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A silver plating bath that deposites \(2.60 \mathrm{~g}\) of silver in 40 minute, is connected in series with an ammeter, which reads \(0.90 \mathrm{~A}\). By what percent is the ammeter reading is incorrect ? (Given: Atomic weight of silver \(=108,1\) farad \(=96500 \mathrm{C}\) ) (a) \(7 \%\) less than true value (b) \(7 \%\) greater than true value (c) \(8 \%\) greater than true value (d) \(5 \%\) greater that true value

Short Answer

Expert verified
The ammeter reading is 7% less than the true value.

Step by step solution

01

Calculate Charge Required for Silver Deposition

The first step is to calculate the charge required to deposit 2.60 g of silver. Using the formula:\[ Q = \frac{m \cdot 96500}{M} \]where \( m = 2.60 \) g and \( M = 108 \) g/mol. Thus, \( Q = \frac{2.60 \times 96500}{108} = 2323.15 \text{ C} \). This is the required charge to deposit 2.60 g of silver.
02

Calculate the Actual Current

We know \( Q = I \cdot t \), where \( Q \) is charge, \( I \) is current, and \( t \) is time. Rearrange to find the true current.Time \( t = 40 \times 60 = 2400 \text{ s} \). So the true current \( I = \frac{2323.15}{2400} = 0.968 \text{ A} \).
03

Calculate Error in Ammeter Reading

Now compare the ammeter reading with the actual current:\( \text{Actual Current} = 0.968 \text{ A} \) and \( \text{Ammeter Reading} = 0.90 \text{ A} \).Calculate the error percentage:\[ \text{Error Percentage} = \left( \frac{0.968 - 0.90}{0.968} \right) \times 100\]
04

Solve Error Percentage

Substituting values into the error percentage formula:\[ \text{Error Percentage} = \left( \frac{0.968 - 0.90}{0.968} \right) \times 100 = 7 \%\]This means the ammeter reading is 7% less than the true current.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Faraday's Laws of Electrolysis
Faraday's laws of electrolysis are fundamental principles in electrochemistry. These laws explain how chemical changes occur during the process of electrolysis due to the movement of electric charge. Faraday's first law states that the amount of substance deposited or dissolved at an electrode is directly proportional to the amount of electric charge passed through the electrolyte. Simply put, the more charge you pass, the more substance you can deposit.
This is expressed mathematically by the formula \[ Q = n imes F \]where \( Q \) is the total electric charge, \( n \) is the amount of substance in moles, and \( F \) is Faraday's constant (approximately 96500 C/mol). Faraday's second law takes it further by stating that the amount of chemical reaction (substance deposited or dissolved) is directly proportional to the equivalent weight of the substance.
  • One mole of electrons equals Faraday's constant in charge.
  • Understanding this helps calculate necessary charge for particular deposit masses.
These laws are crucial for understanding and calculating reactions in processes like silver plating or copper refining.
Silver Plating
Silver plating is a process where a thin layer of silver is electrochemically deposited onto the surface of another material. This is often done for decorative purposes, corrosion resistance, or to improve electronic conductivity.
In a silver plating bath, silver ions in the solution are reduced and deposited onto the surface of the object that acts as the cathode. The effectiveness of the plating process is dependent on various factors such as the current applied, the time of deposition, and the concentration of silver ions in the solution.
  • The object being plated acts as a cathode where silver ions gain electrons during deposition.
  • This process is commonly used in jewelry to give objects a shiny, silver finish.
Understanding the charge requirement and Faraday’s laws is vital in calculating the appropriate current and time for effective plating.
Electrodeposition
Electrodeposition is the overarching term for processes like silver plating, where a material is deposited onto a surface using electricity. This method is widely used to coat or change the properties of surfaces, offering benefits in durability, appearance, and resistance to corrosion.
The basic mechanism of electrodeposition involves:
  • Passing an electric current through an electrolyte solution.
  • The object to be plated takes on the role of cathode (negative electrode).
  • Metal ions in the solution are reduced and adhere to the cathode.
This process needs precise control over current, time, and electrolyte composition. Electrodeposition plays a key role in various industries, from aerospace to microelectronics.
Ammeter Accuracy
In electrochemical processes, an ammeter is used to measure the current flowing through the circuit. However, precise readings are crucial for accurate calculations and process efficiency. Sometimes, ammeter readings may not reflect the true current due to various issues such as calibration errors or connection problems.
To measure the ammeter's accuracy, compare its reading to a calculated true current derived from charge and time data. In our exercise, we identified the true current using Faraday’s laws and compared it to the ammeter's reading:
  • True current is calculated: \( I = \frac{Q}{t} \).
  • The difference in calculated versus actual readings reveals the ammeter's error percentage.
Understanding and correcting these errors ensures precision in electroplating and related industrial applications, thereby maintaining product quality and process efficiency.

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Most popular questions from this chapter

There are 45 number of cells with internal resistance of each cell is \(0.5 \Omega\). To get the maximum current through a resistance of \(2.5 \Omega\), one can use \(m\) rows of cells, each row having \(n\) cells. The values of \(m\) and \(n\) are : (a) \(m=3, n=15\) (b) \(m=5, n=9\) (c) \(m=9, n=5\) (d) \(m=15, n=3\)

A lamp having tungsten filament consumes \(50 \mathrm{~W}\). Assume the temperature coefficient of resistance for tungsten is \(4.5 \times 10^{-3} /{ }^{\circ} \mathrm{C}\) and the room temperature is \(20^{\circ} \mathrm{C}\). If the lamp burns, the temperature of its filament 13 becomes \(2500^{\circ} \mathrm{C}\), then the power consumed at the moment switch is on, is : (a) \(608 \mathrm{~W}\) (b) \(710 \mathrm{~W}\) (c) \(215 \mathrm{~W}\) (d) \(580 \mathrm{~W}\)

An electric kettle boils some water in 16 minutes. Due to some defect, it becomes necessary to remove \(10 \%\) turns of heating coil of the kettle. Now, how much time will it take to boil the same mass of water : (a) \(17.7\) minute (b) \(14.4\) minute (c) \(20.9\) minute (d) \(13.7\) minute

A voltmeter having resistance of 1800 ohm is employed to measure the potential difference across \(200 \Omega\) resistance which is connected to D.C. power supply of \(50 \mathrm{~V}\) and internal resistance \(20 \Omega\). What is percentage change in p.d. across \(200 \Omega\) resistance as a result of connecting voltmeter across it ? (a) \(1 \%\) (b) \(5 \%\) (c) \(10 \%\) (d) \(20 \%\)

The amount of chlorine produced per-second through electrolysis in a plate which consumes \(100 \mathrm{~kW}\) power at \(200 \mathrm{~V}\) is: (Given: Electrochemical equivalent of chlorine \(\left.=0.367 \times 10^{-3} \mathrm{~g} / \mathrm{C}\right)\) (a) \(18.35 \mathrm{~g}\) (b) \(1.835 \mathrm{~g}\) (c) \(183.5 \mathrm{~g}\) (d) \(0.1835 \mathrm{~g}\)

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