Answer:
First, we need to calculate how much heat was lost by the metal as it cooled from 100°C to the final temperature (which we will assume is 25°C, since we are not given the exact temperature). The formula for calculating heat is:
q = mcΔT
where q is heat, m is mass, c is specific heat capacity, and ΔT is the change in temperature.
The metal lost heat in this process, so the value of q will be negative. We can rearrange the formula to solve for the mass of the metal:
m = q / (cΔT)
We are given the specific heat capacity of the metal (0.475 J/gºC), the initial temperature (100°C), and the final temperature (25°C). We also know that the heat lost by the metal (q) must be equal to the heat gained by the water. We can use the formula:
qmetal = -qwater
to relate the heat lost by the metal to the heat gained by the water. We know the specific heat capacity of water (4.184 J/gºC), the volume of water (199.0 mL, or 199.0 g), and the initial and final temperatures of the water (22°C and 25°C). We can use the formula:
qwater = mcΔT
to calculate the heat gained by the water. Plugging in the given values, we get:
qwater = (199.0 g)(4.184 J/gºC)(25°C - 22°C) = 2503.8 J
Therefore, the heat lost by the metal must be:
qmetal = -2503.8 J
Now we can use the formula for mass to calculate the mass of the metal:
m = q / (cΔT)
m = (-2503.8 J) / (0.475 J/gºC)(100°C - 25°C)
m = 35.6 g
Therefore, the mass of the metal is 35.6 g.