[whatabohr]

For example,

HCl + H2O --> H3O+ + Cl-

the HCl is clearly donating its hydrogen to the water. Thus HCl is a very strong acid, more so than the H3O+ in solution.

but for NaOH, we get

NaOH + H2O --> OH- + Na+ + H2O

Unlike the HCl reaction, we get water in the products. Also, it is not clear how NaOH is "accepting" a hydrogen. All I see is NaOH dissociating, not accepting!

So why is there only water left over in the reaction for a strong base?

[Dan]

Hydroxide can (and does) remove a hydrogen from water. I have coloured the H that is being transferred:

HO^- + HOH  HOH + ^-OH

You will notice that both sides of the equilibrium are identical though, so you don't notice a reaction.

Q: What happens when you dissolve NaOH in acetic acid?

[Borek]

Why is the reaction for a strong acid different than that of a strong base?

Basically you are saying something like "why black and white are not identical colors?" Well, one is white, the other is black - period. Similarly, you can't expect acid and base to behave identically, as they are different. Would they behave identically, they would be identical.

[Arkcon]

Additionally, the reaction:

HCl + H₂O  H₃O⁺ + Cl^-

doesn't actually happen.

When I was in school, we "diagrammed" that reaction as:

HCl (aq)  H⁺ + Cl^-

But someone, at some point, decided that was silly.  A free proton, an H⁺ floating about in solution can't interact chemically.  So they opted to describe it as the hydromium ion, H₃O⁺.  Problem is, even that doesn't exist.  Acids ionizing in water affect clusters of water molecules, and those clusters are responsible for the properties we associate with acids.  Likewise, although we describe NaOH as dissociating, and there is no physics reason why Na+ and OH- can't exist in solution, the properties we associate with base in water is likely again based on water molecules clustered about the ions.

This is kinda an advanced topic for high school chemistry.  But if you're wondering about these sort of topics, you might as well have the beginnings of the explanation.  This is kinda over my head as well, so I can really only give you the beginnings.

[vmelkon]

One of the reactions is
NaOH + H+ --> Na+ + H2O

so adding NaOH to water,  reduces the amount of H+, so the pH goes up.
The K for water @ 25 °C is 1.0 x 10^-14.

If you want to know how much H+ is left over when you add NaOH, you do
K / concentration of OH-