3. A calibration curve plotting E vs. pNi is used to measure the concentration of Ni2+ in solution at 25 °C using a solid Ni electrode. What is the slope of the calibration curve?

the slope of the calibration curve is - 0.0295

Explanation:

as things are not under standard conditions that is;  1M of each reactants at T = 25°C and P = 1 atm; therefore we will use the Nernst Equation.

E = a × pNi + b

a is the slope

pNi = -log [Ni²⁺] = log 1/[Ni²⁺]

therefore the Half reaction;

Ni²⁺ (aq) + 2e⁻ = Ni (s)

here; E = E₀ + RT/zF ln[Ni²⁺]

we know that;

gas constant R = (8.31 J/mol-K)

absolute temperature T =25°C =  298 K

number of moles of electrons transferred by the cell's reaction z  = 2

F is Faraday constant, = 9.64853399(24)×10⁴ C mol−1

E₀ = b

RT/zF ln[Ni²⁺] = alog 1/[Ni²⁺]

Logx = Ln x / Ln 10 = Ln (x/2.3)

so

a = (RT/zF ln[Ni²⁺])/log 1/[Ni²⁺]

= (RT/zF ln[Ni²⁺]) / ((ln 1/[Ni²⁺]) / 2.3)  

= (2.3RT/zF ln[Ni²⁺]) / (ln 1/[Ni²⁺])

= (2.3RT/zF ln[Ni²⁺]) / (-ln [Ni²⁺])

= -2.3RT/zF

so we substitute

= (-2.3 × 8.31 ×298 ) / (2 × 9.64853399(24) × 10⁴)

= - 0.0295

therefore the slope of the calibration curve is - 0.0295