Heat/fusion/vaporization question?

[pirates01]

Homework Statement

Given 150g of ice at -15^oC, how much steam (at 100^oC in g) is required to give a resultant of 50^oC water?

Homework Equations

q=lm
q=cmT
heat for vap: 2256j
heat for fusion: 333J

The Attempt at a Solution

I got something like
remaining heat: 49950-2256m
change heat with remaining water: 4.19(150+m)T
and that m(100)/(150+m)=50 (error here?)

In the end, i got something like m=9g, which is too little, cause answers says 33g

 

[kuruman]

I got something like
remaining heat: 49950-2256m

What exactly is your reasoning for this "remaining heat"? What is 49950 and how did you get it?

 

[pirates01]

remaining heat: 49950-2256m

I got this from q=lm
where 49950 is the joules taken to melt ice to liquid, and 2256m (where m is the mass of gas) is the joules given off to turn steam to liquid.

 

[kuruman]

When you end up with water at 50 ^oC, you need to say that the heat lost by the steam is equal to the heat gained by the ice. In other words,

Heat to turn steam to liquid + Heat to reduce T of condensed steam from 100 ^oC to 50 ^oC

is equal to

Heat to turn ice to liquid + Heat to raise T of melted ice from 0 ^oC to 50 ^oC.