2}\text{O}_{3}^{2-} \rightarrow \text{S}_{4}\text{O}_{6}^{2-} + 3 \text{I}^{-} \]

• In this reaction, \( \text{I}_{3}^{-} \) acts as the oxidizing agent, supported by its role in accepting electrons to revert to \( \text{I}^{-} \).
• The \( \text{S}_{2}\text{O}_{3}^{2-} \) is the reducing agent, providing electrons and getting oxidized to \( \text{S}_{4}\text{O}_{6}^{2-} \).

Understanding which species act as oxidizing and reducing agents helps in balancing reactions and predicting the outcome of chemical processes.

Titration

Titration is a laboratory technique used to determine the concentration of an unknown solution. It involves the gradual addition of a titrant (a solution of known concentration) to a solution with an unknown concentration until a reaction is completed, often indicated by a color change or reaching a specific measurement point with an instrument.

In the copper alloy exercise, titration is used to quantify the amount of iodine in the solution after the reaction with copper ions. The iodine liberated as \( \text{I}_{3}^{-} \) reacts with sodium thiosulfate as outlined in the equation:
\[ \text{I}_{3}^{-} + 2 \text{S}_{2}\text{O}_{3}^{2-} \rightarrow \text{S}_{4}\text{O}_{6}^{2-} + 3 \text{I}^{-} \]

• Titration allows the determination of how much \( \text{I}_{3}^{-} \) was produced from the initial copper reaction with iodide ions by calculating the volume of thiosulfate solution needed.
• In this case, using 26.32 mL of a 0.101 M \( \text{Na}_{2}\text{S}_{2}\text{O}_{3} \) solution helps find the amount of iodine liberated, which is then used to calculate copper content.

Titration is reliable and precise, making it invaluable for quantitative chemical analysis.

Weight Percent Calculation

Weight percent is a measurement that helps express the concentration of a component in a mixture, such as an alloy, as a percentage of the total mass. It is calculated using the formula:\[\text{Weight Percent} = \left( \frac{\text{Mass of the Component}}{\text{Total Mass of the Mixture}} \right) \times 100\%\]
In the context of the copper alloy problem, we calculate the weight percent of copper as follows:

• Determine the mass of copper using its moles, calculated from the titration data. The reaction provided the necessary stoichiometric relationships between copper and iodine.
• Given that the atomic weight of copper is 63.55 g/mol, you multiply the moles of copper detected (\( 0.00265932 \text{ mol} \)) by this atomic weight to get the mass of copper, which amounts to 0.16895 g.
• Finally, calculate the weight percent by dividing this mass by the initial alloy sample mass (0.251 g) and multiplying by 100%.

The solution finds the weight percent of copper to be approximately 67.33%. This method is commonly used in analytical chemistry to understand the composition of mixtures and ensure quality control in manufacturing processes.