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A piece of solid lead weighing 45.2 g at a temperature of 317 °C is placed in 452 g of liquid leadat a temperature of 371 °C. After a while, the solid melts and a completely liquid sample remains. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings. The enthalpy of fusion of solid lead is ΔHfus = 4.77 kJ/mol at its melting point of 328 °C, and the molar heat capacities for solid and liquid lead are Csolid = 26.9 J/mol K and Cliquid = 28.6 J/mol K.

Question


A piece of solid lead weighing 45.2 g at a temperature of 317 °C is placed in 452 g of liquid leadat a temperature of 371 °C. After a while, the solid melts and a completely liquid sample remains. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings. 

The enthalpy of fusion of solid lead is ΔHfus = 4.77 kJ/mol at its melting point of 328 °C, and the molar heat capacities for solid and liquid lead are Csolid = 26.9 J/mol K and Cliquid = 28.6 J/mol K.

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Step 1

First, the heat required to melt 45.2 grams of lead is calculated as follows,

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Step 2

Heat released by the liquid lead is then calculated as shown below,

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Step 3

The given condition says that no heat is lost to surroundings, therefore, heat rel...

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