Problem 100 - Chemistry Principles and Practice

Question

In the analytical technique called electrogravimetry, electrolysis is used to separate the analyte from a solution by depositing it on an inert electrode. The electrode is weighed before and after the experiment to find the mass of analyte deposited. A \(0.122-\mathrm{g}\) sample of a copper-zinc alloy was treated with concentrated sulfuric acid to produce a solution containing copper(II) and zinc(II) sulfates. The platinum cathode used in the electrolysis of this solution increased in mass by \(0.073 \mathrm{~g}\) after exhaustive electrolysis. (a) Which metal was deposited on the cathode during the electrolysis? Write the balanced equation for the electrolysis reaction. (b) What was the mass percentages of copper and zinc in the alloy sample?

Step-by-Step Solution

Answer

Copper was deposited. Mass percentages: Copper 59.84%, Zinc 40.16%.

Step 1: Identify the deposited metal

The increase in mass of the platinum cathode is due to the deposition of one of the metals from the alloy, either copper or zinc. The deposition of copper is more favorable because it has a higher reduction potential compared to zinc. Thus, the metal deposited is copper.

Step 2: Write the balanced equation for electrolysis

Copper(II) ions are reduced to form solid copper at the cathode. The balanced equation for this electrolysis reaction is: \[ \text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s) \] This shows copper being reduced and deposited as a solid metal on the cathode.

Step 3: Calculate mass percentage of copper

First, determine the mass of copper deposited, which is equivalent to the increase in the mass of the cathode: 0.073 g. The mass percentage of copper is: \[ \text{Mass percentage of Cu} = \left( \frac{0.073 \, g}{0.122 \, g} \right) \times 100 = 59.84\% \] So the copper self-deposited and its mass percentage is 59.84%.

Step 4: Calculate mass percentage of zinc

The initial alloy mass was 0.122 g. With 0.073 g contained as copper, the rest of the mass is zinc. Calculate the mass of zinc: \[ \text{Mass of Zn} = 0.122 \, g - 0.073 \, g = 0.049 \, g \] Now, calculate the mass percentage of zinc: \[ \text{Mass percentage of Zn} = \left( \frac{0.049 \, g}{0.122 \, g} \right) \times 100 = 40.16\% \] This means zinc accounts for 40.16% of the original alloy composition.

Key Concepts

Electrolysis

Electrolysis is a fascinating process where electrical energy is used to bring about a non-spontaneous chemical reaction. In the context of electrogravimetry, this process separates a specific component or analyte from a solution, effectively depositing it on an electrode. In an electrolysis setup, two electrodes—an anode and a cathode—are submerged in an electrolyte solution where ions move to their respective electrodes under the influence of an external electric current.
For example, in the case of a copper-zinc alloy solution, copper ions move towards the platinum cathode and get reduced (gain electrons), while depositing copper metal onto the electrode. This deposited copper contributes to the increase in mass observed on the cathode.
Electrolysis is crucial for various industries and scientific studies, as it allows for precise separation and deposition of elements based on their chemical properties.

Copper-Zinc Alloy

A copper-zinc alloy represents a mixture of copper and zinc metals. These alloys are commonly used in applications such as brass, known for its strength and corrosion resistance. In chemical processes like electrogravimetry, alloys like these are typically dissolved in acids to produce a solution that contains their constituent metal ions.
Once dissolved, the metal ions—namely, copper(II) and zinc(II) ions—are present in the solution. Their individual properties, such as standard reduction potentials, determine how they behave during the electrolysis process.
In practical terms in this example, a copper-zinc alloy sample undergoes extensive electrolysis where copper, due to its favorable reduction potential, is selectively deposited as a pure metal on the electrode surface, allowing the mass of individual metals in the alloy to be calculated.

Reduction Potential

Reduction potential is a key concept in understanding why some metals are more likely to gain electrons and be deposited in electrolysis. It defines the tendency of a compound to acquire electrons and be reduced. The higher the reduction potential, the greater the likelihood of reduction.
For metals in solution during electrogravimetry, like copper and zinc, their standard reduction potentials determine the sequence of deposition. Copper has a higher reduction potential than zinc, meaning copper ions are more readily reduced and thus, are preferentially deposited at the cathode. This selectivity is crucial to correctly identifying which metal will build up on the electrode first.
The marked difference in reduction potentials is why copper is deposited first over zinc in such electrochemical setups, allowing insightful analysis and separation of these metals.

Mass Percentage Calculation

Mass percentage calculation is a straightforward method to determine the proportion of a specific component in a mixture or alloy. After the electrolysis process, the increase in mass of the electrode allows us to determine precisely the mass of the deposited metal.
In the example of a copper-zinc alloy, we first calculate the mass of separated copper by measuring the increase in the mass of the platinum cathode. We use this increase to derive the mass percentage of copper as follows:
\[ \text{Mass percentage of Cu} = \left( \frac{\text{mass of Cu deposited}}{\text{initial alloy mass}} \right) \times 100 \]
This value gives the fraction of the initial sample that was copper. To find the mass percentage of zinc, subtract the copper mass from the total sample mass to get the zinc mass, and then calculate:
\[ \text{Mass percentage of Zn} = \left( \frac{\text{mass of Zn}}{\text{initial alloy mass}} \right) \times 100 \]
This straightforward calculation provides a complete distribution of metallic components in the alloy, essential for precise analytical investigations.