[slu1986]

How much heat is released when 75.0 g of steam at 100.0 °C is cooled to ice at -15.0 °C? The enthalpy of vaporization of water = 40.67 kJ/mol, the enthalpy of fusion for water = 6.01 kJ/mol, the molar heat capacity of liquid water = 75.4 J/(mol °C), and the molar heat capacity of ice is 36.4 J/(mol°C).

A. 54.8 kJ
B. 195 kJ
C. 228 kJ <----This is the right answer, but I don't understand how to set up the equation to solve the problem and get that answer.
D. 248 kJ

If someone could help me with this problem, I would greatly appreciate it 

[Yggdrasil]

Split the problem into multiple parts (steam at 100^oC to liquid water at 100^oC, liquid water at 100^oC to liquid water at 0^oC, etc), and find the heat released in each step.

[CopperSmurf]

calculate your heat for phase change steam to liquid.
Then calculate heat for the change in temperature from 100 to 0. T
hen calculate heat for phase change from liquid to solid ice.
Then calculate the heat due to temperature change from 0 to -15.

It's like doing so many of these steps of the same heat calculation but with different numbers. Then add up all the heats.

[slu1986]

Ok this is how I tried solving the problem according to the directions that yall gave me, however I am still coming up with the wrong answer.

75.0 g H2O * mol H2O/18.02 g H2O = 4.16 mol H2O

 -delta H vap = 4.16 mol H2O * -40.67 kJ/mol H2O = -169

4.16 mol H20 ( 0-100 C) (75.4 J / mol * C) = -31366.4 J

- delta H fus = 4.16 mol H2O * -6.01 kJ/mol H2O = -25.0 kJ

4.16 mol H20 ( 0 - -15 C) (36.4 J/ mol * C) = 2271.36 J

-169 kJ + -31.3664 kJ + -25.0 kJ + 2.27136 J = -223 kJ<-----this is the answer that I keep getting when the right answer is = 228 kJ

Could someone please tell me what I am doing wrong?

[Yggdrasil]

Do you expect cooling ice from 0^oC to -15^oC to consume or release heat?

[slu1986]

Release Heat because the temperature is getting colder. 

[slu1986]

I'm sorry, but I still do not understand what I am doing wrong in this problem.  Could you give me a better explanation of how to set up the equation please?

[Yggdrasil]

-169 kJ + -31.3664 kJ + -25.0 kJ + 2.27136 J = -223 kJ

Right so if the last step releases heat, why is the value positive?  If you subtract the last value instead of add it, your answer will be correct.

For these types of problems, it is better to conceptually think about whether the number should be positive or negative.  It's too easy to switch a sign somewhere and come up with a number that is correct except for the sign.

[slu1986]

Thank you soo much for your *delete me*