Final answer:
To convert solid lead to liquid lead, the heat required can be calculated by considering the specific heat capacity and heat of fusion of lead. First, we calculate the heat needed to raise the temperature of the solid lead to its melting point. Then, we calculate the heat needed to convert the solid lead to liquid lead. Adding the two values together gives us the total heat required.
Step-by-step explanation:
To calculate the amount of heat needed to convert solid lead to liquid lead, we need to consider the specific heat capacity of lead and the heat of fusion of lead. The specific heat capacity of lead is 0.128 J/g·°C and the heat of fusion of lead is 24.5 J/g.
First, we need to calculate the heat required to raise the temperature of the solid lead from 30.°C to its melting point, which is 327.5°C. We can use the formula:
q = m × c × ΔT
where q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Substituting the values, we get q = 5.0 g × 0.128 J/g·°C × (327.5°C - 30.°C) = 2025.92 J.
Next, we need to calculate the heat required to convert the solid lead at its melting point to liquid lead. We can use the formula:
q = m × ΔHf
where q is the heat, m is the mass, and ΔHf is the heat of fusion.
Substituting the values, we get q = 5.0 g × 24.5 J/g = 122.5 J.
Finally, we add the two values together to get the total heat required: 2025.92 J + 122.5 J = 2148.42 J.
Therefore, the amount of heat that must be added to 5.0 g of solid lead at 30.°C to convert it to liquid lead at the melting point is approximately 2148.42 J.