Answer: 0.094%
Explanation:
1) Equilibrium chemical equation:
Only the ionization of the formic acid is the important part.
HCOOH(aq) ⇄ HCOO⁻(aq) + H⁺(aq).
2) Mass balance:
HCOOH(aq) HCOO⁻(aq) H⁺(aq).
Start 0.311 0.189
Reaction - x +x +x
Final 0.311 - x 0.189 + x x
3) Acid constant equation:
Ka = [HCOO-] [N+] / [HCOOH] = (0.189 + x) x / (0.311 -x)
= (0.189 + x )x / (0.311 - x) = 0.000177
4) Solve the equation:
You can solve it exactly (it will lead to a quadratic equation so you can use the quadratiic formula). I suggest to use the fact that x is much much smaller than 0.189 and 0.311.
With that approximation the equation to solve becomes:
0.1890x / 0.311 = 0.000177, which leads to:
x = 0.000177 x 0.311 / 0.189 = 2.91 x 10⁻⁴ M
5) With that number, the percent of ionization (alfa) is:
percent of ionization = (moles ionized / initial moles) x 100 =
percent ionization = (concentration of ions / initial concentration) x 100 =
percent ionization = (0.000291 / 0.311)x 100 = 0.0936% = 0.094%
