Problem 74 - A Complete Resource Book in Chemistry for JEE Main

Question

A solution of \(\mathrm{CuSO}_{4}\) is electrolyzed for 7 minutes with a current of \(0.6 \mathrm{~A}\). The amount of electricity passed equal to (a) \(26 \mathrm{C}\) (b) \(4.2 \mathrm{C}\) (c) \(2.6 \times 10^{-4} \mathrm{~F}\) (d) \(2.6 \times 10^{-3} \mathrm{~F}\)

Step-by-Step Solution

Answer

The charge is 252 C; none of the given options match this value.

Step 1: Identify the formula for electric charge

To find the amount of electricity (or electric charge) passed during electrolysis, we use the formula \(Q = I \times t\), where \(Q\) is the electric charge in Coulombs (C), \(I\) is the current in Amperes (A), and \(t\) is the time in seconds (s).

Step 2: Convert time to seconds

The electrolysis process lasts 7 minutes. We need to convert this time into seconds before substituting it into the equation. Since 1 minute equals 60 seconds, 7 minutes is equal to \(7 \times 60 = 420\) seconds.

Step 3: Calculate the charge passed

Substitute the values for current \(I = 0.6\) A and time \(t = 420\) s into the formula \(Q = I \times t\). This gives us:\[ Q = 0.6 \, \text{A} \times 420 \, \text{s} = 252 \, \text{C} \]

Step 4: Compare with given options

The calculated electric charge is 252 C, which unfortunately does not match any of the given options. Double check calculations and understand that the absence of a matching option suggests a possible error in options provided.

Key Concepts

Electric Charge Calculation

Electrolysis involves passing an electric current through a solution to cause a chemical change, usually separating the elements in a compound. In this process, calculating the electric charge is fundamental, as it indicates how much electricity has been transferred during the reaction. The formula to find the electric charge passed through the system is straightforward:

• \( Q = I \times t \)

Here, \( Q \) represents the electric charge in Coulombs (C). The parameter \( I \) is the current, measured in Amperes (A), and \( t \) stands for the time in seconds.

When doing these calculations, it is important to ensure that the time is always converted to seconds, as the standard unit of time in physics equations. This conversion aligns with the International System of Units (SI). Always double-check unit conversions to prevent any minor mistakes from skewing your final results. This proper understanding and application of units (Amperes for current and seconds for time) is crucial in electrolysis calculations.

Coulomb's Law

Coulomb's Law is a pivotal concept in understanding electrolysis and electrochemistry, as it elaborates on the force between charged entities. Although it directly doesn't deal with the quantity of electric charge passed, it helps explain interactions that occur during electrolysis. Coulomb’s Law quantitatively describes the electrostatic force between two point charges. The formula is:

• \[ F = k \frac{|q_1 \times q_2|}{r^2} \]

Where:

• \( F \) is the magnitude of the force between the charges,
• \( k \) is Coulomb's constant \( (8.988 \times 10^9 \, \text{N m}^2/\text{C}^2) \),
• \( q_1 \) and \( q_2 \) are the amounts of the charges,
• \( r \) is the distance between the centers of the two charges.

So, while Coulomb’s Law provides insights on charged particle interactions in electrolysis, it complements our calculations by emphasizing the necessity for precise control over distances and charges involved.

Current and Time Conversion

In solving electrolysis problems and understanding calculations, converting units of time is often a key step. As many problems involve time presented in minutes or hours, converting to seconds ensures that units are compatible with those of the charge formula.

Let's break it down:

• The current, symbolized as \( I \), should always be in Amperes (A). Often, the current will already be in the appropriate unit as part of the problem’s parameters.
• The time, \( t \), is more commonly given in minutes. To convert minutes to seconds, simply multiply by 60. For example, 7 minutes would be converted to \( 7 \times 60 = 420 \) seconds.

Using these conversions, plug these values back into the electric charge formula \( Q = I \times t \) to calculate the charge transferred during the electrolysis process. Converting units accurately and consistently helps ensure that your charge calculations will be correct and aligned with computational standards. Thus, mastering time conversions is a simple yet critical step in electrolysis problem-solving.