Use tabulated electrode potentials to calculate ΔG∘ for the following reaction: 2Na(s)+2H2O(l)→H2(g)+2OH−(aq)+2Na+(aq)

Answer 1

From a table of standard reduction potentials:

2H₂O(l) + 2e- → H₂(g) + 2OH-(aq) .. Eº = -0.83 V (cathode - reduction)

2Na⁺(aq) + 2e- → 2Na(s) .. Eº = -2.71 V (anode - oxidation)

2Na(s) + 2H2O(l) → H2(g) + 2OH^-(aq) + 2Na+(aq) .. balanced redox equation

Eºcell = cathode - anode = -0.83 - (-2.71) = +1.88 V

∆Gº = -nFE

∆Gº = ?

n = 2 moles of electrons

F = 96485 coulombs/mol electrons

E = 1.88 V

∆Gº = - (2)(96485)(1.88)

∆Gº = - 362,783 Joules

∆Gº = -363 kJ

Answer 2

The Gibbs free energy change (ΔG) for a chemical reaction can be calculated from the standard Gibbs free energy change (ΔG∘) and the reaction quotient (Q) using the equation:

ΔG = ΔG∘ + RTlnQ

where R is the gas constant (8.314 J/K·mol), T is the temperature in kelvin, and ln is the natural logarithm.

To calculate ΔG∘ for the given reaction, we need to first write the balanced half-reactions and determine their standard electrode potentials (E∘) from a table of standard electrode potentials. Then, we can calculate the overall cell potential (E∘cell) and use it to calculate ΔG∘.

The balanced half-reactions are:

2H2O(l) + 2e^- → H2(g) + 2OH^-(aq) E∘ = -0.83 V

2Na+(aq) + 2e^- → 2Na(s) E∘ = -2.71 V

The overall reaction is obtained by adding these two half-reactions together and canceling out the electrons:

2Na(s) + 2H2O(l) → H2(g) + 2OH^-(aq) + 2Na+(aq)

The overall cell potential (E∘cell) can be calculated by subtracting the standard electrode potential of the anode (2Na(s) → 2Na+(aq) + 2e^-) from the standard electrode potential of the cathode (2H2O(l) + 2e^- → H2(g) + 2OH^-(aq)):

E∘cell = E∘cathode - E∘anode = (-0.83 V) - (-2.71 V) = 1.88 V

The reaction quotient (Q) can be calculated from the concentrations of the reactants and products:

Q = [OH^-]^2[N a+]^2/[H2O]^2

Since the reaction involves pure solids and pure liquid, their concentrations remain constant and do not affect the value of Q. Therefore, we can simplify the expression as:

Q = [OH^-]^2[N a+]^2

From the balanced equation, we can see that the concentrations of OH^- and Na+ are equal, so we can substitute [OH^-] = [Na+] into the equation:

Q = [Na+]^4

The standard Gibbs free energy change (ΔG∘) can be calculated from the standard cell potential (E∘cell) using the equation:

ΔG∘ = -nFE∘cell

where n is the number of electrons transferred in the balanced equation, and F is the Faraday constant (96,485 C/mol).

Since two electrons are transferred in this reaction, we have:

ΔG∘ = -2(96,485 C/mol)(1.88 V) = -365,052 J/mol

Therefore, the standard Gibbs free energy change for the given reaction is -365,052 J/mol.