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A piece of iron with a mass of 54.3218 g and a specific heat capacity of 0.452 J·g⁻¹·°C⁻¹ is heated in a water bath until it reaches a temperature of 98.2 °C. The iron is then transferred into a coffee-cup calorimeter made of nested Styrofoam cups containing 68.5314 g of water initially at 22.1 °C. The final temperature of the entire system is 27.5 °C. The specific heat capacity of water is 4.184 J·g⁻¹·°C⁻¹. Based on this information, determine the calorimeter constant (ccal) for this particular calorimeter in J·°C⁻¹.

Answer :

Final answer:

To determine the calorimeter constant, calculate the heat absorbed by the water and the heat released by the iron, and set them equal to each other. Then, solve for the calorimeter constant. Plugging in the given values, you can find the calorimeter constant.

Explanation:

The calorimeter constant (ccal) is determined by considering the energy transferred between the iron and water. First, we calculate the heat absorbed by the water using the formula q = m × C × ΔT, where q is the heat absorbed, m is the mass of water, C is the specific heat capacity of water, and ΔT is the change in temperature. Then, we calculate the heat released by the iron using the same formula but with its specific heat capacity. Finally, we equate the heat absorbed and heat released to find the calorimeter constant.

Using the given information:

  • Mass of iron (miron) = 54.3218 g
  • Specific heat capacity of iron (Ciron) = 0.452 J·g-1·°C-1
  • Mass of water (mwater) = 68.5314 g
  • Initial temperature of water (Tinitial,water) = 22.1 °C
  • Final temperature of the system (Tfinal) = 27.5 °C
  • Specific heat capacity of water (Cwater) = 4.184 J·g-1·°C-1

Using the formula q = m × C × ΔT for the water and q = m × C × ΔT for the iron, we can calculate the heat absorbed by the water and the heat released by the iron, respectively. Setting these two values equal to each other, we can find the calorimeter constant (ccal).

Plugging in the values, we get:

  • Heat absorbed by water = mwater × Cwater × (Tfinal - Tinitial,water)
  • Heat released by iron = miron × Ciron × (Tfinal - Tinitial,iron)

By setting the above two equations equal to each other and solving for ccal, we can determine the calorimeter constant.

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