Final answer:
To determine the specific heat of the metal, use the formula q = mcΔT. With the values given, the specific heat capacity of the metal is calculated to be 0.5235 J/g°C.
Step-by-step explanation:
To calculate the specific heat of the metal, we can use the formula q = mcΔT, where q is the heat absorbed or released in joules, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature. Plugging in the values provided, we have 67.2 J = 10.7 g * c * (25.0 °C - 13.0 °C). Simplifying, we get 67.2 J = 10.7 g * c * 12.0 °C.
To solve for c, the specific heat capacity, we rearrange the equation to get c = q / (mΔT). So, c = 67.2 J / (10.7 g * 12.0 °C). Calculating this gives us c = 67.2 J / 128.4 g°C, which simplifies to c = 0.5235 J/g°C. Therefore, the specific heat of the metal is 0.5235 J/g°C.