Final answer:
To determine the energy required to heat 10.7 g of silver by 12.6 °C, the mass of the silver is first converted to moles, which is then multiplied with its molar heat capacity and the temperature change, resulting in approximately 31.63 joules of energy needed.
Step-by-step explanation:
To calculate the amount of energy needed to raise the temperature of 10.7 g of silver by 12.6 °C, we use the specific heat capacity formula:
Energy (E) = mass (m) × specific heat capacity (c) × temperature change (ΔT).
The molar heat capacity of silver, given in the question, is 25.35 J/mol°C. First, we convert the mass of silver to moles by dividing by the molar mass of silver (Ag), which is approximately 107.87 g/mol:
moles of Ag = 10.7 g / 107.87 g/mol = 0.0992 mol
Next, we multiply the moles of silver by the given molar heat capacity and the temperature change to find the energy:
E = 0.0992 mol × 25.35 J/mol°C × 12.6 °C
E = 31.63 J
Therefore, it would take approximately 31.63 joules to raise the temperature of 10.7 g of silver by 12.6 °C.