Thanks to Dr. Bob for answering all these questions!
I always do poorly on conceptual problems.
Consider the following equilibrium system at 25°C and select the true statement below: H2PO4−(aq) + SO42−(aq) ↔ HSO4−(aq) + HPO42−(aq)
ΔG°rxn > 0 at 25°C
(1) this is a product-favored reaction
(2) H2PO4− is a stronger acid than HSO4−
(3) The Kb of SO42− is less than the Ka of HSO4−
(4) the Keq of this reaction is > 1.0
(5) if ΔG°rxn > 0, then ΔGrxn must also be > 0
I know that 3 is the correct answer but I was wondering why? How could you know that the Kb of SO42- was less if HSO4 is not a strong acid?
Also, how would you know it was product favored? How would you know if Keq is greater than 0?
When dG is - (i.e., <0) the reaction is favored. Therefore, if dGo is >0 it must be + and that means the system is not favorable for a reaction. That is the equilibrium lies to the left. That takes care of 1 and 5.
2. Knowing that the equilibrium lies to the left means H2PO4^- is not likely to be transformed to HSO4^-.
4. If dG<0 (that is -) keq is to the right and >1/
If dG = 0, the Keq = 1
If dG > 0 (that is +) then Keq <1
So 4 can't be right.
3. Ka for HSO4^- is k2 and you can look that up. I think it's about 0.012 but you should confirm that.
Kb for SO4^2- = Kw/k2 = 1E-14/0.012 = about 3E-13 and this is < Ka (which equals 0.012) so 3 is OK.
Hope this helps.
To determine why option (3) is the correct answer, let's break down the given equilibrium system:
H2PO4−(aq) + SO42−(aq) ↔ HSO4−(aq) + HPO42−(aq)
In this reaction, H2PO4− and HSO4− act as acids, while SO42− and HPO42− act as bases. The acidity of an acid is reflected by its acid dissociation constant (Ka), while the basicity of a base is reflected by its base dissociation constant (Kb).
To determine the correctness of option (3), we need to compare the Ka value of HSO4− with the Kb value of SO42−.
Since H2PO4− and HSO4− are both acids, the stronger acid will have a higher value for Ka. So, if H2PO4− is a stronger acid than HSO4−, as given in the option, then the Ka of HSO4− must be less than the Kb of SO42−. This makes option (3) true.
Now let's address how to determine if the reaction is product-favored and if the equilibrium constant (Keq) is greater than 1.0:
A reaction is product-favored when the concentration of products is larger than the concentration of reactants at equilibrium. To determine this, one can compare the stoichiometric coefficients of the reactants and products. In this case, we have one molecule of reactant on each side of the equation. Therefore, we cannot conclude if the reaction is product-favored based on the given information.
The equilibrium constant (Keq) can be used to determine if a reaction is product-favored or reactant-favored. When Keq is greater than 1.0, it indicates that the products are favored at equilibrium. However, we cannot determine the value of Keq from the provided information, so we cannot conclusively say if Keq is greater than 1.0.
Therefore, based on the given information, we can confidently say that option (3) is true, but we do not have enough information to determine if the reaction is product-favored or if Keq is greater than 1.0.