How much energy is required to raise the temperature of 217 g of solid mercury at its freezing point to mercury vapor at its boiling point.

To calculate the energy required to raise the temperature of a substance from its freezing point to its boiling point, we need to consider two steps: 1) heating the substance from its freezing point to its melting point, and 2) converting the substance from its liquid state to its vapor state.

Step 1: Heating from freezing point to melting point.
To calculate the energy required to raise the temperature of solid mercury from its freezing point to its melting point, we use the formula:
E1 = mass × specific heat capacity × ΔT,
where
E1 is the energy required,
mass is the mass of the mercury (217 g),
specific heat capacity is the specific heat capacity of solid mercury (0.138 J/g°C), and
ΔT is the change in temperature, which is the difference between the melting point and freezing point of mercury (melting point: -38.83°C, freezing point: -38.83°C).

E1 = 217 g × 0.138 J/g°C × (-38.83 - (-38.83))°C.

Step 2: Melting to boiling.
To calculate the energy required to convert liquid mercury at its melting point to mercury vapor at its boiling point, we use the formula:
E2 = mass × heat of fusion + mass × specific heat capacity × ΔT,
where
E2 is the energy required,
mass is the mass of the mercury (217 g),
heat of fusion is the heat of fusion of mercury (11.79 kJ/mol = 65.84 J/g),
specific heat capacity is the specific heat capacity of liquid mercury (0.139 J/g°C), and
ΔT is the change in temperature, which is the boiling point of mercury (boiling point: 356.73°C) minus the melting point (-38.83°C).

E2 = 217 g × 65.84 J/g + 217 g × 0.139 J/g°C × (356.73 - (-38.83))°C.

Finally, the total energy required is the sum of E1 and E2:
Total energy = E1 + E2.

Calculating this should give you the energy required to raise the temperature of 217 g of solid mercury at its freezing point to mercury vapor at its boiling point.