CHEM1B:  From Kinetics to Thermodynamics

A student wishes to determine all the standard thermodynamic parameters for the reaction

Ag⁺(aq) + Fe²⁺(aq) ⇄ Ag(s) + Fe³⁺(aq)

 

From literature she obtains the following data:

 

Species	DHfo kJ mol-1	So J K-1	DGfo kJ mol-1
Ag+(aq)		73.45	77.11
Fe2+(aq)	-87.9	-113.4	-84.94
Ag(s)		42.6
Fe3+(aq)	-47.69

To complete the values in this table, she performs a series of kinetic measurements measuring the initial rates for both the forward and reverse reactions individually.  The data obtained for the forward reaction are:

 

Table 1.  Summary of measured initial-rate kinetic data for Ag⁺(aq) + Fe²⁺(aq) ® products

 

Reaction	Temp. oC	[Ag+] M	[Fe2+] M	Initial Rate M s-1
Ag+(aq) + Fe2+(aq) ® products	10.0	0.10	0.10	1.20 x 10-5
	20.0	0.10	0.10	5.13 x 10-5
	25.0	0.10	0.10	1.02 x 10-4
	25.0	0.10	0.20	2.04 x 10-4
	25.0	0.20	0.20	4.08 x 10-4
	30.0	0.10	0.10	1.99 x 10-4
	40.0	0.10	0.10	7.05 x 10-4
	50.0	0.10	0.10	2.31 x 10-3

 

Similarly, she measures the equivalent set of kinetic data for the reverse reaction:

 

Table 2:  Summary of measured initial-rate kinetic data for Ag(s) + Fe³⁺(aq) ® products

 

Reaction	Temp. oC	[Fe3+] M	Initial Rate M s-1
Ag(s) + Fe3+(aq) ® products	10.0	0.10	9.80 x 10-6
	20.0	0.10	1.08 x 10-4
	25.0	0.10	3.37 x 10-4
	25.0	0.20	6.74 x 10-4
	30.0	0.10	1.02 x 10-3
	40.0	0.10	8.27 x 10-3
	50.0	0.10	5.92 x 10-2

 

From these initial rate data perform the following calculations and include all values in your report:

 

• Determine the reaction order for each species in both the forward and reverse reactions (you can assume that the order for Ag(s) is one).

 

Order for Ag⁺ = ___ Order for Fe²⁺ = ___ Order for Fe³⁺ = ___

• Assuming that the reaction order remains the same, calculate the individual rate constants for both the forward and reverse reactions at each temperature.  Remember that for the general reaction A + B ®products

we have Rate = k[A]^m[B]ⁿ  where m and n are the reaction orders.

 

Attach Table of Calculated rate constants

• Using your calculated rate constants at different temperatures, determine the activation energies and pre-exponential factors for both the forward and reverse reactions by graphing the Arrhenius equation

Ea Forward Reaction = ____________ Ea Reverse Reaction = ____________

       A for Forward Reaction = __________ A for Reverse Reaction = __________  

Attach the 2 Graphs and any values needed to have been calculated to make the graphs

 

• Calculate equilibrium constants at each temperature.  Remember that the equilibrium constant at any specific temperature is given by

 

Show in Excel Table

• Calculate DH^o_rxnand DS^o_rxn for the overall reaction as written.  These values can be obtained from graphing the general equation given:

 

DH^o_rxn = __________ DS^o_rxn = ___________

Attach graph and any values needed to have been calculated to make the graphs

• Calculate DG^o_rxnfor this reaction as written at room temperature.  This is given by the standard equation

ΔG^ᵒ_rxn = __________

• Calculate E^o_rxnfor the reaction as written at room temperature.  This is given by the standard equation

E^ᵒ_cell = _________

Using these calculated values, as well as your chemical understanding, complete the above thermodynamic table.  Use an Excel spreadsheet to create your graphs, and include these as well as showing all calculations for each step in your report to receive appropriate credit.