Suppose a chemical reaction like: AH + B = A + BH, where AH is a paramagnetic metal complex with acidic hydrogen and B is a base. I want to determine the equilibrium constant of this reaction in THF. In 1H NMR I can see a clean conversation. The reaction is completed within few minutes. How can I proceed to do this or how should I titrate for this purpose and how would be the calculation for it?
One way to determine the equilibrium constant of a reaction by 1H NMR spectroscopy is to use the integration of the NMR signals of the reactant and product to calculate the concentrations of each species at equilibrium.
To determine the equilibrium constant for the reaction AH + B = A + BH in THF, you could start by preparing a series of solutions with varying concentrations of AH and B. For example, you could prepare solutions with different ratios of AH and B, ranging from pure AH to pure B.
Next, you would monitor the reaction using 1H NMR spectroscopy. As the reaction proceeds, the NMR signals of the reactant and product will shift and change intensity. By integrating the NMR signals of the reactant and product at each time point, you can calculate the concentrations of each species as a function of time.
Once the reaction reaches equilibrium, the concentrations of AH, B, A, and BH will no longer change over time. At this point, you can use the integrated NMR signals to calculate the equilibrium concentrations of each species.
Finally, you can use the equilibrium concentrations to calculate the equilibrium constant (K) using the following equation:
K = [A][BH]/[AH][B]
where [A], [B], [AH], and [BH] are the equilibrium concentrations of each species.
Note that it is important to carefully control the experimental conditions to ensure that the reaction is carried out under equilibrium conditions. This may involve optimizing the reaction time and temperature, as well as using appropriate solvents and concentrations of reactants. Additionally, it is important to carefully integrate the NMR signals to ensure accurate quantification of each species.
Another way to determine the equilibrium constant of a reaction by 1H NMR spectroscopy is to use the chemical shift of a proton that is involved in the reaction as a function of the concentration of one of the reactants. This method is called chemical shift titration.
In this method, you would start with a solution containing a known concentration of one of the reactants, for example, B. You would then gradually add increments of the other reactant, AH, to the solution while monitoring the chemical shift of a proton in AH that is involved in the reaction, such as the proton that is lost upon deprotonation of the acidic hydrogen in AH.
As you add more AH, the chemical shift of the proton will shift due to the change in the equilibrium concentration of the reactants. By plotting the chemical shift of the proton as a function of the concentration of AH, you can determine the concentration of AH at which the chemical shift reaches a maximum. This corresponds to the point at which the concentrations of AH and B are in equilibrium.
Using the equilibrium concentration of AH and the initial concentration of B, you can then calculate the equilibrium constant for the reaction using the following equation:
K = [A][BH]/[AH][B]
where [A], [B], [AH], and [BH] are the equilibrium concentrations of each species.
Note that it is important to carefully control the experimental conditions and to use appropriate solvents and concentrations of reactants. Additionally, this method may require multiple titrations with different initial concentrations of B to accurately determine the equilibrium constant.
Now the choice is yours.
Lamia Fatima thanks for your suggestion. Can you give any reference if have with you regarding this?
@sandipan Maji
Approach can be found in the following paper:
"Equilibrium Constants by NMR Spectroscopy. A Noninvasive Method for Measurement of K Values of Reversible Reactions" by P. L. Fuchs and S. W. Kauzmann, J. Am. Chem. Soc. 1982, 104, 5026-5028.
"Chemical shift titration in the determination of equilibrium constants by NMR spectroscopy" by C. R. Johnson and C. M. Keeler, J. Am. Chem. Soc. 1990, 112, 6193-6195.
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