Use activity coefficients to find the concentration of hydrogen ions in a solution of 65.0 mM butanoic acid and 0.05 M NaCl. The ionization constant of butanoic acid is Ka = 1.52 × 10-5. Take the size of C3H7COO– to be 500 pm.

Question

Use activity coefficients to find the concentration of hydrogen ions in a solution of 65.0 mM butanoic acid and 0.05 M NaCl. The ionization constant of butanoic acid is Ka = 1.52 × 10-5. Take the size of C3H7COO– to be 500 pm.
Find [H+], pH, and alpha.
Can you please show me step by step with equations?
Thanks

DrBob222 · Answer

This is a huge undertaking. Can you tell us what your problem is. Surely you know how to do parts of this.

Anonymous · Answer

Yes, I do... The only part that I do not know is how to find the activity coefficients... [H+]=(x)(?)(x)(?)/0.05 The rest of the problem I can do... Thanks! :)

DrBob222 · Answer

Thanks. You scare me away when I see that much work ahead.
Here is a table I have in my quant text. I don't know if you're allowed to use that or not but I'll follow up with the Debye-Huckel equation (which you probably have in your text, too).
4-4.5 Angstrom for diameter of the acetate ion. activity coefficient is 0.82 for 0.05M ionic strength.

-log fx = 0.51Z^2*sqrt (u)/[1+0.33ax*sqrt (u)]
fx is the activity coefficient of the species x.
Z is the charge on the species which is +1 for H^+ and -1 for acetate.
u is ionic strength of the solution; I assume you know how to calculate that. It will be dictated largely by the NaCl.
ax (alpha x) is the effective diameter of the hydrated ion X. For acetate the problem tells you to use 500 pm and that should be changed to 5 Angstroms and about 9 for (H3O^+) from my book table. Activity coefficient for H3O^+ at 0.05 u is 0.86 from the same table.