The equilibrium constant for the reaction 3 NO (g) ⇌ N₂O (g) + NO₂ (g) at 25 °C is closest to: [ΔG° = −104.18 kJ; R = 8.314 J mol^₋₁ K⁻¹ ]

Concept:

Gibb's Free Energy:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The non-available energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

expressions for Gibb's Free energy are:

ΔG = ΔH - TΔS

dG = dq -dq rev

ΔGo = -nFE0​

ΔG = ΔGo + RTlnKc

• Gibbs free energy is denoted by ΔG and has the units J/mol.

Gibbs Free Energy and EMF of a cell:

• In a voltaic cell, the heat energy liberated during the chemical change is converted into electrical energy.
• The electrical energy produced for one equivalent of product is FE, where F = faradays constant 96500
• The electrical energy produced for 'n' equivalents is nFE.
• According to Helmholtz, the decrease in free energy of a reaction is equal to the electrical energy obtained from a galvanic cell. 

ΔGo = -nFE0​........................1

At Equilibrium, 

Eo =\({RT\over nF} lnK_c\).....................2, where Kc = Equilibrium constant Keq.

Equating Relation 1 and 2, we get:

\(ΔG^o = -nF​​​​{RT\over nF}lnK_{eq}\)

Or, ΔG° = - 2.303 RT Iog Keq

Hence, the relationship between the equilibrium constant K and Δ G is:​ 

ΔG° = - 2.303 RT Iog Keq

Calculation:

Given:

• ΔG° for the reaction 3 NO (g) ⇌ N2O (g) + NO2 (g) = −104.18 kJ = -104180Joules
• Temperature of the reaction = 25C = 298K
• Value of R = 8.314 J mol−1 K−1
• We know that: 

ΔG° = - 2.303 RT Iog Keq

• So substituting the given values in the above equation, we get:

-104180Joules​ = -2.303 × 8.314 J mol−1 K−1× 298 K ×  Iog Keq

or, Iog Keq = 18.255

or, K_eq = 1.8 × 10¹⁸.

Hence, the equilibrium constant for the reaction is Keq = 1.8 × 1018.