Answer:
Q1= 9.42
Q2= 227 KJ
Q3= 31.4 KJ
Qt=269 KJ
Explanation:
First you have to find the heat needed to make ice at a temperature of -45 C to pass to a temperature of 0 C.
You're given the formula so all you have to do is replace by the data you're given (remember to make the Celsius, Kelvin by adding 273.15 to the Celsius since the magnitudes of temperature they're giving you in the constants are the Kelvin)
Q1= (2.093 J/gxK)(100 g)(45 K)
Q1=9418.5 J
Q1=9.4185 KJ≈9.42 Kj(you're asked to give your answer in KJ)
You know have to find the energy needed to liquify the ice, in other words you need to use the enthalpy of fusion to determine the energy that's being used, and since you have 100 grams of water, you only need to find the number of moles present in 100 grams of water by dividing the number of grams by the molar mass of water (18 g/mol) and then replace in the equation.
Q2=(5.56 mol)(40.7 KJ/mol)
Q2=227 KJ
You know have to find the energy needed to raise the temperature of water from 0 C to 75 C. You do the same thing as you did in the first step:
Q3=(4.184 J/gxK)(100 g/)(75K)
Q3=31380 J
Q3=31.38 KJ≈31.4 KJ
For the final step, you only add the Qs of each step:
9.42KJ+227KJ+31.4KJ= 267.82 KJ ≈ 267.8 KJ
Why do you use these procedures?
Well, you could simply have made a unique equation at first sight that involved the changes of temperature from -45 C to 75 C, but you have a phase change in the middle. Phase change keep temperature constant but they require heat from the surroundings in order to, in the case of ice, break the bonds that keep the molecules tight together.
This heat required from the surroundings is the Enthalpy of phase change, in this case enthalpy of fusion.
