# Why does [1H2O->1(H) + 1(OH)], yet [10^(-14)M=10^(-7)M+10^(-7)M]?

1. Oct 7, 2012

### LearninDaMath

Say I have 10(H2O) that ionizes into H and OH. The reaction would be

10(H2O)→10(H) +10(OH)

Because if you have 10 of something, and then then split it into 2 pieces, you have 10 of each piece.

If I have 1 piece of paper and I tear it into 2 pieces, I have 1 piece in my right hand and 1 piece in my left hand. It makes sense.

The reactions is
1 full paper → 1 torn piece + 1 torn piece.

So just like 1 torn piece of paper + 1 torn piece of paper ≠ 2 full pieces of paper,

10(H)+10(OH) ≠ 20(H2O).

But how the the heck is this following equation true:

$10^{-14}M(H2O) = 10^{-7}M(H^{+})+10^{-7}M(OH^{-})$

Why is it not:

$10^{-7}M(H2O) = 10^{-7}M(H^{+})+10^{-7}M(OH^{-})$?

2. Oct 7, 2012

### LearninDaMath

I wonder if this question makes any sense or not?

If I have 10 blue marbles and drop them into a Liter of water, the concentration will be 10 blue marbles/1L

If I have 10 red marbles and drop them into a liter of water, the concentration will be 10 red marbles/1L

With 10 blue marbles + 10 red marbles dropped into a Liter of water, I will obviously have 20 seperate marbles/1L

But if each red and blue marble fused into a purple marble, I'd end up with 10 purple marbles/1L.

What I'm saying is, the concentration of marbles/Liters stays the same. There is no reason to do any addition if the marbles are fusing into purple marbles.

So why is there addition when speaking on this reaction:

$10^{-14}M(H2O) = 10^{-7}M(H^{+})+10^{-7}M(OH^{-})$

How is concentration so different than quantity, that in one instance 1A+1B→1(AB), yet for another instance, 1M(A)+1M(B) → 2M(AB)

3. Oct 8, 2012

### Staff: Mentor

$$K_w = [H^+][OH^-] = 10^{-14}$$