Question

An 80.0 g sample of metal, initially at 96.0°C, is placed into 150. g of water initially at 26.0°C in a calorimeter. The final temperature of the water is 28.1°C. What is the identity of the metal? (The specific heat of water is 4.18 J/g･°C.)

Answer 1

To determine the specific heat and identity of the metal, you need to calculate the heat lost by the metal, using the formula q = mcΔT. By substituting the given values into the equation, you can find the specific heat of the metal. Then, compare the value to known values of specific heat for different metals to determine the identity of the metal.

Step-by-step explanation:

First, we need to calculate the amount of heat lost by the metal, which is equal to the amount of heat gained by the water.

The heat lost by the metal can be calculated using the formula: q = mcΔT, where q is the heat lost, m is the mass of the metal, c is its specific heat, and ΔT is the change in temperature. Assuming the specific heat of water, which is known to be 4.18 J/g·°C, we can rearrange the formula to solve for the specific heat of the metal:

c metal = (q metal) / (m metal * ΔT)

Substituting the given values into the equation, we find that the specific heat of the metal, c metal, is approximately 0.97 J/g·°C.

Now, we can compare the value of the specific heat to known values of specific heat for different metals. By comparing the calculated value to reference values, we can determine that the metal is most likely iron (c iron = 0.46 J/g·°C) or aluminum (c aluminum = 0.897 J/g·°C).