What is the Ka of the amino acid serine if it is 34.5% dissociated at pH- 9.46?

To determine the Ka (acid dissociation constant) of an amino acid like serine, you need to use the concentration of the dissociated and undissociated forms of the acid, as well as the pH of the solution.

The Ka value represents the equilibrium constant for the dissociation of an acid and can be calculated using the equation:

Ka = [H+][A-]/[HA]

In this case, serine is an amino acid that can act as both an acid (donating a proton) and a base (accepting a proton). At a specific pH, it will be partially dissociated into its conjugate base (A-) and hydrogen ions (H+). Therefore, knowing the percentage of dissociation (% diss) provides the ratio of dissociated to total acid concentration.

% diss = (dissociated acid concentration / total acid concentration) × 100

To calculate the Ka, we need to convert the percentage dissociation to a decimal value. In this case, the % diss is given as 34.5%.

Step 1: Convert % dissociation to decimal
% diss = 34.5% = 34.5/100 = 0.345

Step 2: Set up the equation using the Ka expression:
Ka = [H+][A-]/[HA]

Step 3: Substitute the known values:
[H+] = concentration of dissociated acid = % diss = 0.345
[A-] = concentration of conjugate base = % diss = 0.345
[HA] = concentration of undissociated acid = 1 - % diss = 1 - 0.345 = 0.655

Step 4: Substitute the values into the equation and solve for Ka:
Ka = (0.345)(0.345)/(0.655) = 0.184

Therefore, the Ka of serine at pH 9.46 is approximately 0.184.