A typical buffer used by biochemists is called Tris, which can be depicted as R3N. A buffer that is prepared by mixing 500ml of .05M R3N with 500ml of .05MR3NHCl at 25 C has a pH of 8.40. If this same buffer is placed in a cold room at 4 C the pH increases to 9.2. From this data determine the delta Hrxn for R3NH^+(aq) --> R3N(aq)+H^+(aq)
To determine the delta Hrxn for the reaction R3NH+(aq) --> R3N(aq) + H+(aq), we can make use of the Van't Hoff equation, which relates the change in equilibrium constant (K) with temperature:
ln(K2/K1) = -ΔHrxn/R * (1/T2 - 1/T1)
Where:
- K1 and K2 are the equilibrium constants at temperatures T1 and T2, respectively.
- ΔHrxn is the enthalpy change for the reaction.
- R is the ideal gas constant (8.314 J/(mol·K)).
- T1 and T2 are the temperatures in Kelvin.
Given that the buffer has a pH of 8.40 at 25°C (298 K) and a pH of 9.2 at 4°C (277 K), we can calculate the equilibrium constants (K1 and K2) using the pH values:
pH = -log[H+]
[H+] = 10^(-pH)
For K1:
pH1 = 8.40 --> [H+]1 = 10^(-8.40)
K1 = [R3N][H+]/[R3NH+]1
K1 = [R3N][H+]/(0.05M)
For K2:
pH2 = 9.2 --> [H+]2 = 10^(-9.2)
K2 = [R3N][H+]/[R3NH+]2
K2 = [R3N][H+]/(0.05M)
Now we have the equilibrium constants at the given temperatures. We can substitute these values into the Van't Hoff equation and solve for ΔHrxn:
ln(K2/K1) = -ΔHrxn/R * (1/T2 - 1/T1)
ln([R3N][H+]/(0.05M) / [R3N][H+]/(0.05M)) = -ΔHrxn/8.314 * (1/277 - 1/298)
Simplifying the equation further:
ln(1) = -ΔHrxn/8.314 * (0.0036 - 0.00335)
0 = -ΔHrxn/8.314 * 0.00025
Finally, solve for ΔHrxn:
ΔHrxn = 0 J/mol