Chemistry Question - Enthalpy change of self-ionization of water...

Hmm, I’ve been going through this assignment, and there’s only one question that I can’t quite see how to answer. It’s an extension one, and I want to be able to have a go at answering it.

The question is:

How would you find the enthalpy change for the ionization of water experimentally, using standard solutions of hydrochloric acid and sodium hydroxide?

I know that we can find out the enthalpy change for the neutralization of the acid and base, and can work out how many [H[sub]3[/sub]O[sup]+[/sup]] ions there are, and I’m sure it’s got something to do with the relationship; K[sub]w[/sub] = [H[sub]3[/sub]O[sup]+[/sup]][OH[sup]-[/sup]], but from there on, i’m a little bit lost.

If someone could just point me in the right direction, or give me a hint of how to tackle this one, I’d be extremely grateful.

Thankyou all;