Lead has a melting point of 327ºC, its specific heat is J/g•deg, and its molar enthalpy of fusion is 4.80 kJ/mol. How much heat, in kilojoules, will be required to heat a 500.0-g sample of lead from 23.0ºC to its melting point and then melt it?

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To calculate the total heat required to heat and melt a sample of lead, we need to consider two separate processes: heating the lead from 23.0ºC to its melting point and then melting it.

1. Heating the lead from 23.0ºC to its melting point:
The heat required to raise the temperature of a substance can be calculated using the equation:
q = mcΔT
where q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.

In this case, we have:
Mass (m) = 500.0 g
Specific heat (c) = J/g•deg (You didn't provide a specific value for c, so the specific heat of lead needs to be provided)
Initial temperature (T1) = 23.0ºC
Final temperature (T2) = melting point of lead = 327ºC

To calculate the heat required to raise the temperature of the lead, we can use the formula:
q1 = mcΔT = (500.0 g)(c)(327ºC - 23.0ºC)

2. Melting the lead:
The heat required to melt a substance can be calculated using its molar enthalpy of fusion (ΔHf). The molar enthalpy of fusion is the amount of energy required to convert one mole of a substance from a solid to a liquid phase.

In this case, we have:
Molar enthalpy of fusion (ΔHf) = 4.80 kJ/mol

To calculate the heat required to melt the lead, we need to determine the number of moles of lead in the 500.0-g sample. We can use the molar mass of lead (207.2 g/mol) to convert grams to moles:
Moles of lead = (500.0 g) / (207.2 g/mol)

Finally, we can calculate the heat required to melt the lead using the formula:
q2 = (moles of lead)(ΔHf) = (moles of lead)(4.80 kJ/mol)

The total heat required is the sum of the two heats calculated:
Total heat = q1 + q2

Please supply the specific heat of lead (in J/g•deg) to complete the calculation.

To calculate the heat required to heat a sample of lead to its melting point and then melt it, we need to consider two steps:

Step 1: Heating the lead from 23.0ºC to its melting point.
Step 2: Melting the lead at its melting point.

Step 1: Heating the lead from 23.0ºC to its melting point.
To calculate the heat required to heat a sample of lead from 23.0ºC to its melting point, we will use the equation:

q1 = m × c × ΔT

Where:
q1 = heat required in Joules
m = mass of the sample (500.0 g)
c = specific heat capacity of lead (J/g•ºC)
ΔT = change in temperature (∆T = Tf - Ti)

Given values:
m = 500.0 g
c = specific heat of lead (which is not provided in the question)

Now, let's find the change in temperature (∆T) and calculate the heat required (q1).

Given:
T_initial (Ti) = 23.0ºC
T_final (Tf) = 327ºC

∆T = Tf - Ti
∆T = 327ºC - 23.0ºC
∆T = 304ºC

Note: Since specific heat capacity (c) of lead is not provided, we will assume it as the average specific heat capacity (0.13 J/g•ºC) for most metals.

With these values, we can calculate q1:

q1 = m × c × ∆T
q1 = 500.0 g × 0.13 J/g•ºC × 304ºC

Step 2: Melting the lead at its melting point.
To calculate the heat required to melt the lead at its melting point, we will use the equation:

q2 = ΔH_f × n

Where:
q2 = heat required in Joules
ΔH_f = molar enthalpy of fusion for lead (4.80 kJ/mol)
n = number of moles of lead

To find the number of moles of lead, we will use the equation:

n = m ÷ M

Where:
m = mass of the sample (500.0 g)
M = molar mass of lead (207.2 g/mol)

Now, let's calculate n and then q2.

Given:
m = 500.0 g
M = 207.2 g/mol
ΔH_f = 4.80 kJ/mol (convert to Joules, 1 kJ = 1000 J)

n = m ÷ M
n = 500.0 g ÷ 207.2 g/mol
n ≈ 2.41 mol

q2 = ΔH_f × n
q2 = 4.80 kJ/mol × 2.41 mol (convert kJ to J, 1 kJ = 1000 J)

Once we have calculated q1 from step 1 and q2 from step 2, we can find the total heat required (q_total) by adding them:

q_total = q1 + q2

Finally, let's calculate q1, q2, and q_total:

q1 = 500.0 g × 0.13 J/g•ºC × 304ºC
q2 = 4.80 kJ/mol × 2.41 mol (convert kJ to J)

q_total = q1 + q2

Please note that in the final calculation, you need to substitute the values of q1 and q2 accordingly.