Question

In a calorimetry experiment, an unknown metal with a mass of 27.4 g that has been in

heated to a temperature of 94.0 °C is placed in a coffee cup calorimeter containing 79.8
g of water initially at a temperature of 22.6 °C. After the water and metal have reached
thermal equilibrium, the final temperature reading of the calorimeter is 28.7 °C.
Calculate the specific heat of the unknown metal in J/gºC.

Answer 1

To calculate the specific heat of the unknown metal, use the formula q_metal = -q_water. The specific heat of the metal can be found by rearranging the equation and plugging in the given values. In this case, the specific heat of the unknown metal is 0.970 J/gºC.

Step-by-step explanation:

To calculate the specific heat of the unknown metal, we can use the formula:

qmetal = - qwater

where qmetal is the heat absorbed by the metal and qwater is the heat released by the water. The heat released by the water can be calculated using the equation:

qwater = mwater * Cwater * ΔT

where mwater is the mass of the water, Cwater is the specific heat of water, and ΔT is the change in temperature of the water.

Plugging in the given values, we can solve for Cmetal:

qwater = (79.8g) * (4.18 J/gºC) * (28.7ºC - 22.6ºC)

qwater = 1662.24 J

Now, using the fact that qmetal = -1662.24 J, we can solve for Cmetal:

qmetal = mmetal * Cmetal * ΔT

-1662.24 J = (27.4g) * Cmetal * (28.7ºC - 94.0ºC)

Cmetal = -1662.24 J / (27.4g * (-65.3ºC))

Cmetal = 0.970 J/gºC

Therefore, the specific heat of the unknown metal is 0.970 J/gºC.