Question

Propose a method for determining the specific heat for a metal like sodium which reacts violently with water.

Answer 1

You can put a known amount sodium into some sort of time release mechanism such as a pill made from soluble material.  Then you can place the sodium into a calorimeter with a known mass of water and record the temperature change the water undergoes during the reaction.  Then you can use the equation q(water)=m(water)c(water)ΔT to find the amount of heat absorbed by the water.  since the amount of heat absorbed by the water is the amount of heat released from the sodium, q(sodium)=-q(water).  Than you can use the equation q(sodium)=m(sodium)c(sodium)ΔT and solve for c(sodium)

I hope this helps and feel free to ask about anything that was unclear in the comments.