Achieve HW #10

[Kaleigh Olla 1L]

Question 10 on weeks 3-4 achieve says:

An ice cube with a mass of 47.2 g at 0.0 ∘C is added to a glass containing 448 g of water at 45.0 ∘C . Determine the final temperature of the system at equilibrium. The specific heat capacity of water, Cs , is 4.184 J/g⋅∘C , and the standard enthalpy of fusion, ΔH∘fus , of water is 6.01×103 J/mol . Assume that no energy is transferred to or from the surroundings.

Could someone explain how to go about solving this? After I find the energy required to melt the ice, I get stuck.

[Amy Xia 1J]

For this question, you are using this equation to solve:

heat required to melt ice + heat required to bring the melted ice to final temperature = heat released to cool water to final temperature

You already calculated the heat required to melt ice which is a good start, now you need to show the other two variable with an unknown T as the final temperature which can be written as the following:
heat required to bring the melted ice to final temperature = 47.2g * 4.184 J/g⋅∘C *T
heat released to cool water to final temperature = 448g * 4.184 J/g⋅∘C * (45-T)

And then plug back into the equation and solve for the final temperature!