Calculate the heat energy released when 29.7 g of liquid mercury at 25.00 °C is converted to solid mercury at its melting point.

Constants for mercury at 1 atm: Heat capacity of Hg (l) 28.0 J/Mol*K, Melting pt 234.32 k, and enthalpy of fusion 2.29 kg/mol

To calculate the heat energy released when liquid mercury at 25.00 °C is converted to solid mercury at its melting point, we need to follow these steps:

Step 1: Determine the temperature change:
The initial temperature of the liquid mercury is 25.00 °C, and the melting point of mercury is 234.32 K. We need to convert the temperatures to the same scale (Kelvin):
Initial temperature (T1) = 25.00 °C + 273.15 = 298.15 K
Final temperature (T2) = 234.32 K (melting point)

Step 2: Calculate the heat released during cooling:
The heat released during cooling can be calculated using the formula:

Q1 = m * C * ΔT
where:
Q1 = heat released during cooling (in joules)
m = mass of the substance (in grams)
C = heat capacity of the substance (in J/mol*K)
ΔT = change in temperature (final temperature - initial temperature)

In this case, the mass of mercury (m) is given as 29.7 g, and the heat capacity of mercury (C) is given as 28.0 J/mol*K. We have already calculated the change in temperature as ΔT = T2 - T1.

Q1 = 29.7 g * (1 mol/200.59 g) * 28.0 J/mol*K * (234.32 K - 298.15 K)

Step 3: Calculate the heat released during fusion:
The heat released during fusion can be calculated using the formula:

Q2 = n * ΔH_fus
where:
Q2 = heat released during fusion (in joules)
n = number of moles of the substance
ΔH_fus = enthalpy of fusion (in J/mol)

The number of moles (n) of a substance can be calculated using its molar mass (M) and the given mass (m) with the formula:

n = m/M

In this case, the molar mass of mercury (M) is given as 200.59 g/mol and the given mass (m) is 29.7 g. The enthalpy of fusion (ΔH_fus) is given as 2.29 kJ/mol, which needs to be converted to joules.

Q2 = (29.7 g)/(200.59 g/mol) * (2.29 kJ/mol * 1000 J/kJ)

Step 4: Calculate the total heat energy released:
To find the total heat energy released when liquid mercury at 25.00 °C is converted to solid mercury at its melting point, add the heat released during cooling (Q1) and the heat released during fusion (Q2):

Total heat energy released = Q1 + Q2

I'll calculate the result for you now.

See below.