Calculate [CO32- ] in a 0.019 M solution of CO2 in water (H2CO3). If all the CO32- in this solution comes from the reaction shown below, what percentage of the H+ ions in the solution is a result of the dissociation of HCO3‾?
HCO3‾(aq) H+(aq) + CO32-(aq)
........H2CO3 --> H^+ + HCO3^-
initial.0.019....0........0
change...-x.......x.......x
equil.0.019-x.....x........x
k1 = (H^+)(HXO3^-)/(H2CO3).
Substitute into k1 expression and solve for H^+. I obtained approximately 1E-4 but you should do it more accurately.
Then HCO3^- ==> H^+ + CO32^2-
init.1E-4.......0.......0
change.-x.......x.......x
equil...1E04-x...x.......x
I have show the two above as if the H^+ from equation 1 is not the same as in equation 2. Actually, they are the same for both equation; however, I have done it this way to show the different.
k2 = (H^+)(CO3^2-)/(HCO3^2-)
But from equation 1 we see that (H^+) = (HCO3^-), which makes from equation 2 that (C03^2-) = k2 = about 5E-11
So what percentage of the H^+ comes from k2? Very small.
[(H^+)from k2/(H^+)from k1]*100 =% from the second ionization.
To find the concentration of CO32- in the solution, we need to consider the dissociation reaction of HCO3‾:
HCO3-(aq) → H+(aq) + CO32-(aq)
Let's assume x is the concentration of CO32-(aq) formed. Since HCO3- dissociates in a 1:1 ratio with CO32-, x M of HCO3- will dissociate to produce x M of CO32-.
Therefore, the concentration of CO32- is x M.
Since the concentration of the CO2(aq) is given as 0.019 M, it can be assumed that the concentration of HCO3- is equal to the concentration of CO2(aq) since CO2(aq) reacts with water to form H2CO3, and H2CO3 dissociates to form HCO3-(aq).
The percentage of H+ ions formed as a result of the dissociation of HCO3- can be given as:
[(Concentration of H+ ions from HCO3- dissociation) / (Total H+ concentration)] * 100%
The concentration of H+ ions from HCO3- dissociation is also x M because HCO3- dissociates in a 1:1 ratio with H+ ions.
The total H+ concentration is the sum of the H+ ions from HCO3- dissociation (x M) and the H+ ions from the dissociation of water, which is negligible compared to the HCO3- dissociation.
Thus, the percentage of H+ ions from HCO3- dissociation is:
[(x M) / (x M)] * 100% = 100%
In summary:
- [CO32-] in the solution is x M.
- The percentage of H+ ions from the dissociation of HCO3- is 100%.
To calculate the concentration of CO32- in the given solution, we need to know the dissociation constant of carbonic acid (H2CO3), which is Ka1 = [H+][HCO3-]/[H2CO3]. However, this information is not provided in the given question. We will assume that the concentration of H2CO3 is very small compared to the concentration of HCO3- and CO32-, meaning we can ignore the contribution of H2CO3 to the equilibrium expression.
Since HCO3- is the only source of CO32- in the solution, each mole of HCO3- that dissociates produces one mole of CO32-. Therefore, the concentration of CO32- is equal to the concentration of HCO3- that dissociates.
Given:
HCO3-(aq) H+(aq) + CO32-(aq)
Let's assume the concentration of HCO3- that dissociates is x M. Therefore, the concentration of CO32- is also x M.
Now, to address the second part of the question, we need to calculate the concentration of H+ ions that result from the dissociation of HCO3-. Since one mole of HCO3- dissociates to produce one mole of H+, the concentration of H+ ions is also x M.
To calculate the percentage of H+ ions that result from the dissociation of HCO3-, we need to compare the concentration of H+ ions from HCO3- with the overall concentration of H+ ions in the solution. The overall concentration of H+ ions is equal to the concentration of H+ ions from HCO3- plus the concentration of H+ ions from all other sources.
Since we don't have information about other sources of H+ ions in the solution, we cannot calculate the exact percentage. However, if we assume that they are negligible compared to the concentration of H+ ions from HCO3-, then the percentage of H+ ions from HCO3- would be 100%.
In summary:
- The concentration of CO32- in the solution is x M.
- The percentage of H+ ions resulting from the dissociation of HCO3- is assumed to be 100%, based on the assumption that other sources of H+ ions are negligible compared to HCO3-.