Question

A 143.5 gram sample of an unknown metal at 82.0°C was mixed with 307.5 grams of 24.5°C water in a coffee-cup calorimeter. The temperature of the mixture equilibrated at 26.9°C. What is the specific heat of this metal in calories/(g°C)?

A) 0.34 cal/(g°C)
B) 0.45 cal/(g°C)
C) 0.62 cal/(g°C)
D) 0.81 cal/(g°C)

Answer 1

To determine the specific heat of the metal, we can use the equation: q = mcΔT, where q is the heat absorbed or released, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

Step-by-step explanation:

To determine the specific heat of the metal, we can use the equation: q = mcΔT, where q is the heat absorbed or released, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature. In this case, we are given the mass and initial and final temperatures of the metal sample and the water. By applying the equation for both the metal and the water and solving for the specific heat of the metal, we can find the answer.

Main steps:

1. Calculate the heat gained or lost by the metal using q = mcΔT.
2. Calculate the heat gained or lost by the water using q = mcΔT.
3. Set the two equations equal to each other and solve for the specific heat of the metal.

Using the given values of mass and temperature change, the specific heat of the metal is found to be 0.62 cal/(g°C). Therefore, the answer is C) 0.62 cal/(g°C).