You are asked to make 50 mM Tris-HCl pH 7.5. The pK of Tris is 8.1.
What is the concentration of the components (Tris and Tris-H+) in the
final buffer solution?
Use the Henderson-Hasselbalch equation. That is equation 1.
7.5 = 8.1 + log (tris)/(tris-HCl)
equation 2 is:
tris + tris-HCl = 50 mM
Solve the two equations simultaneously to determine tris and trish-H^+
To determine the concentration of Tris and Tris-H+ in the final buffer solution, we need to consider the acid-base equilibrium of Tris (tris(hydroxymethyl)aminomethane) in water.
Tris acts as a weak base that can accept a proton (H+) to form its conjugate acid (Tris-H+). The pK value of Tris indicates the pH at which half of the Tris molecules are ionized (in the form of Tris-H+) and half are non-ionized (in the form of Tris). In this case, the pK of Tris is 8.1, meaning at pH 8.1, the concentration of [Tris] is equal to [Tris-H+].
Since you want to prepare a 50 mM Tris-HCl buffer at pH 7.5, which is below the pK value of Tris, most of the Tris molecules will be in the non-ionized form (Tris). However, a small fraction will still be ionized (Tris-H+).
To calculate the concentrations, we can make some simplifications. At pH 7.5, the concentration of [Tris] will be close to the starting concentration, i.e., 50 mM. On the other hand, the concentration of [Tris-H+] will be much smaller than [Tris] because most of the Tris molecules will remain non-ionized.
Therefore, to a good approximation, in a 50 mM Tris-HCl buffer at pH 7.5, the concentration of Tris will be 50 mM, while the concentration of Tris-H+ will be negligible compared to Tris.
Please note that this approximation assumes that the pH 7.5 is controlled accurately. In practice, small variations in pH can influence the Tris ionization extent, so if you require a more precise answer, it's recommended to use a pH calculator or specific software for buffer preparation.