Problem 123 - Chemistry and Chemical Reactivity

Question

You wish to determine the weight percent of copper in a copper-containing alloy. After dissolving a \(0.251-\mathrm{g}\) sample of the alloy in acid, an excess of KI is added, and the \(\mathrm{Cu}^{2+}\) and \(1^{-}\) 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 \(I_{3}^{-}\) 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 mL of \(0.101 M N a_{2} S_{2} O_{3}\) is required for titration to the equivalence point, what is the weight percent of Cu in the alloy?

Step-by-Step Solution

Answer

The weight percent of Cu in the alloy is 67.39%.

Step 1: Identify the Redox Agents

In 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 \(\mathrm{Cu}^{2+}\) ions are reduced to \(\mathrm{CuI}\) (copper is gaining electrons), so \(\mathrm{Cu}^{2+}\) is the oxidizing agent. In contrast, \(\mathrm{I}^{-}\) is oxidized to \(\mathrm{I}_3^{-}\) (iodine is losing electrons), hence \(\mathrm{I}^{-}\) is the reducing agent.In the reaction \(\mathrm{I}_3^{-}(\mathrm{aq}) + 2 \mathrm{S}_2 \mathrm{O}_3^{2-}(\mathrm{aq}) \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}(\mathrm{aq}) + 3 \mathrm{I}^{-}(\mathrm{aq})\), \(\mathrm{I}_3^{-}\) is reduced (it gains electrons to become \(\mathrm{I}^{-}\)), thus acting as the oxidizing agent, while \(\mathrm{S}_2 \mathrm{O}_3^{2-}\) is oxidized (losing electrons to form \(\mathrm{S}_4 \mathrm{O}_6^{2-}\)), making it the reducing agent.

Step 2: Calculate Moles of \(\mathrm{I}_3^{-}\)

Use the volume and molarity of sodium thiosulfate to find moles of \(\mathrm{I}_3^{-}\). The stoichiometry \[\mathrm{I}_3^{-}(\mathrm{aq}) + 2 \mathrm{S}_2 \mathrm{O}_3^{2-}(\mathrm{aq}) \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}(\mathrm{aq}) + 3 \mathrm{I}^{-}(\mathrm{aq})\]shows 1 mole of \(\mathrm{I}_3^{-}\) reacts with 2 moles of \(\mathrm{S}_2 \mathrm{O}_3^{2-}\). Calculate moles of \(\mathrm{S}_2 \mathrm{O}_3^{2-}\) consumed:\[\text{Moles of } \mathrm{S}_2 \mathrm{O}_3^{2-} = 0.101 \,\mathrm{mol/L} \times 0.02632 \, \mathrm{L} = 0.00266 \, \mathrm{mol}\]From the reaction stoichiometry, the moles of \(\mathrm{I}_3^{-}\) are:\[\text{Moles of } \mathrm{I}_3^{-} = \frac{0.00266 \, \mathrm{mol}}{2} = 0.00133 \, \mathrm{mol}\]

Step 3: Calculate Moles of \(\mathrm{Cu}^{2+}\)

The initial redox reaction given is:\[2 \mathrm{Cu}^{2+}(\mathrm{aq}) + 5 \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2 \mathrm{CuI}(\mathrm{s}) + \mathrm{I}_3^{-}(\mathrm{aq})\]From this, 2 moles of \(\mathrm{Cu}^{2+}\) produce 1 mole of \(\mathrm{I}_3^{-}\).Thus, moles of \(\mathrm{Cu}^{2+}\) are:\[\text{Moles of } \mathrm{Cu}^{2+} = 2 \times 0.00133 \, \mathrm{mol} = 0.00266 \, \mathrm{mol}\]

Step 4: Calculate Mass of Copper

The molar mass of copper, \(\mathrm{Cu}\), is 63.55 \(\mathrm{g/mol}\).Calculate the mass of copper using moles:\[\text{Mass of Cu} = 0.00266 \, \mathrm{mol} \times 63.55 \, \mathrm{g/mol} = 0.1691 \, \mathrm{g}\]

