A reversible gaseous reaction at 450K has a reported standard Gibbs free energy change, ΔG∘, of +8.35kJ mol−1. A separate experiment monitors the same reaction mixture as it proceeds toward equilibrium at 450K, determining ΔG at several values of the reaction quotient Q. One data point of particular interest is highlighted by the researcher:
Q=0.020, ΔG=−3.26kJ mol−1
Use this information to explore the thermodynamic meaning of the graph of ΔG versus lnQ that the researcher could construct.
(1) Part 1: (a) Write the mathematical relationship that connects ΔG, ΔG∘, and Q at constant temperature and pressure. Identify the independent and dependent variables if ΔG is plotted against lnQ.
(2) Part 2: (b) Determine the numerical slope and y-intercept of the straight line that would appear on such a plot at 450K. Include units.
(3) Part 3: (c) Using the data point provided (Q=0.020, ΔG=−3.26kJ mol−1), graphically (not algebraically) locate the point where the line crosses the ΔG=0 axis. From that graphical approach, estimate the equilibrium constant K at 450K to two significant figures. Show your reasoning.
(4) Part 4: (d) A literature source gives K=1.7 for this reaction at 450K. Evaluate whether your graphically obtained K is in reasonable agreement. Discuss possible sources of discrepancy.