At equilibrium, a solution of formic acid at 25°C has a pH of 2.18. The pKa of formic acid, HCOOH, is 3.74. Which of the following is the initial concentration of the solution?
Not sure what to do my thoughts:
use henderson hasselback equation
pH = pKa + log [conj base/acid]
use the provided pH to find [H+]
use an ICE table
Im not really sure
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from what i have done i have been able to work out all the parts of the henderson hassel back but i don't know how to find the initial concentration of the entire solution.
This is not a buffer problem; therefore, the HH equation is not applicable.
......HCOOH ==> H^+ + HCOO^-
I......Y........0......0
C......-x.......x......x
E.....Y-x.......x......x
You know pKa, convert that to Ka.
Ka = (H^+)(HCOO^-)/(HCOOH)
The problem gives you pH so you know (H^+) = (HCOO^-) = x.
Substitute that into the Ka expression and solve for Y
thank you! :)
To find the initial concentration of the solution, you can use the Henderson-Hasselbalch equation and solve for the concentration of the acid, [HCOOH]. Here's how you can do it step by step:
1. Start with the Henderson-Hasselbalch equation:
pH = pKa + log([conj base]/[acid])
2. Substitute the known values in the equation:
pH = 2.18
pKa = 3.74
pH = pKa + log([conj base]/[acid])
2.18 = 3.74 + log([conj base]/[acid])
3. Rearrange the equation to solve for [conj base]/[acid]:
log([conj base]/[acid]) = 2.18 - 3.74
log([conj base]/[acid]) = -1.56
4. Convert the logarithmic equation to exponential form:
[conj base]/[acid] = 10^-1.56
5. Calculate the value of 10^-1.56 using a calculator:
[conj base]/[acid] = 0.0262
6. Since formic acid dissociates into HCOO- and H+, we can consider [H+] as [acid].
Therefore, [HCOO-]/[H+] = 0.0262
7. At equilibrium, the concentration of HCOO- and H+ will be the same.
So, [HCOO-] ≈ [H+].
8. Let's assume the concentration of H+ (or [acid]) is x.
Then, [HCOO-] is also x.
9. Now we can set up an ICE (Initial, Change, Equilibrium) table for formic acid dissociation:
HCOOH ⇌ HCOO- + H+
Initial Change Equilibrium
[HCOOH] -x [HCOOH] - x
[HCOO-] x [HCOO-] + x
[H+] x [H+] + x
10. Since [HCOO-] ≈ [H+] ≈ x, we can represent them as x in the table:
Initial Change Equilibrium
[HCOOH] -x [HCOOH] - x
[HCOO-] x x
[H+] x x
11. The equilibrium expression for the dissociation of formic acid is:
Ka = ([HCOO-] * [H+]) / [HCOOH]
12. Substitute the equilibrium values into the expression:
Ka = (x * x) / ([HCOOH] - x)
13. The Ka value for formic acid is the same as the acid dissociation constant (Ka):
Ka = [H+] * [HCOO-] / [HCOOH]
Ka = 10^-pKa
14. Substitute the known pKa value into the equation:
10^-3.74 = (x * x) / ([HCOOH] - x)
15. Rearrange the equation and solve for x:
x^2 = (10^-3.74) * ([HCOOH] - x)
x^2 = (10^-3.74) * [HCOOH] - (10^-3.74) * x
16. Since we're assuming that [HCOOH] is the initial concentration, we can substitute the initial concentration value into the equation.
Working through these calculations will give you the initial concentration of the formic acid solution.