When 1.0g of solid naoh dissolves in 10 l of water, how much heat is released?

When ΔH = - 445.1 KJ/mol (given) missing in your question.

and this value is per mole NaOH.

∴ the amount of heat = ΔH / mol NaOH * (mass NaOH) (1 mol NaOH / molar mass NaOH)

by substitution:

= - 445.1 KJ/mol / mol NaOH * 1 g NaOH * 1molNaOH / 40 g NaOH

= - 11.1 KJ