Final answer:
To find the specific heat capacity of the metal, use the heat transfer formula considering the mass and temperature change for both metal and water, assuming the heat lost by the metal equals the heat gained by the water. Solve for the metal's heat capacity by rearranging the equality of heat transfer equations for both substances.
Step-by-step explanation:
To calculate the specific heat capacity of the unknown metal, we need to use the formula for heat transfer Q = mcΔT, where 'm' is the mass, 'c' is the specific heat capacity, and ΔT is the change in temperature. Assuming no heat loss to the surroundings, the heat lost by the metal will be equal to the heat gained by the water. Using the given values, the equation for the metal (Q_metal = m_metal * c_metal * ΔT_metal) can be set equal to the equation for the water (Q_water = m_water * c_water * ΔT_water) and solved for c_metal.
The mass of the water can be found by converting the volume of the water (125 mL) to grams, which is similar to its mass in grams since the density of water is approximately 1 g/mL. We then get m_water = 125 g. The specific heat capacity of water, c_water, is commonly accepted as 4.18 J/(g°C). With the mass of the metal m_metal being 134.0 g, and the initial and final temperatures provided, we can rearrange and solve for the unknown c_metal.
For the metal: Q_metal = -Q_water
Therefore: m_metal * c_metal * (ΔT_metal) = - m_water * c_water * (ΔT_water)
Given that ΔT_metal = T_initial - T_final_metal and ΔT_water = T_final_water - T_initial_water, this becomes:
134.0 g * c_metal * (91.0 °C - 31.0 °C) = - 125 g * 4.18 J/(g°C) * (31.0 °C - 25.0 °C).
Next, fill in the numbers and solve for c_metal.