17.10
Free Energy and Equilibrium
The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the proce…
Both the equilibrium constant and the standard free energy change can be used to determine whether a reaction is product or reactant favored.
For any reaction mixture composition, the ΔG for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient.
When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So the standard free energy change equals −RT ln K.
If ΔG naught is less than zero, ln K is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the more negative the free energy.
Take, for example, the breakdown of dinitrogen tetroxide at 298 kelvin, in which K is 1.34 × 1017.
Substituting the known values into the equation, the standard free energy for the reaction equals −98 kJ/mole, and product formation is favored.
Conversely, if ΔG naught is greater than zero, ln K is negative, meaning K is less than 1 and the reverse direction of the reaction is favored.
Consider the breakdown of sulfur trioxide gas at 298 kelvin, which has a ΔG naught of 141.6 kJ/mole.
The equation can be rearranged so ln K equals negative ΔG over RT.
Substituting the known values into the equation, and raising e to the power of the result, K is very small—indicating that the reactant is favored.
Notably, if the temperature varies, the equilibrium constant will also change.
The temperature dependence of the equilibrium constant can be derived from the equation that directly relates K to the ΔG naught for the reaction.
The ΔG naught can be replaced by the standard enthalpy minus temperature times the standard entropy. Dividing both sides by negative RT yields ln K equals negative ΔH over RT plus ΔS over R.
This equation is in the form of a straight line where the natural log of K can be plotted against the inverse of the temperature in kelvins with a slope of negative ΔH over R and a y-intercept of ΔS over R.
If the values of K are measured at two slightly different temperatures, then this graph can also be used to calculate the change in enthalpy, assuming it remains constant over a limited temperature range.
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Q1: How does the equilibrium constant relate to standard free energy change?
The standard free energy change equals negative RT times the natural logarithm of the equilibrium constant. When ΔG° is negative, the equilibrium constant is greater than 1, favoring product formation. Conversely, when ΔG° is positive, K is less than 1, favoring reactants. This relationship allows you to predict reaction favorability from either thermodynamic property.
Q2: What does a negative free energy change indicate about a reaction?
A negative ΔG represents a driving force for the process in the forward direction, indicating the reaction is spontaneous and product-favored at equilibrium. The more negative the free energy, the larger the equilibrium constant and the greater the tendency for reactants to convert to products. This thermodynamic property predicts whether a reaction will proceed spontaneously under given conditions.
Q3: How does temperature affect the equilibrium constant?
Temperature changes alter the equilibrium constant according to the relationship ln K equals negative ΔH over RT plus ΔS over R. Plotting the natural log of K against inverse temperature yields a straight line with slope negative ΔH over R and y-intercept ΔS over R. This temperature dependence allows calculation of enthalpy changes from equilibrium data measured at two different temperatures.
Q4: What is the relationship between the reaction quotient and equilibrium?
The reaction quotient Q measures the current ratio of products to reactants. When Q is less than the equilibrium constant K, the reaction proceeds forward until equilibrium is reached and Q equals K. When Q exceeds K, the reaction shifts in reverse. At equilibrium, Q equals K and the free energy change is zero, meaning forward and reverse driving forces are equal.
Q5: How is free energy change calculated for nonstandard conditions?
The free energy change under nonstandard conditions is calculated as ΔG equals ΔG° plus RT times the natural log of Q, where Q is the reaction quotient. This equation applies to reactants and products at pressures other than 1 bar or concentrations other than 1 M. It allows prediction of reaction spontaneity under any given set of conditions by comparing actual conditions to standard states.
Q6: What does it mean when ΔG° equals zero at equilibrium?
When ΔG° equals zero, the system is at equilibrium with reactants and products comparably abundant. The equilibrium constant K equals 1, and the forward and reverse reaction rates are equal. At this point, the reaction quotient Q equals the equilibrium constant, and there is no net driving force for the reaction to proceed in either direction.
Q7: Why is the Van't Hoff equation useful for analyzing equilibrium data?
The Van't Hoff equation, expressed as ln K equals negative ΔH over RT plus ΔS over R, creates a linear relationship between ln K and inverse temperature. This straight-line form enables graphical determination of enthalpy and entropy changes from experimental equilibrium constants measured at different temperatures, assuming enthalpy remains constant over the limited temperature range studied.