Final answer:
The amount of heat transfer needed to raise the temperature and melt 0.500 kg of lead, starting from 25.0°C, is 13.7 kJ.
Step-by-step explanation:
The heat transfer required to raise the temperature and melt 0.500 kg of lead can be calculated using the equation:
Q = mcΔT + mL
Where:
Q is the heat transfer
m is the mass of the lead (0.500 kg)
c is the specific heat capacity of lead (0.128 J/g°C)
ΔT is the change in temperature (the final temperature of the lead minus the initial temperature)
L is the heat of fusion of lead (24.5 kJ/mol)
To calculate ΔT, we need to know the final temperature of the lead. Let's assume it is the melting point of lead, which is 327.5°C. Therefore, ΔT = 327.5°C - 25.0°C = 302.5°C.
Plugging these values into the equation, we get:
Q = (0.500 kg)(0.128 J/g°C)(302.5°C) + (0.500 kg)(24.5 kJ/mol)
Solving this equation gives us:
Q = 13.7 kJ
The amount of heat transfer needed to raise the temperature and melt 0.500 kg of lead, starting from 25.0°C, is 13.7 kJ. Therefore, the correct option is (a) 13.7 kJ.