Question

An irregularly shaped metal part made from a particular alloy was galvanized with zinc using a Zn(NO₃)₂ solution. When a current of 2.599 A was used, it took exactly 1 hour to deposit a 0.01123-mm layer of zinc on the part. What was the total surface area of the part? The density of zinc is 7.140 g/cm³.

a) 4.02 cm²
b) 6.89 cm²
c) 9.45 cm²
d) 12.18 cm²

Answer 1

To find the total surface area of the metal part, we need to calculate the volume of zinc deposited, find the mass of the zinc, and then determine the total surface area using the mass and thickness of zinc deposited.

Step-by-step explanation:

In order to find the total surface area of the metal part, we need to calculate the volume of zinc deposited on the part using the given current and time. We can then find the mass of the zinc deposited by multiplying the volume with the density of zinc. Finally, we can use the mass and thickness of zinc deposited to determine the total surface area of the part.

Given:
Current (I) = 2.599 A
Time (t) = 1 hour = 60 minutes
Thickness (d) = 0.01123 mm
Density of zinc (ρ) = 7.140 g/cm³

Step 1: Calculate the volume of zinc deposited:

Volume = Current × Time = 2.599 A × 60 minutes = 155.94 A·min

Note: Since the volume is given in A·min, we need to convert it to cm³.

1 A·min = 1 cm³

Therefore, Volume = 155.94 cm³

Step 2: Calculate the mass of zinc deposited:

Mass = Volume × Density = 155.94 cm³ × 7.140 g/cm³ = 1113.79 g

Step 3: Calculate the total surface area of the part:

Surface Area = Mass / (Density × Thickness) = 1113.79 g / (7.140 g/cm³ × 0.01123 cm) = 13869.246 cm²

So, the total surface area of the metal part is approximately 13869.246 cm².