Ch 27: Current and Resistance

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 27: Current and Resistance

Problem 42

Chapter 27, Problem 42

A sculptor has asked you to help electroplate gold onto a brass statue. You know that the charge carriers in the ionic solution are singly charged gold ions, and you've calculated that you must deposit 0.50 g of gold to reach the necessary thickness. How much current do you need, in mA, to plate the statue in 3.0 hours?

Verified step by step guidance

Determine the number of moles of gold to be deposited. Use the molar mass of gold (Au), which is approximately 197 g/mol. The formula to calculate moles is: \( n = \frac{m}{M} \), where \( m \) is the mass of gold (0.50 g) and \( M \) is the molar mass of gold.

Calculate the total charge required to deposit the gold. Since each gold ion (\( Au^+ \)) carries a charge of \( 1e \) (the elementary charge, \( e = 1.602 \times 10^{-19} \ \text{C} \)), the total charge \( Q \) can be found using \( Q = n \cdot N_A \cdot e \), where \( N_A \) is Avogadro's number (\( 6.022 \times 10^{23} \ \text{mol}^{-1} \)).

Convert the total charge \( Q \) into current \( I \) using the relationship \( I = \frac{Q}{t} \), where \( t \) is the time in seconds. First, convert the given time of 3.0 hours into seconds by multiplying by 3600 (since there are 3600 seconds in an hour).

Substitute the values of \( Q \) and \( t \) into the formula \( I = \frac{Q}{t} \) to calculate the current in amperes (A).

Convert the current from amperes to milliamperes (mA) by multiplying the result by 1000 (since 1 A = 1000 mA).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electrolysis

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In the context of electroplating, it involves passing an electric current through an ionic solution, causing metal ions to migrate and deposit onto a conductive surface. Understanding electrolysis is crucial for determining how much current is needed to deposit a specific mass of metal, such as gold, onto the statue.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis quantify the relationship between the amount of substance deposited during electrolysis and the electric charge passed through the solution. The first law states that the mass of a substance deposited is directly proportional to the total electric charge. This principle is essential for calculating the current required to deposit a specific mass of gold in a given time frame.

Current and Time Relationship

The relationship between current, charge, and time is described by the equation Q = I × t, where Q is the total charge, I is the current, and t is the time in seconds. This relationship allows us to determine the necessary current to achieve a desired charge over a specified duration, which is critical for solving the problem of how much current is needed to electroplate the brass statue in 3.0 hours.

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