posted by Emmanuel .
How do i determine the mass of ice initially in the calorimeter when dry saturated steam is passed into 250g of a mixture of ice and water in a calorimeter of thermal capacity 45J/K when all the ice has just melted,and the mass of the content in the calorimeter has increased by 10g due to condensed steam ?
If all the ice has "just" melted, the liquid is still 0 degrees C. That is the same temperature that the ice-water mixture started out. The calorimeter also remained 0 C during the ice melting, so you can ignore its heat capacity. The 10 g of steam cooled from 100 to 0 C and released 540*10 + 100*10 = 6400 calories to the icewater. That is enough heat to just melt 6400/80 = 80 g of ice.
80 g of ice was initially present.
The amount of icewater initially present and the heat capacity of the calorimeter were not needed in this case.