Question 10, Achieve Assignment 3/4 [ENDORSED]

[Sara Bakhsheshy 2B]

Hi there!
I'm struggling to figure out how to solve this problem on the Achieve assignment on thermochemistry. The question asks:

An ice cube with a mass of 53.8 g at 0.0 ∘C is added to a glass containing 376 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.

Does anyone know how to solve this?
Thank you!

[Chem_Mod]

Use the hint in Achieve I gave for this question:

Express the total heat exchange as a single large formula, where the final temperature, T_f, is the only unknown value.

heat required to melt ice + heat required to bring the 53.0 g of melted ice to the final temperature = heat released that cools 417 g of water to the final temperature

The standard enthalpy of fusion, ΔH∘_f, is used to calculate the heat required to melt the ice.

The heat flow in the other two terms of the equation can be calculated via the equation:

q = m C (T_f − T_i)

where T_f is the final temperature and T_i is the initial temperature. Solve for T_f.

See the detailed hints in Achieve.