Introduction:
The oxidation potential of a hydrogen gas electrode can be determined based on the conditions under which it is prepared and operated. In this case, the electrode is made by dipping a platinum wire in a solution of hydrochloric acid (HCl) with a pH of 10 and passing hydrogen gas around the platinum wire at one atmospheric pressure.

Determination of Oxidation Potential:
The oxidation potential of the electrode can be calculated using the Nernst equation, which relates the concentration of the species involved in the redox reaction to the electrode potential. The Nernst equation is given as:

E = E° - (0.0592/n) * log(Q)

Where:
E = Electrode potential
E° = Standard electrode potential
n = Number of electrons transferred in the redox reaction
Q = Reaction quotient

Standard Electrode Potential:
The standard electrode potential for the hydrogen gas electrode is known to be 0.00V. This means that under standard conditions, the hydrogen gas electrode is neither oxidized nor reduced.

Reaction Quotient:
In this case, the reaction taking place at the hydrogen gas electrode can be represented as follows:

2H⁺ + 2e⁻ → H₂

The reaction quotient (Q) for this reaction can be expressed as the ratio of the product of the hydrogen ion concentration ([H⁺]) to the square of the hydrogen gas pressure (P(H₂)):

Q = [H⁺]² / P(H₂)²

Calculation:
Given that the pH of the HCl solution is 10, we can determine the hydrogen ion concentration using the equation:

pH = -log[H⁺]

[H⁺] = 10^(-pH)

[H⁺] = 10^(-10)

[H⁺] = 1 x 10^(-10) M

Since the hydrogen gas pressure is given as one atmosphere, we can substitute the values of [H⁺] and P(H₂) into the reaction quotient equation:

Q = (1 x 10^(-10))² / (1 atm)²

Q = 1 x 10^(-20) atm⁻²

Substituting the Values:
Substituting the values of E°, n, and Q into the Nernst equation, we can calculate the oxidation potential (E):

E = 0.00V - (0.0592/2) * log(1 x 10^(-20))

E = 0.00V - (0.0296) * (-20)

E = 0.00V + 0.592V

Answer:
Therefore, the oxidation potential of the hydrogen gas electrode under the given conditions is 0.592V.

Explanation:
The oxidation potential of the electrode is determined by the concentration of hydrogen ions and the pressure of hydrogen gas. In this case, the low concentration of hydrogen ions (resulting from the high pH) and the one atmospheric pressure of hydrogen gas contribute to a positive oxidation potential. The calculated value of 0.592V indicates that the hydrogen gas electrode has a tendency to undergo oxidation under these conditions.

A) 10×.059= .59