Question

A 32.0-g sample of an unknown metal at 99°C was placed in a constant-pressure calorimeter containing 70.0 g of water at 24.0°C. The final temperature of the system was found to be 28.4°C. Calculate the specific heat of the metal. (The heat capacity of the calorimeter is 14.4 J/°C.).

____J/g °C

Answer 1

To find the specific heat of the unknown metal, we use the principle of conservation of energy to equate the heat lost by the metal to the heat gained by the water and the calorimeter. By putting the given values into the formula Q_metal = - (Q_water + Q_calorimeter), we solve for the specific heat of the metal (c_metal).

Step-by-step explanation:

To calculate the specific heat of the unknown metal, we'll assume no heat loss to the environment and apply the principle of conservation of energy which states that the heat lost by the metal will be equal to the heat gained by the water and the calorimeter. The formula for heat transfer (Q) is mass (m) times specific heat capacity (c) times the change in temperature (ΔT). We use the formula:

Qmetal = Qwater + Qcalorimeter

For the water:

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For the calorimeter:

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For the metal:

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By combining and rearranging the above equations, we can solve for cmetal.

Qmetal = - (Qwater + Qcalorimeter)

This results in:

cmetal = - (mwater * cwater * ΔTwater + Ccalorimeter * ΔTcalorimeter) / (mmetal * ΔTmetal)