Week 3 and 4 Achieve #10

[Alondra Cortes 1F]

An ice cube with a mass of 54.2 g at 0.0 ∘C is added to a glass containing 352 g of water at 45.0 ∘C . Determine the final temperature of the system at equilibrium. The specific heat capacity of water, Hs , 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.

So far, what I've done is set up my equation like this: (54.2g)(4.184 J/g*C)(Tf - 0C) = - (352g)(4.184 J/g*C)(Tf - 45C). But I keep getting the wrong answer. Am I missing anything? I assumed it was probably the energy required to melt the ice, but I'm having trouble figuring out how to calculate that.

Thanks to anyone who helps!

[Ethan Crofut 1E]

Yes, since they give the standard enthalpy of fusion of the ice in J/mol, you use the mass of the ice cube (54.2 g) to calculate the number of moles of H2O in it, then you multiply the enthalpy of fusion by the number of moles to find the amount of energy required to melt the ice. q for the ice will be the sum of the enthalpy of fusion and the expression using heat capacity which you have used already.

[Audrey Hanna]

You did everything right, but on the left side of the equation, you need to add in the energy required to make the ice melt [like quite literally you just add it to the RHS]. Hope this helps!