Voltage of the cell Pt,H2(1atm)|HOCN(1.3*10power(-3)M)||Ag+(0.8M)|Ag(s) is 0.982 V.Calculate disociation constant of HOCN.Neglect [H+] decause of oxidation of H2(g) standard reduction potential of Ag+|Ag=0.8 V

To find the dissociation constant of HOCN given the cell voltage and the standard reduction potential, we can use the Nernst equation and some principles of electrochemistry. Let's break this down step by step.

Understanding the Cell Reaction

The cell you've described consists of two half-cells: one involving the reduction of silver ions (Ag⁺) to silver (Ag), and the other involving the oxidation of hydrogen gas (H₂) and the dissociation of HOCN. The overall cell reaction can be represented as:

• Oxidation: H₂ → 2H⁺ + 2e^-
• Reduction: Ag⁺ + e^- → Ag

Cell Voltage and Nernst Equation

The standard cell potential (E_cell) is given as 0.982 V. The standard reduction potential for the Ag⁺/Ag half-cell is 0.8 V. We can use the Nernst equation to relate the cell potential to the concentrations of the reactants and products:

The Nernst equation is:

E = E_° - (RT/nF) * ln(Q)

Where:

• E = cell potential
• E_° = standard cell potential
• R = universal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin (assume 298 K unless stated otherwise)
• n = number of moles of electrons transferred (2 for this reaction)
• F = Faraday's constant (96485 C/mol)
• Q = reaction quotient

Calculating the Reaction Quotient (Q)

For the reaction, the reaction quotient Q can be expressed in terms of the concentrations of the species involved:

Q = [H⁺]² / [HOCN]

Since we are neglecting [H⁺] due to the oxidation of H₂, we can assume that the concentration of H⁺ is very low compared to the concentration of HOCN. Thus, we can simplify our calculations.

Finding the Standard Cell Potential (E_°)

We can calculate the standard cell potential using the half-cell potentials:

E_° = E_Ag - E_H2

Given that E_Ag = 0.8 V and E_H2 = 0 V (standard hydrogen electrode), we have:

E_° = 0.8 V - 0 V = 0.8 V

Substituting into the Nernst Equation

Now we can substitute the known values into the Nernst equation:

0.982 V = 0.8 V - (8.314 J/(mol·K) * 298 K / (2 * 96485 C/mol)) * ln(Q)

Calculating the term involving R, T, n, and F:

(8.314 * 298) / (2 * 96485) ≈ 0.0041 V

Now, rearranging the equation gives:

0.982 V - 0.8 V = -0.0041 * ln(Q)

0.182 V = -0.0041 * ln(Q)

ln(Q) = -0.182 V / -0.0041 V ≈ 44.39

Q = e^44.39

Calculating the Dissociation Constant (K_a)

The dissociation constant K_a for HOCN can be related to Q as follows:

K_a = [H⁺]² / [HOCN]

Assuming that the concentration of H⁺ is negligible, we can express K_a in terms of Q. Since Q is a function of the concentrations at equilibrium, we can approximate K_a as:

K_a ≈ Q = e^44.39

Final Calculation

Calculating e^44.39 gives us a very large value for K_a, indicating that HOCN dissociates significantly in solution. This suggests that HOCN is a weak acid, but it has a relatively high dissociation constant compared to many weak acids.

In summary, the dissociation constant of HOCN can be calculated using the cell voltage and the standard reduction potential, leading us to a significant value that reflects its behavior in solution.