Solving Charge Balance for 1 M CaCl_{2}

[Qube]

Homework Statement

For 1 M $CaCl_{2}$ what is the correct "charge balance" for all species?

Homework Equations

Charge balance is an algebraic statement of electroneutrality.

The sum of positive charges = sum of negative charges.

The Attempt at a Solution

My prof never really explained how to do this, so I'm relying on this website:

http://ramsey1.chem.uic.edu/audrey/chem222/assign_docs/fall_12/mass_charge_ANS.pdf

Anyway it says to consider all possible equilibrium reactions.

Well, one equilibrium reaction to always consider is the autoionization of water.

$$H_{2}O \leftrightharpoons H_{3}O^{+} + OH^{-}$$

And since we're dealing with calcium chloride in water:

$$CaCl_{2} \leftrightharpoons Ca^{2+} + 2Cl^{-}$$

Consulting a acid/base strength table, I can't even find calcium ion on the table. So I shouldn't have to worry about calcium ion acting as either an acid or base in solution. I do, however, see chloride ion on there, but it's a weaker base than water. So it's not going to behave as a base in water solution. Chloride ion doesn't show up on the acid side of the table either. So it's not going to behave as an acid in water either. So there will be no conjugate acid/base stuff to worry about with calcium chloride, correct?

So these species are present in solution:

$$H_{3}O^{+}, OH^{-}, Ca^{2+}, 2Cl^{-}$$

So the charge balance equation would be (bearing in mind stoichiometric relationships):

$$[H_{3}O^{+}] + [Ca^{2+}] = 2[Cl^{-}] + [OH^{-}]$$

 

[Borek]

$$[H_{3}O^{+}] + [Ca^{2+}] = 2[Cl^{-}] + [OH^{-}]$$

No, that's not correct. You don't look for stoichiometric coefficients, but for charges:

$$[H_{3}O^{+}] + 2[Ca^{2+}] = [Cl^{-}] + [OH^{-}]$$

Actually there will be another ion, CaOH⁺, present, so the correct balance would be

$$[H_{3}O^{+}] + 2[Ca^{2+}] + [CaOH^+] = 2[Cl^{-}] + [OH^{-}]$$