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A chemist is performing a calorimetric experiment to determine the specific heat capacity of an unknown metal. They heat a 50.0 g sample of the metal to 100.0°C and then place it into 75.0 g of water initially at 20.0°C. The final equilibrium temperature of the water and metal mixture is 25.5°C. The specific heat capacity of water is 4.18 J/(g°C). Which of the following calculations correctly determines the specific heat capacity of the metal?
- A(75.0 g * 4.18 J/(g°C) * (100.0°C - 25.5°C)) / (50.0 g * (25.5°C - 20.0°C))
- B(75.0 g * 4.18 J/(g°C) * (25.5°C - 20.0°C)) / (50.0 g * (100.0°C - 25.5°C))
- C(50.0 g * 4.18 J/(g°C) * (25.5°C - 20.0°C)) / (75.0 g * (100.0°C - 25.5°C))
- D(50.0 g * (100.0°C - 25.5°C)) / (75.0 g * 4.18 J/(g°C) * (25.5°C - 20.0°C))
Show answer & explanationAnswer & explanation
Correct answer: B. (75.0 g * 4.18 J/(g°C) * (25.5°C - 20.0°C)) / (50.0 g * (100.0°C - 25.5°C))
In calorimetry, the heat lost by the hotter substance (metal) equals the heat gained by the colder substance (water). The formula for heat transfer is Q = mcΔT. Therefore, (m_metal * c_metal * ΔT_metal) = (m_water * c_water * ΔT_water). Rearranging to solve for c_metal gives c_metal = (m_water * c_water * ΔT_water) / (m_metal * ΔT_metal).
Why the other options are wrong
- A. This incorrectly places the metal's mass and temperature change in the denominator and uses the metal's temperature change for water.
- C. This incorrectly uses the metal's mass and specific heat for the water's heat gain.
- D. This incorrectly places the metal's specific heat (which is what we are solving for) in the numerator and inverts the water's heat calculation.
Calorimetry (Specific Heat)
The science of measuring the heat of chemical reactions or physical changes. In determining specific heat, it relies on the principle that heat lost by one substance equals heat gained by another in an isolated system.
- Q = mcΔT (Heat = mass * specific heat * change in temperature).
- Heat lost = -Heat gained (or Heat lost = Heat gained for magnitude).
- Specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.
Memory trick: MCAT for Heat, Lost Equals Gained