One of the most obvious ways to tell that a chemical reaction has occurred, as we all know, is that the color of 'stuff' changes. Ligand exchange reactions are one class of reactions where this is very evident, as exemplified by the color change of a green Ni(H2O)62+ solution to the yellow-green of a NiCl64- solution with the substitution of H2O ligands for Cl- ligands.

Ni(H2O)62+ (aq) + 6 Cl- (aq) equilibrium arrow NiCl64- (aq) + 6 H2O (l)

The equilibrium constant for this reaction is 1.0 x 109. Calculate the change in Gibbs free energy for the reaction at 400 K in kJ mol-1. (Note R = 8.314 J mol-1 K-1)

3 answers

delta G = -RT*lnK

nkllj;

To calculate the change in Gibbs free energy for a reaction using the equilibrium constant, you can use the equation:

ΔG = -RT ln(K)

where ΔG is the change in Gibbs free energy, R is the gas constant (8.314 J mol-1 K-1), T is the temperature in Kelvin, and K is the equilibrium constant.

In this case, the equilibrium constant for the reaction is given as K = 1.0 x 10^9.

To convert the temperature from Celsius to Kelvin, you need to add 273.15 to the temperature. In this case, the temperature is given as 400 K, so no conversion is needed.

Now, let's substitute the values into the equation and solve for ΔG:

ΔG = -(8.314 J mol-1 K-1)(400 K) ln(1.0 x 10^9)

First, let's simplify the equation inside the parentheses:

ln(1.0 x 10^9) = ln(1.0) + ln(10^9)
= 0 + 9ln(10)
= 9(2.303)
= 20.727

Now, substitute the values:

ΔG = -(8.314 J mol-1 K-1)(400 K)(20.727)

Now, multiply the numbers:

ΔG = -66,672.864 J mol-1

To convert J to kJ (kilojoules), divide the result by 1000:

ΔG = -66,672.864 J mol-1 / 1000
= -66.672864 kJ mol-1

So, the change in Gibbs free energy for the reaction at 400 K is approximately -66.67 kJ mol-1.