Nernst Equation MCQ Quiz - Objective Question with Answer for Nernst Equation - Download Free PDF

CONCEPT:

Nernst Equation

E_cell = E^o_cell − (0.059/n) log(Q)

• The cell potential under non-standard conditions is calculated using the Nernst equation:
• Where:
  • E_cell = Cell potential at non-standard conditions
  • E^o_cell = Standard cell potential
  • n = Number of moles of electrons transferred in the reaction
  • Q = Reaction quotient, given by the ratio of the concentrations of products to reactants raised to the power of their stoichiometric coefficients.

EXPLANATION:

• For the reaction:

  Ni(s) + 2Ag⁺(aq) → Ni²⁺(aq) + 2Ag(s)

  • n = 2 (number of electrons transferred)
  • Reaction quotient (Q):

    Q = [Ni²⁺]/([Ag⁺]²)

    Q = 0.160 / (0.001)² = 0.160 / 0.000001 = 160,000

• Using the Nernst equation:

  E_cell = E^o_cell − (0.059/2) log(Q)

  E_cell = 1.05 − (0.059/2) log(160,000)

  E_cell = 1.05 − 0.0295 × log(160,000)

  E_cell = 1.05 − 0.0295 × 5.204 (log of 160,000)

  E_cell = 1.05 − 0.1536

  E_cell = 0.89 V

Therefore, the calculated cell emf is approximately 0.90 V.

CONCEPT:

Nernst Equation for Cell Potential Calculation

• The Nernst equation is used to calculate the cell potential under non-standard conditions.
• The equation relates the standard electrode potential to the actual potential based on the concentrations of the reactants and products.
• The Nernst equation is given as:
  • Where is the actual cell potential, is the standard cell potential, n is the number of electrons transferred, and Q is the reaction quotient.

CALCULATION:

• For the reaction:
• Given:
  • Standard reduction potential of
  • Standard reduction potential of 
• Using the Nernst equation for a reaction where :
• Hence, the ratio .

The ratio of  for which  is approximately .

Correct answer: 2)

concept:

• Electrode Potential: The potential difference which facilitates the flow of electrons between two phases is called electrode potential.
• Depending on whether oxidation or reduction has occurred, the electrode potential will be designated as an oxidation or reduction potential.
• The greater the value of electrode potential, the greater is the tendency to react.
• The electrode potential at any concentration measured with respect to the standard electrode can be given by the Nernst equation

​EXPLANATION:

• ​The given equation is Nernst equation.
• Here is the cell potential at the given concentration.
• Log [Mg2+] is the logarithm of the concentration of ion Mg2+.
• They are directly proportional to each other because increase in concentration increases the cell potential.
• The given equation is equivalent to the equation of the straight line y = = mx + c. Therefore the graph will be a straight line with a y-intercept and a positive slope of 0.059/2.
• The equation is arranged in the form y = mx+c.

conclusion:

Thus, the graph of  vs log [Mg2+] is given in option 2.

CONCEPT:

Intensive and Extensive Properties

• Intensive properties are those that do not depend on the amount of matter or the size of the system. Examples include temperature, density, and cell potential (E_cell).
• Extensive properties are those that do depend on the amount of matter or the size of the system. Examples include mass, volume, and Gibbs free energy change (∆rG) of the cell reaction.

EXPLANATION:

• The cell potential (E_cell) is an intensive property because it is a measure of the potential difference between two electrodes, and it does not depend on the amount of material in the system.
• The Gibbs free energy change (∆rG) of the cell reaction is an extensive property because it depends on the amount of reactants and products in the reaction.

Therefore, the correct statement is: E_cell is an intensive property while ∆rG of cell reaction is an extensive property.

Correct answer: 2)

concept:

• Electrode Potential: The potential difference which facilitates the flow of electrons between two phases is called electrode potential.
• Depending on whether oxidation or reduction has occurred, the electrode potential will be designated as an oxidation or reduction potential.
• The greater the value of electrode potential, the greater is the tendency to react.
• The electrode potential at any concentration measured with respect to the standard electrode can be given by the Nernst equation

​EXPLANATION:

• ​The given equation is Nernst equation.
• Here is the cell potential at the given concentration.
• Log [Mg2+] is the logarithm of the concentration of ion Mg2+.
• They are directly proportional to each other because increase in concentration increases the cell potential.
• The given equation is equivalent to the equation of the straight line y = = mx + c. Therefore the graph will be a straight line with a y-intercept and a positive slope of 0.059/2.
• The equation is arranged in the form y = mx+c.

conclusion:

Thus, the graph of  vs log [Mg2+] is given in option 2.

