A 0.100 M solution of the weak acid HA has a pH of 3.00. What is the Ka for this acid?

To calculate the acid dissociation constant (Ka) for the weak acid HA with a solution concentration of 0.100 M and a pH of 3.00, you can follow these steps:

1. Calculate the hydrogen ion concentration [H+]: The pH of a solution is defined as the negative logarithm to base 10 of the hydrogen ion concentration. pH = -log[H+]

Since the pH is given as 3.00, you can find the concentration of hydrogen ions as follows: [H+] = 10^(-pH) = 10^(-3.00) = 0.001 M

2. Write the acid dissociation equation: HA <-> H+ + A-

3. Set up the expression for the acid dissociation constant (Ka): Ka = [H+][A-] / [HA]

At equilibrium, the concentration of HA will have decreased by the same amount that the concentrations of H+ and A- have increased. If x is the amount that dissociates, then the concentrations of H+ and A- each increase by x, and the concentration of HA decreases by x.

4. Because the concentration of H+ is given as 0.001 M, and assuming that all of the [H+] comes from the dissociation of HA, you can say: [H+] = [A-] = x = 0.001 M [HA] = initial concentration of HA - x = 0.100 M - 0.001 M ≈ 0.100 M

Since x is much smaller than 0.100 M (1% rule for weak acid dissociation), we can approximate [HA] to remain close to its initial concentration.

5. Calculate Ka using the expression and your approximations: Ka = [H+][A-] / [HA] = (0.001 M)(0.001 M) / (0.100 M) = 1 x 10^-5

Therefore, the Ka for the acid HA is 1 x 10^-5.