Problem 106 - Chemistry: The Central Science

Question

Copper is an excellent electrical conductor widely used in making electric circuits. In producing a printed circuit board for the electronics industry, a layer of copper is laminated on a plastic board. A circuit pattern is then printed on the board using a chemically resistant polymer. The board is then exposed to a chemical bath that reacts with the exposed copper, leaving the desired copper circuit, which has been protected by the overlaying polymer. Finally, a solvent removes the polymer. One reaction used to remove the exposed copper from the circuit board is $$ \mathrm{Cu}(s)+\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}(a q)+4 \mathrm{NH}_{3}(a q) \underset{2 \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}(a q)} $$ A plant needs to produce 5000 circuit boards, each with a surface area measuring \(2.0\) in. \(\times 3.0\) in. The boards are covered with a 0.65-mm layer of copper. In subsequent processing, \(85 \%\) of the copper is removed. Copper has a density of \(8.96 \mathrm{~g} / \mathrm{cm}^{3} .\) Calculate the masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\) \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) needed to produce the circuit boards, assuming that the reaction used gives a \(97 \%\) yield.

Step-by-Step Solution

Answer

The masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) needed to produce the 5000 circuit boards are approximately \(314281.69\,\text{g}\) and \(105957.95\,\text{g}\), respectively.

Step 1: Calculate the total surface area of copper

Multiply the surface area of one circuit board by the number of circuit boards to find the total surface area of copper: $$ 2.0\,\text{in.} \times 3.0\,\text{in.} \times 5000 = 30000\,\text{in.}^2 $$

Step 2: Find the volume of the copper layer in one board

Convert the given thickness of the copper layer into inches, and then multiply it by the surface area of one board to find the volume of copper in one board: $$ 0.65\,\text{mm} \times \frac{1\,\text{in.}}{25.4\,\text{mm}} = 0.0256\,\text{in.} $$ Now, we find the volume of copper for one board: $$ 0.0256\,\text{in.} \times 2.0\,\text{in.} \times 3.0\,\text{in.} = 0.1536\,\text{in.}^3 $$

Step 3: Calculate the mass of copper to be removed

Convert the volume of copper in inches to cubic centimeters, and then use the density of copper to find the mass: $$ 0.1536\,\text{in.}^3 \times \frac{2.54\,\text{cm}}{1\,\text{in.}}^3 = 2.515\,\text{cm}^3 $$ Now, we find the mass of copper: $$ 2.515\,\text{cm}^3 \times 8.96\,\frac{\text{g}}{\text{cm}^3} = 22.55\,\text{g} $$

Step 4: Calculate the total mass of copper to be removed

Multiply the mass of copper from one board by the percentage of copper to be removed and the number of boards to find the total mass: $$ 22.55\,\text{g} \times 0.85 \times 5000 = 95962.5\,\text{g} $$

Step 5: Determine the moles of copper to be removed

Divide the total mass of copper to be removed by its molar mass to find the number of moles of copper: $$ \frac{95962.5\,\text{g}}{63.55\,\frac{\text{g}}{\text{mol}}} = 1510.14\,\text{mol} $$

Step 6: Calculate moles of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\)

Considering the yield and stoichiometry, we will find the moles of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) required: $$ \frac{1510.14\,\text{mol}\,\mathrm{Cu}}{0.97} = 1555.93\,\text{mol}\,\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2} $$ $$ 1555.93\,\text{mol}\,\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2} \times \frac{4\,\text{mol}\,\mathrm{NH}_{3}}{1\,\text{mol}\,\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}} = 6223.71\,\text{mol}\,\mathrm{NH}_{3} $$

Step 7: Calculate masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\)

Multiply moles of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) by their molar masses to find the required masses: $$ 1555.93\,\text{mol}\,\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2} \times \frac{202.1\,\text{g}}{\text{mol}} = 314281.69\,\text{g} $$ $$ 6223.71\,\text{mol}\,\mathrm{NH}_{3} \times \frac{17.03\,\text{g}}{\text{mol}} = 105957.95\,\text{g} $$ Thus, the masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) needed to produce the 5000 circuit boards are approximately \(314281.69\,\text{g}\) and \(105957.95\,\text{g}\), respectively.

Key Concepts

Electrical Conductivity

Copper is prized in circuit board production primarily for its high electrical conductivity, which is the measure of a material's ability to conduct electric current. This is a critical property in electronics because it allows for efficient transmission of electrical signals with minimal resistance, ensuring the rapid and precise operation of devices.

When engineers design circuit boards, they often choose copper as the conducting layer due to its superior conductivity compared to other metals. This efficiency is essential as it directly impacts the performance and speed of electronic devices. High conductivity also means less energy is lost as heat, making copper a reliable and energy-efficient choice for the electronics industry.

Chemical Reactions in Electronics

The manufacturing of circuit boards involves complex chemical reactions, as illustrated by the use of a chemical bath in the process of etching away unwanted copper. The reaction in the exercise demonstrates the precision required in such chemical processes, which are foundational in electronics manufacturing.

The specific reaction used to etch copper in circuit board production involves a compound known as tetraamminecopper(II) chloride. Through this reaction, precisely controlled areas of copper are removed to create the intricate paths needed for the circuit, while the remaining desired copper is protected by a polymer. Understanding these chemical reactions is crucial for optimizing the production process and achieving high-quality electronic components.

Stoichiometry Calculations

Stoichiometry is the aspect of chemistry that relates to measuring and calculating the amounts of reactants and products in chemical reactions. In the context of circuit board production, stoichiometry calculations are instrumental in determining the precise amounts of chemicals required to etch copper.

The exercise provides a practical application of stoichiometry by calculating the mass of chemicals needed to manufacture a set number of circuit boards. Through these calculations, which consider the surface area, density of copper, and reaction yield, engineers can not only estimate material costs but also anticipate and mitigate potential waste. Proper stoichiometry ensures that the plant operates efficiently and economically, using just the right quantities of reactants to achieve the desired outcome without excess.