Achieve HW #10

[Shane_Yu_3K]

Hello,

Can someone explain how to solve this problem?

An ice cube with a mass of 52.0 g at 0.0 ∘C is added to a glass containing 431 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, deltaH∘fus , of water is 6.01×103 J/mol . Assume that no energy is transferred to or from the surroundings.

Thank you!

[Brian Diehl 2B]

In this system, the ice cube has to melt completely before a temperature change on the sample occurs. Therefore, the heat of fusion must be taken into account in addition to the heat absorbed by the ice from the surrounding water molecules.
The basic frame of our system is:
q_fus + q_sample = -q_water
Which can be broken down into:
ΔH_fus + m_sampleC_sΔT_sample = -m_waterC_sΔT_water

You can calculate the heat of fusion by finding the moles of water in the ice sample and then multiplying this value by the standard enthalpy of fusion. By plugging in the respective mass values, the specific heat of liquid water, and the initial temperature values given in the problem, you can then solve for the final temperature value for the system at equilibrium.

Hope this helps!