Final answer:
The specific heat of an unknown metal that absorbs 652.1 J to raise its temperature of a 55.5 g sample from 12.92 °C to 64.76 °C is calculated to be 0.229 J/g°C.
Step-by-step explanation:
To calculate the specific heat of an unknown metal, we use the formula q = mcΔT, where q is the heat in joules, m is the mass in grams, c is the specific heat capacity in J/g°C, and ΔT is the change in temperature in Celsius.
The mass m of the metal is already given as 55.5 g. The heat added, q, is 652.1 J.
The change in temperature can be calculated from the given initial and final temperatures.
ΔT is the final temperature (64.76 °C) minus the initial temperature (12.92 °C), which is 51.84 °C.
Now we can solve for the specific heat capacity c by rearranging the formula to c = q / (mΔT).
Substituting the known values we get c = 652.1 J / (55.5 g × 51.84 °C) = 0.229 J/g°C.
The specific heat of the metal is 0.229 J/g°C.