A modified Frost diagram for a transition metal M plots the product nE^ (where E^ is the standard reduction potential from oxidation state +n to 0 ) against the oxidation state n . The coordinates (n, nE^ ) for the +2 and +3 oxidation states are given as (2, -0.88 V ) and (3, -0.11 V ) respectively. The standard electrode potential for the M³⁺/M²⁺ half-cell in Volts is:

Step-by-step solution

The standard Gibbs free energy change for the reduction to the metal is given by G^ = -nFE^ . From the given coordinates, the value of nE^ directly gives us the free energy term without needing to multiply by n again. For the +2 state: M²⁺ + 2e⁻ M G^ ₁ = -F(nE^ _ M²⁺/M ) = -F(-0.88) = 0.88F For the +3 state: M³⁺ + 3e⁻ M G^ ₂ = -F(nE^ _ M³⁺/M ) = -F(-0.11) = 0.11F The required half-reaction is: M³⁺ + e⁻ M²⁺ This reaction is obtained by subtracting the first reaction from the second reaction: G^ ₃ = G^ ₂ - G^ ₁ G^ ₃