Problem 87 - A Complete Resource Book in Chemistry for JEE Main

Question

By passing \(0.50\) ampere current in an aqueous solution \(0.5 \mathrm{~g}\) of an element (Eq. wt = 96.5) is liberated. The time of passing current in seconds is (a) \(100 \mathrm{~s}\) (b) \(500 \mathrm{~s}\) (c) \(1000 \mathrm{~s}\) (d) \(2000 \mathrm{~s}\)

Step-by-Step Solution

Answer

The time of passing current is 1000 seconds (option c).

Step 1: Understand the relationship

We know that the mass (in grams) of an element liberated during electrolysis is proportional to the product of the current (in amperes), the time (in seconds), and the equivalent weight of the element, divided by the Faraday's constant. This is expressed by the formula: \[ m = \frac{I \times t \times \, \text{Eq. wt.}}{F} \] where \( m \) is the mass of the element liberated, \( I \) is the current, \( t \) is the time, and \( F \) is the Faraday's constant (approximately \( 96500 \) C/mol).

Step 2: Plug in given values

From the problem, we have the following values:- Current (\(I\)) is \(0.50\) A- Mass (\(m\)) is \(0.5\) g - Equivalent weight is \(96.5\)We want to solve for the time \(t\) in seconds. The Faraday's constant \(F\) is \(96500\) C/mol. Plug these into the formula:\[ 0.5 = \frac{0.50 \times t \times 96.5}{96500} \]

Step 3: Solve for time

Rearrange the formula to solve for \(t\):\[ t = \frac{0.5 \times 96500}{0.50 \times 96.5} \]Calculate \( t \):\[ t = \frac{0.5 \times 96500}{48.25} = 1000 \text{ seconds} \]

Step 4: Verify correct option

The calculated time is \(1000\) seconds. Check the available options, which are:(a) 100 s (b) 500 s (c) 1000 s (d) 2000 sThe correct option is \(\text{(c) } 1000\text{ s}\).

Key Concepts

Faraday's constant

Faraday's constant plays a crucial role in electrochemistry, particularly in calculations involving electrolysis. It represents the amount of electric charge carried by one mole of electrons. This constant is denoted by the letter "F" and has an approximate value of \( 96500 \) coulombs per mole (C/mol).
This value is fundamental when calculating how substances react to electric current. Essentially, it allows us to quantify the relationship between electric charge and the number of moles of electrons involved.

• One mole of electrons carries \( 96500 \) C of charge.
• It is used to bridge the gap between the macroscopic quantities (current and time) and microscopic quantities (electrons and chemical changes).

When you perform electrolysis, Faraday's constant helps determine how much of a substance will be produced at an electrode based on the current supplied and the duration. It shows us that the amount of substance can be directly linked to the energy supplied via the current.

Equivalent weight

Equivalent weight is a vital concept used in electrolysis calculations to express the reactive capacity of an element. It is defined as the mass of the element that reacts with or displaces 1 mole of hydrogen ions.
In the context of electrolysis, it tells us how much of the element will be produced at an electrode per mole of electrons provided. The equivalent weight is essential because it allows for the application of Faraday's laws of electrolysis in a practical manner.

• Equivalent weight simplifies the calculation of substance amounts in reactions.
• It is calculated based on the element's chemical equivalents.
• For metallic elements, equivalent weight can be found by dividing the atomic weight by the element's valency (number of electrons involved in the exchange).

Therefore, during electrolysis, knowing the equivalent weight helps in predicting the mass of an element that can be liberated for a given amount of electric charge.

Current and time relationship in electrolysis

In electrolysis, the relationship between current, time, and the amount of substance liberated is key to understanding how electrochemical cells operate. The mass of a substance produced at an electrode is directly proportional to both the electric current applied and the duration for which it is applied.
This concept is encapsulated by Faraday's first law of electrolysis, which mathematically is expressed as \[ m = \frac{I \times t \times \text{Eq. wt.}}{F} \]

• "m" stands for mass of the substance liberated.
• "I" represents current in amperes.
• "t" denotes time in seconds.
• "Eq. wt." is the equivalent weight of the element.
• "F" is Faraday's constant.

From this equation, you can see that increasing the current or the time results in a larger quantity of the substance being produced. Essentially, if you apply more current or extend the time, more electrons are moved and, thus, more of the element can be deposited. This relationship provides a practical way to control the amount of element deposited at the electrodes during electrolysis.