Chemistry - Common Ion Effect

[sam.]

What is the pH change of a 0.270 M solution of citric acid (pKa = 4.77) if enough sodium citrate is added to make the final concentration of the common citrate ion 0.145 M?

Okay so first I did an ice-table using the equation:
citric acid + water <--> hydronium + citric ion
Using an inital concentration of 0.270 for citric acid and then just solving for x using the Ka value and I got pH = 2.67 (which is the initial pH).
Now I'm having a problem with how to find the final pH. I think you're supposed to set up another ice table but I'm not too sure what values are supposed to be my initial concentrations. Any help would be greatly appreciated!

 

[lightarrow]

What is the pH change of a 0.270 M solution of citric acid (pKa = 4.77) if enough sodium citrate is added to make the final concentration of the common citrate ion 0.145 M?

Okay so first I did an ice-table using the equation:
citric acid + water <--> hydronium + citric ion
Using an inital concentration of 0.270 for citric acid and then just solving for x using the Ka value and I got pH = 2.67 (which is the initial pH).
Now I'm having a problem with how to find the final pH. I think you're supposed to set up another ice table but I'm not too sure what values are supposed to be my initial concentrations. Any help would be greatly appreciated!

HA + H2O <--> H3O+ + A-

[HA] = 0.270 - x
[H3O+] = x
[A-] = 0.145

[H3O+]*[A-]/[HA] = Ka = 10^(-4.77)

--> x*0.145/(0.270 - x) = 10^(-4.77)

--> x = 3.16*10^(-5) --> pH = 4.50

 

[ravenprp]

The common ion effect is a phenomenon in which the presence of a common ion in a solution containing a weak acid or base causes a decrease in the ionization of the weak acid or base. In this case, the common ion is the citrate ion, which is present in both the citric acid and sodium citrate.

To find the final pH, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa of the weak acid and the ratio of the concentrations of the conjugate base and weak acid.

pH = pKa + log([A-]/[HA])

In this case, the weak acid is citric acid and the conjugate base is the citrate ion. We know the pKa is 4.77 and the concentration of citrate ion is 0.145 M. To find the concentration of citric acid, we can use the common ion effect equation:

[Citric acid] = [Initial citric acid] - [Citrate ion added]

= 0.270 M - 0.145 M

= 0.125 M

Now we can plug in these values into the Henderson-Hasselbalch equation:

pH = 4.77 + log(0.145/0.125)

= 4.77 + 0.12

= 4.89

Therefore, the final pH of the solution is 4.89, which is slightly more acidic than the initial pH of 2.67. This is because the addition of the common citrate ion has decreased the ionization of citric acid, resulting in a lower concentration of hydronium ions and a higher pH.