Chemistry Equilibrium temperature of a water and ice system

[il postino]

Homework Statement

Equal masses of ice at –10ºC and water at 80ºC are placed in an insulated container and allowed to reach thermal equilibrium. Calculate the equilibrium temperature

Relevant Equations

m.Lf
m.C.dT

Equal masses of ice at –10ºC and water at 80ºC are placed in an insulated container and allowed to reach thermal equilibrium. Calculate the equilibrium temperature
Data:
Water(ice): 37,65 J/mol.K Agua (l): 75,29 J/mol.K
$Lf = 6011 J/mol$

I solved it this way:

$-Q_{l} = Q_{ice}$

$m.(75,29).(80 - T) = m. (37,65).(0 +10) + m.(6011) + m.(75,29).(T - 0)$

simplifying $m$ since they are equal masses, and solving for $T$:

$T = - 2,4 °C$

My teacher's response was:
"The result contradicts the procedure since it calculates the heat absorbed by the ice to become superheated liquid but the obtained temperature is below the melting point"

I don't realize what I have done wrong.
Can you give me help?
Thank you!

 

[Chestermiller]

Have you considered the possibility that some of the ice will melt (but not all), and that the final temperature of the ice and water will be 0 C?

 

[il postino]

Have you considered the possibility that some of the ice will melt (but not all), and that the final temperature of the ice and water will be 0 C?

Yes, I have considered it.
But does that mean the result is wrong?

 

[Chestermiller]

Yes, I have considered it.

What was your assessment when you considered this?

But does that mean the result is wrong?

Well, if the final temperature is 0 C, then yes, the result is wrong. There is only one final state.

 

[Ygggdrasil]

Yes, I have considered it.
But does that mean the result is wrong?

It doesn't seem like you considered it. Your equations assume that the ice fully melted (which cannot be true if you think the final temperature is below zero).

It may be helpful to break the problem up into stages. First consider the temperature changes until one phase reaches the melting point, and then consider the phase change, then any temperature change occurring after the phase change (if necessary).