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# PH problem - Buffer

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1. A typical buffer used by biochemists is called Tris, which can be depicted as R3N (i.e. a tertiary amine). A buffer that is prepared by mixing 500 ml of 0.05 M R3N with 500 ml of 0.05 M R3NHCL at 25 degrees Celsius has a pH of 8.4. If this same buffer is placed in a cold room at 4 degrees Celsius, the pH decreases to 9.2. From this data determine the delta H reaction for R3NH+ (aq) equilibrium R3N (aq) + H+ (aq). R = 8.31447 J/Deg mol

##### Solution Summary

Buffers used for PH problems are analyzed. The enthalpy of reaction is determined using equilibrium chemistry.

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The Gibbs-Helmholtz equation that relates Gibbs free energy (G) to enthalpy (H)and temperature (T) is:

At a reaction with equilibrium constant we have:

Differentiating both sides yield:

To find the change in enthalpy when we change the temperature from Ti to Tf we integrate both sides:

So our task now is to find the equilibrium constants at two different temperatures. We know the pH at each temperature, thus we know the equilibrium concentration of H+ in the solution. We also know the initial concentrations of R3NH+ and R3N.
At 25 degrees the equilibrium concentration of H+ ions is:

The reaction equilibrium constant is:

Notice that

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