Calculate [H30+] in a solution that is 0.0525M HCl and 0.768M NaC2H3O2. Ka(HC2H3O2)= 1.8 x10^-5.
the way i did it is that i used the given molar of HCl to find the moles of Hydronium in the acid, and then i used that to find the moles of OH- in it, using kw. then through the equation:
C2H3O2^- + H2O <==> HC2H3O2 + OH^-
and through ice tables used the mols of OH- as initial and solved for x, then got OH- final, and finally found H3O+......this seems to be a way longer way the way i did it...i am sure ther's an easier way to do this...and this might also be wrong. how to do this?
I would be interested in the calculations you didn't show. If I understand what you did you have (H^+) 0.0525 and that makes the "initial" OH = 1.9 x 10^-13 which seems unreasonably high.
I would approach it a little differently. I would start with HCl is a strong acid and the H^+ will be tied up by the acetate (let's call that Ac^- to make typing simpler).
So if that happens, then
Ac^- + H^+ ==> HAc
I would do the ICE chart with this.
We start with (say 1 L) of 0.768 M Ac^- and 0.0525 H^+. That should combine to form 0.0525 HAc and leave essentially zero free H^+ and Ac^- of 0.768-0.0525=0.7155.
Then solve the Ka expression for H^+ OR use the Henderson-Hasselbalch equation for pH. I get something like 5.88 for pH but check me out on that.
yes, that is exactly what i get(i got 5.87, but that's probably just a simple rounding error). i used the wrong equation, and didn't include the hydrogen ion from HCl in the equation, and just used the acetic ion as the only source of the hydroxide ion. But your process does make more sense, because, as now i understand and which is correct, the hydrogen from HCl should have reacted with acetic ion.
To calculate the concentration of [H3O+] in the solution, you can use the concept of the common ion effect and the expression of the weak acid, HC2H3O2, where it ionizes as:
HC2H3O2 ⇌ H+ + C2H3O2-
The steps to calculate the concentration of [H3O+] are as follows:
1. Calculate the concentration of the common ion, C2H3O2-:
[H3O+] = [C2H3O2-] (since it is a 1:1 ratio)
[C2H3O2-] = 0.768 M (given)
2. Use the expression of the weak acid Ka:
Ka = [H+][C2H3O2-] / [HC2H3O2]
Since [H+] = [C2H3O2-], we can rewrite the expression as:
Ka = [H+]^2 / [HC2H3O2]
Ka = 1.8 x 10^-5 (given)
[H+]^2 = Ka * [HC2H3O2]
[H3O+] = √(Ka * [HC2H3O2])
3. Calculate the concentration of HC2H3O2:
HC2H3O2 is a weak acid, and since it is in a solution with a strong acid (HCl), we can consider its initial concentration as its actual concentration:
[HC2H3O2] = 0.0525 M (given)
4. Plug in the values and calculate [H3O+]:
[H3O+] = √((1.8 x 10^-5) * (0.0525 M))
[H3O+] = 1.82 x 10^-3 M
Therefore, the concentration of [H3O+] in the solution is approximately 1.82 x 10^-3 M.