The problem is as follows:

A flask whose heat capacity is negligible is filled with $20$ grams of ice at $-80^{\circ}C$ and $7$ grams of water at $80^{\circ}C$. Find the composition of the mixture in the flask when the equilibrium is reached.

The alternatives given are as follows:

$\begin{array}{ll}

1.&\textrm{2 g. of water and 25 g. of ice}\\

2.&\textrm{5 g. of water and 22 g. of ice}\\

3.&\textrm{7 g. of water and 20 g. of ice}\\

4.&\textrm{3 g. of water and 21 g. of ice}\\

5.&\textrm{4 g. of water and 23 g. of ice}\\

\end{array}$

For this problem I'm not sure how to proceed. What I've attempted to do was to assume that the warmer water will lose heat and give it to the ice so it will melt. But I don't know exactly how to translate this into an equation.

So what I did was to add the heat to warm up the ice and melt the ice with that of the cooling of the water.

$mL_{f}=q_{water}$

$80m=7\left(1\frac{cal}{g^{\circ}C}\right)\times 80$

$m=7$

But I don't know exactly if this is the right way to approach this problem. Can someone help me with what would be the right concept?

A flask whose heat capacity is negligible is filled with $20$ grams of ice at $-80^{\circ}C$ and $7$ grams of water at $80^{\circ}C$. Find the composition of the mixture in the flask when the equilibrium is reached.

The alternatives given are as follows:

$\begin{array}{ll}

1.&\textrm{2 g. of water and 25 g. of ice}\\

2.&\textrm{5 g. of water and 22 g. of ice}\\

3.&\textrm{7 g. of water and 20 g. of ice}\\

4.&\textrm{3 g. of water and 21 g. of ice}\\

5.&\textrm{4 g. of water and 23 g. of ice}\\

\end{array}$

For this problem I'm not sure how to proceed. What I've attempted to do was to assume that the warmer water will lose heat and give it to the ice so it will melt. But I don't know exactly how to translate this into an equation.

So what I did was to add the heat to warm up the ice and melt the ice with that of the cooling of the water.

$mL_{f}=q_{water}$

$80m=7\left(1\frac{cal}{g^{\circ}C}\right)\times 80$

$m=7$

But I don't know exactly if this is the right way to approach this problem. Can someone help me with what would be the right concept?

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