For 6.0*10^-2 M H2CO3, a weak diprotic acid, calculate the following values. Use ionization constants of H2CO3: Ka1=4.4*10^-7, Ka2=4.7*10^-11, as necessary.
PART A: [H3O^+] M
PART B: [HCO3^-] M
PART C: [CO3^2-] M
A.
........H2CO3 + H2O ==> H3O^+ + HCO3^-
I.......0.06..............0......0
C........-x...............x.......x
E......0.06-x..............x......x
Substitute the values from the ICE chart into ka1 and solve for x = (H3O^+) = (HCO3^-)
I've answered part B in part A answer.
C.
......HCO3^- + H2O ==> H3O^+ + CO3^2-
Note ka2 = (H3O^+)(CO3^2-)/(HCO3^-)
Write that out on a sheet of paper so you can see it. From part A you know (H3O^+) = (HCO3^-). Therefore, )H3O^+) in the numerator cancels (HCO3^-) in the denominator and (CO3^2-) = ka2.
To calculate the values in this problem, we need to understand the dissociation of H2CO3 and its ionization constants.
H2CO3 dissociates in water according to the following reactions:
H2CO3 ⇌ H+ + HCO3-
HCO3- ⇌ H+ + CO3^2-
Given that H2CO3 is a weak diprotic acid, it has two ionization constants: Ka1 and Ka2. These ionization constants represent the equilibrium constant expressions for the first and second ionization reactions, respectively.
PART A: [H3O^+]
[H3O^+] represents the concentration of hydrogen ions in solution. For a weak acid like H2CO3, we need to consider both ionization reactions.
Using the first equilibrium expression:
Ka1 = [H+][HCO3-] / [H2CO3]
Rearranging the equation gives:
[H3O^+] = [H+] = (Ka1 * [H2CO3]) / [HCO3-]
Substituting the given values: Ka1=4.4*10^-7 and [H2CO3]=6.0*10^-2 M, we are missing the concentration of [HCO3-].
To find [HCO3-], we must set up another equilibrium expression using the second ionization constant Ka2:
Ka2 = [H+][CO3^2-] / [HCO3-]
Knowing that [H+] = [H3O+], we can substitute [H+] with (Ka1 * [H2CO3]) / [HCO3-], and rearrange the equation to find [HCO3-].
Ka2 = [(Ka1 * [H2CO3]) / [HCO3-]] * [CO3^2-]
[HCO3-] = [(Ka1 * [H2CO3]) / (Ka2 * [CO3^2-])]
Now we need the concentration of [CO3^2-]. The total concentration of carbonate species ([CO3^2-] + [HCO3-]) in solution is equal to [H2CO3].
[H2CO3] = [HCO3-] + [CO3^2-]
Substituting [HCO3-] with [(Ka1 * [H2CO3]) / (Ka2 * [CO3^2-])], we can solve for [CO3^2-].
[H2CO3] = [(Ka1 * [H2CO3]) / (Ka2 * [CO3^2-])] + [CO3^2-]
Simplifying the equation:
1 = (Ka1 / Ka2) * [H2CO3] / [CO3^2-]
Now we can solve for [CO3^2-]:
[CO3^2-] = (Ka2 / Ka1) * [H2CO3]
Finally, going back to [HCO3-]:
[HCO3-] = [(Ka1 * [H2CO3]) / (Ka2 * [CO3^2-])]
After finding [HCO3-] and [CO3^2-], substitute these values into the equation for [H3O+] to get the final answer.
PART B: [HCO3^-] M
Substitute the calculated value of [HCO3-] into the equation.
PART C: [CO3^2-] M
Substitute the calculated value of [CO3^2-] into the equation.
By following these steps and performing the necessary calculations, you can find the values for [H3O^+], [HCO3^-], and [CO3^2-].