Question
Learning Goal: To understand how free energy relates to equilibrium under standard and nonstandard conditions. The drive toward equilibrium is what makes a reaction spontaneous. This drive is quantified by Delta G, a state function known as free energy. A negative value of Delta G indicates a spontaneous reaction. Standard free energies of formation, Delta Gf, can be used to calculate the standard free energy of reaction, Delta Grxn o, for any given chemical equation. Standard free energy is related to the equilibrium constant K by the equation Delta G degree = -RT In K, where T is the Kelvin temperature and R is the gas constant equal to 8. 314 J/(mol K). Standard thermodynamic conditions are 1 atm and 298 K. Free energy is related to the reaction quotient Q by the equation Delta G = Delta G degree + RTlnQ, where T is the Kelvin temperature and R is the gas constant equal to 8. 314 J/(mol K). Chlorine gas, Cl2(g), reacts with nitric oxide, NO(g), to form nitrosyl chloride, NOCl(g), via the reaction Cl2(g) + 2NO(g) 2NOCl(g) The thermodynamic data for the reactants and products in the reaction are given in the following table: Substance Delta G degree t (kJ/mol) Cl2(g) 0 NO(g) 86. 71 NOCl(g) 66. 30 Using standard free energy of formation values given in the introduction, calculate the equilibrium constant Kp of the reaction Cl2(g) + 2NO(g) 2NOCl(g) The standard free energy of the reaction represents the drive the reaction has under standard conditions to move toward equilibrium from point A to point X in the diagram. Express the equilibrium constant numerically using three significant figures.
Explanation / Answer
First find delta G bydoing products - reactants delta G = 2*(66.30-86.71)= -40.82 kJ/mol, but since we are using the gas constant R which has energy units in J we need to convert delta G into J, so delta G = -40820 J/mol delta G = -RTlnK lnK = 16.48 K = e^(16.48) = 1.430x10^7
