If you start out with a 0.4M solution of Histidine at pH 6 and add an equal volume of 0.1M HCl, what would the final pH be?
To determine the final pH of the solution after adding HCl, we need to consider the protonation and deprotonation reactions of Histidine and the addition of HCl. Histidine is an amino acid with an ionizable side chain, which can act as both an acid and a base.
The reactions involved are as follows:
1. The protonation of Histidine (His) in an acidic solution:
His + H⁺ ⇌ HisH⁺
2. The deprotonation of Histidine in a basic solution:
HisH⁺ ⇌ His + H⁺
3. The neutralization of HCl in water:
HCl + H₂O ⇌ H₃O⁺ + Cl⁻
In this case, we start with a 0.4M solution of Histidine at pH 6, which means [H⁺] = 10⁻⁶ M. After adding an equal volume of 0.1M HCl, the concentration of HCl will be halved, so [HCl] = 0.05M.
To determine the final pH, we need to consider the concentration of H⁺ ions after the reactions occur. The concentration of H⁺ ions will depend on the relative strength of the acid and base reactions.
Given that Histidine is a weak acid and the pKa of the side chain is around 6, we can assume that the deprotonation of Histidine will dominate over the protonation reaction in this pH range. Therefore, we can neglect the reaction between Histidine and HCl.
The final concentration of H⁺ ions will be the sum of [H⁺] from the initial solution and the [H⁺] that results from the self-ionization of water and the reaction of HCl:
[H⁺]final = [H⁺]initial + [H⁺]HCl + [H⁺]water
[H⁺]initial = 10⁻⁶ M (from pH 6)
[H⁺]HCl = [HCl] = 0.05 M (assuming complete dissociation)
[H⁺]water = 10⁻⁷ M (from water's self-ionization constant, pH 7)
Therefore:
[H⁺]final = 10⁻⁶ M + 0.05 M + 10⁻⁷ M
[H⁺]final = 0.05 M + 10⁻⁶ M + 10⁻⁷ M
Now, we can use the concentration of H⁺ ions to calculate the final pH using the equation:
pH = -log[H⁺]
Substituting the value of [H⁺]final into the equation:
pH = -log(0.05 M + 10⁻⁶ M + 10⁻⁷ M)
Calculating this expression will give you the final pH of the solution.