[Humanities]

I really need help on this question. I can't just do the M1C1DT = M2C2DT equation, because I don't know how the enthalpy of fusion fits in. The answer in the back of the book is 10.4 degrees celsius but I don't know how to get there. Thanks in advance for your *delete me*

Suppose an ice cube weighing 36.0g at a temperature of -10.0 degrees celsius is placed in 360 g of water at a temperature of 20 degrees celsius. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings. The enthalpy of fusion of ice is (DHfus) 6.007 kJ/mol. The molar heat capacity (cp) of ice is 38 J K- mol- and cp of water is 75 J K- mol-.

[Astrokel]

Hi humanities, you can't use M2C2DT = M2C2DT because theres a change in state.

As you know heat gained = heat lost

Let start off with heat gain by ice first, it has 3 proportions

1: Heat gain by the ice in raising the temperature from -10 to 0 degree celcius
2: Heat gain by the ice at 0 degree celcius to change the state of matter
3: Heat gain by the ice in raising the temperature from 0 to θ degree celcius, where θ is the equilibrium temperature.

Now heat loss by the water

1: Heat loss by water and as result of drop in temeprature from 20 to θ degree celcius

Computer them and you should get your answer, pay very closely to the units like kJ and mol^-1

[Humanities]

is step 3:
Q=2mol * 38J/mol * x   (where x is the eq. temperature)?

and for heat loss by water, is it
Q= 20*75*(20-x)? 

im not getting 10.4  

[Astrokel]

you are almost there!

is step 3:
Q=2mol * 38J/mol * x   (where x is the eq. temperature)?

Notice in step 2 you already take into account of change in state, at this point the ice already melts and become water, do you still use molar heat capacity of ice?

and for heat loss by water, is it
Q= 20*75*(20-x)? 

Correct

[Humanities]

"Notice in step 2 you already take into account of change in state, at this point the ice already melts and become water, do you still use molar heat capacity of ice?"

ah, i suppose you don't.  thanks a bunch!