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Calculate The Cell Potential for The Following Reaction Cr Sn

Reviewed by Calculator Editorial Team

This calculator helps you determine the cell potential for the Cr-Sn reaction using the Nernst equation. The cell potential is a measure of the electrical energy produced by a galvanic cell, which depends on the standard reduction potentials of the half-reactions and the concentrations of the species involved.

Introduction

The cell potential (or electromotive force) of a galvanic cell is a measure of the electrical energy produced by the cell. For the Cr-Sn reaction, we can calculate the cell potential using the Nernst equation, which takes into account the standard reduction potentials of the half-reactions and the concentrations of the species involved.

The reaction can be written as:

Cr(s) + Sn2+(aq) → Cr3+(aq) + Sn(s)

This reaction involves the reduction of chromium(III) ions to chromium metal and the oxidation of tin metal to tin(II) ions.

How to Calculate Cell Potential

The Nernst equation allows us to calculate the cell potential under non-standard conditions. The general form of the Nernst equation is:

Ecell = E°cell - (RT/nF) * ln(Q)

Where:

  • Ecell = cell potential under non-standard conditions (V)
  • E°cell = standard cell potential (V)
  • R = gas constant (8.314 J/mol·K)
  • T = temperature (K)
  • n = number of electrons transferred
  • F = Faraday's constant (96,485 C/mol)
  • Q = reaction quotient

For the Cr-Sn reaction, we need to know the standard reduction potentials of the half-reactions and the concentrations of the species involved.

Standard Reduction Potentials

The standard reduction potentials (E°) are the potentials measured under standard conditions (1 M concentrations, 298 K, 1 atm pressure). For the Cr-Sn reaction, the half-reactions are:

Reduction half-reaction: Cr3+(aq) + 3e- → Cr(s)

E° = -0.74 V

Oxidation half-reaction: Sn(s) → Sn2+(aq) + 2e-

E° = -0.14 V

The standard cell potential (E°cell) is calculated as the difference between the standard reduction potentials of the half-reactions:

E°cell = E°cathode - E°anode

E°cell = (-0.74 V) - (-0.14 V) = -0.60 V

Example Calculation

Let's calculate the cell potential for the Cr-Sn reaction with the following conditions:

  • Initial concentration of Cr3+: 0.1 M
  • Initial concentration of Sn2+: 0.1 M
  • Temperature: 298 K

The reaction quotient (Q) is given by:

Q = [Cr3+][Sn2+]

Q = (0.1)(0.1) = 0.01

Using the Nernst equation:

Ecell = E°cell - (RT/nF) * ln(Q)

Ecell = -0.60 V - [(8.314 J/mol·K)(298 K)/(3 mol)(96,485 C/mol)] * ln(0.01)

Ecell ≈ -0.60 V - 0.0592 V * (-2)

Ecell ≈ -0.60 V + 0.1184 V ≈ -0.4816 V

The calculated cell potential is approximately -0.4816 V.

Interpreting Results

The negative sign indicates that the reaction is non-spontaneous under standard conditions. However, under non-standard conditions (with different concentrations), the reaction may become spontaneous if the cell potential becomes positive.

Key points to consider:

  • The cell potential depends on the concentrations of the species involved.
  • A positive cell potential indicates a spontaneous reaction.
  • A negative cell potential indicates a non-spontaneous reaction.
  • The temperature affects the cell potential through the RT term in the Nernst equation.

FAQ

What is the difference between standard and non-standard cell potential?

The standard cell potential (E°cell) is measured under standard conditions (1 M concentrations, 298 K, 1 atm pressure). The non-standard cell potential (Ecell) is calculated using the Nernst equation and takes into account the actual concentrations of the species involved.

How does temperature affect the cell potential?

Temperature affects the cell potential through the RT term in the Nernst equation. As temperature increases, the term RT increases, which can make the cell potential more positive or negative depending on the reaction.

What is the significance of a negative cell potential?

A negative cell potential indicates that the reaction is non-spontaneous under the given conditions. This means that energy must be supplied to the system for the reaction to proceed.