Problem 45 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is not correct? (a) aqueous solution of \(\mathrm{NaCl}\) is an electrolyte (b) the units of electrochemical equivalent are g. coulomb (c) in the Nernst equation, 'n' represents the number of electrons transferred in the electrode reaction (d) standard reduction potential of hydrogen electrode is zero volts

Step-by-Step Solution

Answer

The incorrect statement is option (b), as the units are g/C, not g. coulomb.

Step 1: Analyze Option (a)

An aqueous solution of \( \mathrm{NaCl} \) dissociates into \( \mathrm{Na^+} \) and \( \mathrm{Cl^-} \) ions. Therefore, it conducts electricity and is categorized as an electrolyte. Hence, option (a) is correct.

Step 2: Analyze Option (b)

The electrochemical equivalent is defined as the mass of a substance liberated at an electrode during electrolysis per unit coulomb of charge. Its units should be grams per coulomb (g/C), not g. coulomb. Thus, option (b) is incorrect.

Step 3: Analyze Option (c)

In the Nernst equation, \( n \) represents the number of electrons transferred in the overall electrode reaction. Option (c) is therefore correct.

Step 4: Analyze Option (d)

The standard reduction potential of the hydrogen electrode is defined to be zero volts by convention. This makes option (d) correct.

Key Concepts

Electrolyte

Electrolytes are substances that dissociate into ions when dissolved in a solvent, such as water, and allow the solvent to conduct electricity. When you dissolve a salt like sodium chloride (\(\mathrm{NaCl}\)) in water, it separates into positively charged sodium ions \(\mathrm{(Na^+)}\) and negatively charged chloride ions \(\mathrm{(Cl^-)}\).
This process of dissociation enables the solution to conduct electricity because ions carry the electric current.
Common examples of electrolytes include:

• Acids like hydrochloric acid (\(\mathrm{HCl}\))
• Bases like sodium hydroxide (\(\mathrm{NaOH}\))
• Salts like \(\mathrm{NaCl}\)

An electrolyte's ability to conduct electricity depends on:

• The concentration of ions in solution
• Temperature, as higher temperatures increase ion mobility
• The entire solute's dissociation in the solvent

This characteristic of electrolytes is vital in various applications, from biological systems where electrolytes regulate nerve and muscle function, to industrial processes like electroplating.

Electrochemical equivalent

The electrochemical equivalent measures how much of a substance is deposited or liberated during electrolysis per unit charge (coulomb) passed through the solution.
It is expressed in grams per coulomb (g/C). This property helps in understanding the efficiency of electrochemical processes by determining the mass of material transformed at an electrode.
This transformation is according to Faraday's laws of electrolysis:

• The mass of a substance altered at an electrode is proportional to the charge passed through the electrolyte.
• The mass of a substance altered is directly proportional to its equivalent weight.

To calculate the electrochemical equivalent \(Z\), use the equation:
\(Z = \frac{m}{Q}\)
where:

• \(m\) is the mass of the substance deposited or dissolved in grams
• \(Q\) is the total electric charge in coulombs

Understanding electrochemical equivalents is crucial in designing batteries and other energy devices to predict material usage and efficiency.

Nernst equation

The Nernst equation is a fundamental concept in electrochemistry that describes how the electromotive force (EMF) of an electrochemical cell changes with varying concentrations of reactants and products.
Mathematically, the Nernst equation is given by:
\[E = E^0 - \frac{RT}{nF} \ln \left(\frac{[products]}{[reactants]} \right)\]
where:

• \(E\) is the cell potential under non-standard conditions
• \(E^0\) is the standard cell potential
• \(R\) is the universal gas constant (8.314 J/mol·K)
• \(T\) is the temperature in Kelvin
• \(n\) is the number of moles of electrons exchanged per mole of reactant in the balanced equation
• \(F\) is the Faraday constant (96485 C/mol)

This equation indicates that the cell potential is dependent on the current concentration of ions involved in the electrochemical reaction.
The Nernst equation is crucial for:

• Calculating the potential of electrochemical cells, especially in batteries
• Understanding the direction of redox reactions
• Predicting the behavior of cells at various temperatures

These insights are particularly useful in fields such as chemistry, biochemistry, and environmental science.