When Cl2 is dissolved in water , it disproportionate producing chlorid...
Introduction
When Cl2 is dissolved in water, it undergoes disproportionation producing chloride ions and HClO. The potential for the disproportionation changes from a negative value to a positive value at a certain hydronium ion concentration. This concentration can be calculated using the given standard electrode potentials.
Calculating the Equilibrium Constant
The disproportionation reaction of Cl2 is given by:
Cl2 + H2O ⇌ HClO + Cl-
The standard electrode potentials of the half-reactions involved are given as:
E(standard) (Cl2|Cl- ) = 1.36V
E(standard) (HClO2|Cl2) = 1.63V
Using these values, we can calculate the standard potential for the overall reaction:
E(standard) (HClO|Cl- ) = E(standard) (HClO2|Cl2) - E(standard) (Cl2|Cl- )
E(standard) (HClO|Cl- ) = 1.63V - 1.36V
E(standard) (HClO|Cl- ) = 0.27V
The standard potential for the overall reaction can be related to the equilibrium constant (K) using the Nernst equation:
E = E(standard) - (RT/nF)lnK
At 25°C, R = 8.314 J/mol·K, T = 298 K, n = 2 (number of electrons transferred), and F = 96,485 C/mol. Therefore, the equation becomes:
E = 0.27V - (RT/2F)lnK
Calculating the Hydronium Ion Concentration
The potential for the disproportionation changes from a negative value to a positive value when the equilibrium constant (K) is equal to 1. This occurs when the concentration of H3O+ ions reaches a certain value. To calculate this value, we can rearrange the equation above to solve for the hydronium ion concentration ([H3O+]):
lnK = (2F/RT)(E(standard) - E) + ln[H3O+]
ln(1) = (2F/RT)(0.27V - E) + ln[H3O+]
0 = (2F/RT)(0.27V - E) + ln[H3O+]
[H3O+] = e^(-(2F/RT)(0.27V - E))
Substituting the given values, we get:
[H3O+] = e^(-(2 × 96,485 C/mol)/(8.314 J/mol·K × 298 K) × (0.27V - E))
When the potential for the disproportionation changes from a negative value to a positive value, E = 0. Therefore, the hydronium ion concentration at this point is:
[H3O+] = e^(-(2 × 96,485 C/mol)/(8.314 J/mol·K × 298 K) × (0.27V - 0))
[H3O+] = 1.16 × 10^-4 M
Conclusion
The hydronium ion concentration at which the potential for the disproportionation of Cl