CONCEPT:

Nernst Equation

E_cell = E^o_cell − (0.059/n) log(Q)

• The cell potential under non-standard conditions is calculated using the Nernst equation:
• Where:
  • E_cell = Cell potential at non-standard conditions
  • E^o_cell = Standard cell potential
  • n = Number of moles of electrons transferred in the reaction
  • Q = Reaction quotient, given by the ratio of the concentrations of products to reactants raised to the power of their stoichiometric coefficients.

EXPLANATION:

• For the reaction:

  Ni(s) + 2Ag⁺(aq) → Ni²⁺(aq) + 2Ag(s)

  • n = 2 (number of electrons transferred)
  • Reaction quotient (Q):

    Q = [Ni²⁺]/([Ag⁺]²)

    Q = 0.160 / (0.001)² = 0.160 / 0.000001 = 160,000

• Using the Nernst equation:

  E_cell = E^o_cell − (0.059/2) log(Q)

  E_cell = 1.05 − (0.059/2) log(160,000)

  E_cell = 1.05 − 0.0295 × log(160,000)

  E_cell = 1.05 − 0.0295 × 5.204 (log of 160,000)

  E_cell = 1.05 − 0.1536

  E_cell = 0.89 V

Therefore, the calculated cell emf is approximately 0.90 V.

Concept:

The electromotive force (e.m.f.) of a galvanic cell depends on the concentration of the ions involved in the redox reactions. This relationship is given by the Nernst equation, which adjusts the standard electrode potentials based on ion concentrations.

Nernst equation:

 or

At Room temperature(T = 298K), Equation becomes:

Explanation:

The standard cell potential (E_cell) for a zinc-copper galvanic cell can be calculated using the standard reduction potentials and the Nernst equation:

1. Standard reduction potentials at 25°C are:

• Zn²⁺ + 2e^– → Zn: E° = -0.76 V
• Cu²⁺ + 2e^– → Cu: E° = +0.34 V

The standard e.m.f. (E°) for cell I is given by:
E°_cell = E°_cathode - E°_anode
E°_I = 0.34 V - (-0.76 V) = 1.10 V

Using the Nernst equation for different ion concentrations:

Where Q is the reaction quotient:

• For cell II: Q = =
• For cell III: Q = =

Considering the effect of ion concentration:

• Cell II:   ≈ 1.13 V

• Cell III: = ≈ 1.07 V

Thus, the e.m.f. values are in the order E₂ > E₁ > E₃.

Conclusion:

Based on the Nernst equation and given conditions, the true statement is: E₂ > E₁ > E₃

The correct answer is BB'

Concept:-

• The Nernst equation is an important relation in the field of electrochemistry that is used to calculate the potential of an electrochemical reaction (also known as a half-cell or a full-cell reaction). It establishes the relationship between electric potential (or electromotive force, E) and the concentrations of reactants and products. Named after Walther Nernst, a German scientist, the equation is given by:
• E = E° - (RT/nF) x lnQ

where,

E is the cell potential (E_cell) or emf of the cell at non-standard conditions (the conditions you are working with)

E° is the standard cell potential or standard emf of the cell (at standard conditions: 25°C, 1M concentrations for all particles, 1atm pressure for all gases)

R is the gas constant, which equals 8.314 J/(mol-K)

T is the absolute temperature in Kelvin (Kelvin = degrees Celsius + 273.15)

n is the number of moles of electrons (e-) transferred in the balanced redox reaction

F is Faraday’s constant, the amount of electric charge in one mole of electrons, approximately 96485 C/mol (Coulombs per mole)

Q is the reaction quotient, essentially equal to the concentration ratio of the products divided by reactants. It becomes the equilibrium constant (K) when the system is at equilibrium.

• An important note is that the term RT/nF is often replaced with 0.0592/n at room temperature (25°C) when E is measured in volts, yielding a simplified form of the Nernst equation:
• E = E° - (0.0592/n) x logQ
• This equation gives you the voltage that will actually be measured in a real-world cell, taking into account the non-standard conditions that often prevail (such as the non-ideal temperature, and concentrations or pressures).

Explanation:-.

According to the formula of the nernst equation, 

E_cell = E^o_cell - (0.059/ncell ) × log m

This equation is a linear curve, as we can see from the graph. So rewriting it in the form of an equation of line. 

Y = mx + c

Where, y = E_{cell ,} m = 0.059/n_cell and c = E^o_cell 

So, we find that E^o_cell is the intercept of the graph which is BB'. 

Ans. BB' is the correct value of E^o_cell.