PLEASE HELP ASAP WITH THIS PHASE CHANGE CALORIMETRY QUESTION!!! (CHEMISTRY)

Question

I was wondering if you could help me come up with a proper answer for this question. I took a test and have no idea what I did wrong and the teacher will not help. I redid the problem and do not know if the answer is correct.

The question is What is the temperature change of a 2.83 kg tub of water when 500.g of Ice (starting at -12.0 degrees Celsius) is added to it?

So I got the answer 8.7 degrees Celsius and that doesn't feel correct to me.

 

Things I know

2830grams of tub water

4.184 J/g Degrees Celsius is the speccific heat of water

I don't know what Delta T is

 

Mass of the ice was 500 grams

Specific heat of ice is 2.05 J/g Degree Celsius

I do not know the delta T but I know that the temp starts at -12.0 degrees celsius

Then I need to add (The heat of fusion (334 J/g) times the mass of the ice (500g))

Answer 1

Your last statement implies that the ice is supposed to melt completely. If that is the case then:

 

Heat lose by water = Heat gain by ice to rise its temperature from -12^oC to 0^oC + Heat gain by ice to melt completely. Note that while the ice is melting the temperature of the water-ice system remains at 0^oC which is the final temperature (the way your problem is worded).

 

Be careful here:

 

Lose heat is negative and gain heat is positive.

 

So you have to solve an equation like this:  -Q_w = Q_i + mL_f where m = 500 and the unknown is the initial temperature of the water T_i:

 

-2830(4.184)(0-T_i) = 500(2.1)(0-(-12)) + 334(500)

 

Solve above equation for T_i and then find delta T (ΔT) which is the increment of temperature of water in this case.

 

Be careful here again:

 

ΔT can be positive or negative.

 

ΔT = Final temperature - Initial temperature.

 

If you have been paying attention to my explanation above you already know what is the value of the final temperature and the value of initial temperature of water (the one you solve the equation for).