Step 5: Calculate Weight Percent of Copper

The weight percent of copper in the alloy is calculated using its mass and the mass of the sample.\[\text{Weight percent of Cu} = \left( \frac{0.1691 \, \mathrm{g}}{0.251 \, \mathrm{g}} \right) \times 100 = 67.39\%\]

Key Concepts

Copper Alloys

Copper alloys are combinations of copper with other metals or elements, which enhance its properties for specific applications. The most common copper alloys include brass and bronze. Brass contains copper and zinc, while bronze primarily combines copper with tin. Each alloy has distinct characteristics:

• Brass: Known for its gold-like appearance and high corrosion resistance, brass is used in musical instruments and decorative items.


• Bronze: Contains tin and sometimes other elements like aluminum, making it harder and more durable than copper. Its applications include sculptures, bearings, and marine hardware.

Copper alloys retain high thermal and electrical conductivity, but the additional elements provide attributes such as improved strength, hardness, and corrosion resistance. This makes them versatile in applications ranging from electronics to construction. Understanding copper alloys is fundamental when calculating the weight percent of copper in an alloy, as you need to determine how much of the sample is pure copper.

Oxidizing and Reducing Agents

In redox reactions, substances either gain or lose electrons. This is known as reduction and oxidation, respectively.
An oxidizing agent is a substance that gains electrons and is reduced in the process, while a reducing agent loses electrons and is oxidized.

In the exercise provided, we examine two redox reactions:

• In the first reaction, \[2\, \mathrm{Cu}^{2+}(\mathrm{aq}) + 5\, \mathrm{I}^{-}(\mathrm{aq}) \rightarrow 2\, \mathrm{CuI}(\mathrm{s}) + \mathrm{I}_3^{-}(\mathrm{aq})\]Copper(II) ions \(\mathrm{Cu}^{2+}\) act as the oxidizing agent, as they gain electrons to form copper(I) iodide \(\mathrm{CuI}\). The iodide ions \(\mathrm{I}^{-}\) act as the reducing agent by losing electrons to form \(\mathrm{I}_3^{-}\).


• In the second reaction, \[\mathrm{I}_3^{-}(\mathrm{aq}) + 2\, \mathrm{S}_2 \mathrm{O}_3^{2-}(\mathrm{aq}) \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}(\mathrm{aq}) + 3\, \mathrm{I}^{-}(\mathrm{aq})\]Here, \(\mathrm{I}_3^{-}\) is reduced back to \(\mathrm{I}^{-}\), making it the oxidizing agent. Thiosulfate \(\mathrm{S}_2 \mathrm{O}_3^{2-}\), which oxidizes to \(\mathrm{S}_4 \mathrm{O}_6^{2-}\), serves as the reducing agent.

Identifying these agents helps us understand the balance between electron transfer and its importance in calculating quantities like the weight percent of copper.

Titration with Sodium Thiosulfate

Titration is a technique used in chemistry to determine the concentration of a specific substance by reacting it with a solution of known concentration. In this context, titration with sodium thiosulfate \(\mathrm{Na}_2 \mathrm{S}_2 \mathrm{O}_3\) is instrumental in analyzing the copper content in the alloy sample by reacting with \(\mathrm{I}_3^{-}\).

During titration:

• An iodine-starch complex is formed, turning the solution blue, which is a crucial indicator.


• As titration proceeds, sodium thiosulfate reduces \(\mathrm{I}_3^{-}\) to \(\mathrm{I}^{-}\). This causes the blue color to fade, signalling the approach to the end point.


• Upon complete reaction, responsible for decolorizing the solution, the end point is reached, allowing for precise calculation of \(\mathrm{I}_3^{-}\) moles.

This data facilitates the determination of copper moles reacted and consequently, the copper alloy's weight percent. Titration's precision is essential for accurate results in chemical analyses.