A) Calculate the hydrogen-ion concentration of a 5.45*10^-4 M H2CO3, solution, noting that Ka is bigger than Kb.

B)What is the concentration of CO3^2-?

after finding the concentration to A), do i use that concentration (M) as the initial M for CO3^2-?
thanks in advnace

To be honest I don't understand the caution in the problem. I also think the concn of the H2CO3 is so low that it may cause problems but it didn't have that much effect on the final calculation.

H2CO3 ==> H^+ + HCO3^-
Set up an ICE chart, use k1 ONLY, (just think of it as a monoprotic acid and work the H^+ that way). It PROBABLY is a good idea to include the quadratic eqution and solve that.
[(H^+)(HCO3^-)/(H2CO3-(H^+)] = k1 which becomes
[(x)(x)/(H2CO3-x)] = k1.

For part b, the trick here is to think of this diprotic acid as a monoprotic acid. Then (H^+) = (HCO3^-)
Now look at k2 expression.
k2 = (H^+)(CO3^2-)/(HCO3^-)
BUT, if (H^+) = (HCO3^-) then (H^+) in the numerator cancels with (HCO3^-) in the denominator and k2 = (CO3^2-)

To calculate the hydrogen-ion concentration of a solution of H2CO3 (carbonic acid), we need to use its dissociation constant, Ka.

A) Calculating the hydrogen-ion concentration (H+):

1. Write the balanced equation for the dissociation of H2CO3:
H2CO3 ⇌ H+ + HCO3-

2. Set up the expression for Ka:
Ka = [H+][HCO3-] / [H2CO3]

3. Since Ka is given as larger than Kb, it implies that the dissociation of H2CO3 is favored, indicating that most of the H2CO3 will dissociate into its ions.

4. Assume that x is the concentration of H+ and HCO3- ions formed.

5. Since H2CO3 is initially 5.45 × 10^-4 M, the starting concentration of H+ and HCO3- ions is negligible compared to the initial concentration of H2CO3. Thus, we can approximate the change in concentration as x.

6. At equilibrium, the concentration of H2CO3 will decrease by x, while the concentration of both H+ and HCO3- will increase by x. So, [H2CO3] = 5.45 × 10^-4 M - x.

7. Insert the appropriate values in the Ka expression:
Ka = x^2 / (5.45 × 10^-4 M - x)

8. Since Ka is given, solve the equation above for x using the quadratic formula.

9. Once you determine the value of x (concentration of H+ ions), that will be the hydrogen-ion concentration of the H2CO3 solution.

B) Since CO3^2- is the conjugate base of H2CO3, its concentration can be calculated using the relationship between Ka and Kb.

1. Set up the expression for the relationship between the Ka and Kb:
Ka × Kb = Kw

2. The Kw (water dissociation constant) is a constant value at a given temperature, typically 1.0 × 10^-14, representing the product of the hydrogen ion (H+) and hydroxide ion (OH-) concentrations in water.

3. Since the concentration of OH- in water is usually very low, we can approximate [H+] ≈ [H2CO3].

4. Rewrite the equation for Kb as Kb = Kw / Ka.

5. Calculate Kb using the given Ka value.

6. The concentration of CO3^2- can be assumed as y.

7. Using the Kb expression, set up the equation: Kb = y^2 / [CO3^2-]

8. Substitute the calculated value of Kb and solve for [CO3^2-].

Therefore, once you have calculated the concentration of H+ (from part A), you can use that concentration as the initial concentration (M) for CO3^2- (part B).