physics
posted by tim .
What mass (in grams) of steam at 100°C must be mixed with 341 g of ice at its melting point, in a thermally insulated container, to produce liquid water at 57.0°C? The specific heat of water is 4186 J/kg·K. The latent heat of fusion is 333 kJ/kg, and the latent heat of vaporization is 2256 kJ/kg.

add the heats gained, and set the sum to zero.
Heat melting ice + heat raising temp ice to 57C + heat gained condensing steam + heat lowering condensate temp to 57=0
.341*333J+.341*4146(570)+M*2256+M(4146)(57100)=0
solve for Mass (in kilograms). Change it to grams for your answer.