Q. 3.104 - An Introduction to General, Organic, and Biological Chemistry

Question

A $125 g$piece of metal is heated to $288°C$ and dropped into $85.0 g$ of water at $12.0°C$. The metal and water come to the same temperature of $24°C$. What is the specific heat, in $\mathrm{J}/\mathrm{g}{}^{\circ }\mathrm{C}$, of the metal?

Step-by-Step Solution

Answer

The heat gained by water is $4267.68 \mathrm{J}$.

Specific heat of copper is $0.1293 \mathrm{J}/\mathrm{g}°\mathrm{C}$.

Step 1: Given Information

Given data:

Mass of metal is$125 g$.

Temperature of the copper metal is$288°C$.

Mass of water is$85 g$.

Temperature of the water is$12.0°C$.

Final temperature of water and metal is$24.0 °C$.

Step 2: Calculation of heat gained by water

 The heat gained by water is equal to the heat lost by metal.

The equation to calculate the heat gained by water is, 

$Heat=mass\times temperature change\times specific heat$

       $\mathrm{q}={\mathrm{mC}}_{\mathrm{p}}\left(\Delta \mathrm{T}\right)$     

Calculate the temperature change as follows:

The temperature change$=\Delta \mathrm{T}$

                                         $= 24°C-12°C$

                                         $=12°C$

Calculate the heat gained by water as follows:

$\mathrm{q}=(85.0 \mathrm{g})\times \left(4.184 \mathrm{J}/\mathrm{g}°\mathrm{C}\right)\times \left(12°\mathrm{C}\right)$

  $=4267.68 \mathrm{J}$

Step 4: Calculation of specific heat of copper.

Calculate the temperature change as follows:

The temperature change$=\Delta \mathrm{T}$

                                          $=288°\mathrm{C}-24°\mathrm{C}$

                                          $=264°\mathrm{C}$     

Calculate the heat gained by water as follows:

$q=\left(125g\right)\times (specific heat of copper)\times (264°C)$

Calculate the specific heat of copper as follows:

Specific heat of copper$=\frac{q}{m\times \Delta T}$

                                      $=\frac{4267.68 \mathrm{J}}{125\times 264}$

                                      $=0.1293 \mathrm{J}/\mathrm{g}°\mathrm{C}$                         

Therefore, specific heat of copper is

$0.1293 \mathrm{J}/\mathrm{g}°\mathrm{C}$