A 0.285 M solution of the sodium salt, NaA, of the weak monoprotic acid, HA, has a pH of 9.65. Calculate Ka for the acid HA.
I think I am having issues with the equation and then the math part. I figured out what 'x' was from the pH, which I believe is 2.2x10^-10, but when I tried to put it into the rest of the math equation I did not get the answer (I think it is supposed to be 1.43x10^-6).
Can someone walk me through this? Thanks.
-B
1.43 x 10^-6 ix correct.
NaA(aq) ==> Na^+ + A^-
The anion hydrolyzes in water solution to produce a pH of 9.65
A^- + HOH ==> HA + OH^-
Kb = Kw/Ka = (HA)(OH^-)/(A^-)
You know pH. Convert that to pOH and convert that to OH^-. That = (HA) also. You know (A^-) from the problem. That leaves you with one unknown of Ka. Solve for that. I get 1.4284 x 10^-6 which rounds to 1.43 x 10^-6 to three significant figures.
THANKS! I know what I was doing wrong! I didn't find the pOH I just did 10^-9.65 trying to find x! I understand now! Thanks so much!
-B
right. You found (H^+).
Sure! Let's walk through the steps to calculate Ka for the acid HA.
Step 1: Write the chemical equation for dissociation of the weak acid HA:
HA ⇌ H+ + A-
Step 2: Set up an ICE table (Initial, Change, Equilibrium) for the dissociation of HA. Since we have a 0.285 M solution of the sodium salt NaA, we know the initial concentration of A- is 0.285 M. Since HA dissociates into equal amounts of H+ and A-, the initial concentration of HA and H+ is the same and can be represented as x.
Initial: HA = x, H+ = x, A- = 0.285 - x
Change: -x, +x, +x
Equilibrium: x - x = 0, x, 0.285 - x
Step 3: Write the equilibrium expression for Ka:
Ka = [H+][A-] / [HA]
Step 4: Substitute the equilibrium concentrations into the equilibrium expression:
Ka = (x)(0.285 - x) / x
Step 5: Determine the value of x using the pH. The pH equation for a weak acid is pH = -log[H+]. In this case, the pH is 9.65, so [H+] is 10^(-9.65).
[H+] = 10^(-9.65) = 2.2 * 10^(-10)
Step 6: Substitute the value of x into the Ka expression:
Ka = (2.2 * 10^(-10))(0.285 - 2.2 * 10^(-10)) / (2.2 * 10^(-10))
Now, if you calculate this expression, it should give you the correct value for Ka, which is approximately 1.43 * 10^(-6).
Remember to be careful with the calculations, especially when dealing with very small values like 10^(-10). Make sure you are using the correct value for x and performing the math accurately.
I hope this helps! Let me know if you have any further questions.