Aqueous equilibria, buffered solutions

[silenzer]

I have two problems.

Homework Statement

How many moles of Na₂CO₃ must be dissolved in 250 mL of 0,125 M NaHCO₃ so that the solution has a pH of 10,00?

Homework Equations

The powers of the concentrations are the coefficients in the chemical equation. The products of the equation are in the numerator, and the reactants in the denominator.

The Attempt at a Solution

I have an idea for a solution, but I have no way of checking whether it's correct. My solution is as follows.

The sodium ions can be ignored because they have no significant effect on the pH.

The equation is: HCO₃^- ⇔ H⁺ + CO₃^2-

I set [CO₃]^2-=y, and to equilibrium this concentration changes to y+x, but I assume that x is very small compared to y so y+x ≈ y. The same applies to HCO₃^2-. The initial concentration of that is 0,5 M, and it occurs change towards equilibrium that is 0,5 M - x, which is essentially 0,5 M.

If I'm allowed to do the above, the problem is easy. I know K_a for HCO₃^2- so all I have to do is plug everything I know into the K_a equation and solve for [H⁺].

Homework Statement

In a very basic solution the insoluble salt Cr(OH)₃ (K_sp=1,6*10^-30) dissolves and forms the metal complex Cr(OH)₄^- (K_f=8*10²⁸). Calculate the equilibrium constant, K, for the reaction:
Cr(OH)_3(s) + OH^-_(aq) ⇔ Cr(OH)₄^-_(aq).

Homework Equations

Same as in the first problem.

The Attempt at a Solution

I'm not sure how to approach this exact problem. I know how to solve simpler problems that are showcased in my textbook, but there you're given numbers like molarities to work with. Here I only have equilibrium constants.

 

[Borek]

1. Have you heard about Henderson-Hasselbalch equation?

2. Write three equations - Ksp, Kf and K. See if you can express K using Ksp and Kf.

 

[silenzer]

Thanks for the reply.

1. Yes I have, but to my knowledge its only use is that you calculate pH in one step instead of two. I'm wondering whether my y+x=y and 0.5-x=0.5 assumptions are justified.

2. Thanks, I'll try that.

 

[Borek]

Well, it is possible to solve buffer problems using ICE tables. Whether your assumptions are correct you would have to check, solve the problem using them and see if your x and y have values that fit the approximations.

Just note that

If I'm allowed to do the above, the problem is easy. I know K_a for HCO₃^2- so all I have to do is plug everything I know into the K_a equation and solve for [H⁺].

concentration of H⁺ is not what you are looking for. Besides, initial concentration of HCO₃^- is not 0.5M. Are you sure you are solving the problem you have listed?

 

[silenzer]

It's this problem, I just made stupid mistakes. You're correct of course, it's 0.125 M.

Oh, silly me. Of course I'm not supposed to find H+. Well, then I don't know what to do. Now I have a y which is my unknown, but I also know nothing abut the concentration of H+. Do you have any ideas?

edit: Woops, of course I know [H+]. The pH is supposed to be 10,00 at equilibrium. The case is closed! Thanks for the help.

 

[Borek]

My ideas? Obvious: use the HH equation.