Who here is a chemistry genius and wants to solve this hard problem?

Question

Captain X of a ship has been told by his superiors that only a chemist can be trusted with the combination to the safe containing the dilithium crystals that power the ship. The combination is the pH of solution A, described below, followed by the pH of solution C. (example: If the pH of solution A is 3.47 and that of solution C is 8.15, then the combination to the safe is 3-47-8-15). The chemist must determine the combination using only the information below (all sol'n are at 25C)
Sol'n A is 50mL of a .100M solutionof the weak monoprotic acid HX
Sol'n B is a .0500M solution of the salt NaX. It has a pH of 10.02
Sol'n C is made by adding 15mL of .25 M KOH to solution A

What is the combination of the safe?

Answer 1

Solution B is the salt of the conjugate base of the weak acid in Solution A. Subtract 10.02 from 14 for the pOH, make it negative and take the antilog for the concentration of OH- (which is also the concentration of the conjugate acid formed) and you get about 0.000104713. Subtract this from the original concentration and you have about 0.049895287 as the concentration of the remaining base. Square the first number for the concentration of acid times the concentration of OH- and divide this by the concentration of remaining base to get the base dissociation constant for the conjugate base: about 0.00000022. Divide the constant for the self-ionization of water (0.00000000000001 or 1.0*10^-14) by this figure to get the acid dissociation constant for the conjugate acid used in solution A and you get about 0.000000046. Next, multiply this by the concentration of Solution A. We will assume that the loss of protonated acid is trivial to avoid quadratic equations and hope that is the case. Take the square root to find the concentration of conjugate base and H3O+ and you get 0.000067457. This is, indeed, trivial compared to the original concentration, so we're in luck this time. Now, take the negative log of this figure for the pH and you get 4.17, so we have our first number. Now KOH is a strong base and dissociates completely, so the OH- concentration is 0.25. Multiply this by 0.015 L and you have 0.00375 mol OH-. Take the concentration of H3O+ from earlier and multiply by 0.050 L and you have 0.000003373 mol H3O+. Now subtract the H3O+ from the OH- and you get 0.003746627 mol OH- remaining. Divide this by the new volume of 0.065 L and you have a solution with a 0.057640417 molar concentration of OH-. Take the negative of the log and you get a pOH of 1.239272883. Subtract from 14 and you get a pH of 12.76. Your two pH values are thus 4.17 and 12.76, so the combination is 4-17-12-76. Hope this helps.

Answer 2

Can only be done if weak acid dissociates 100%, which is not according to the behaviour of weak acids.

Still I assume the above fact to be true.
For Solution A: [H3O]+ = 0.1 M
pH(A) = 1.00

For Solution B:
pH(B) = 10.02

For Solution C:
millimols of acid present = 5
millimols of base present = 3.75
thus 1.25 millimols of acid is NOT neutralized!
molarity = 1.25/(50+15) = 0.01923 M
pH(C) = 1.72


combination of the safe is: 1-00-10-02-1-72

Answer 3

in case you have in no way studied physics, how does that reconcile with "have constantly found physics exciting" ? while you're solid at math, and that's significant, then i could propose you to take physics. an information of the international is often solid, no count your eventual significant.