DrBob222, HELP!

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

ratio @DrBob222

To calculate the heat energy released when liquid mercury is converted to solid mercury, we need to consider two steps: heating the liquid mercury to its melting point, and then solidifying the mercury at its melting point.

Step 1: Heating the liquid mercury to its melting point
To calculate the heat energy required to raise the temperature of the liquid mercury from 25.00 °C to its melting point, we can use the equation:

q1 = m * C * ΔT

Where:
q1 is the heat energy needed (in joules)
m is the mass of the mercury (in grams)
C is the heat capacity of liquid mercury (in J/mol*K)
ΔT is the change in temperature (in Kelvin)

Given:
Mass of mercury (m) = 29.7 g
Heat capacity of liquid mercury (C) = 28.0 J/mol*K
Initial temperature (T1) = 25.00 °C = 25.00 + 273.15 = 298.15 K
Melting point of mercury (Tm) = 234.32 K

To determine ΔT, we subtract the initial temperature (T1) from the melting point (Tm):

ΔT = Tm - T1

Substituting these values into the equation, we get:

ΔT = 234.32 K - 298.15 K = -63.83 K

Now we can calculate q1:

q1 = m * C * ΔT = 29.7 g * (1 mol / 200.59 g) * 28.0 J/mol*K * -63.83 K

First, we convert the mass of mercury to moles using the molar mass of mercury, which is 200.59 g/mol. Then, we multiply it by the heat capacity and ΔT.

Step 2: Solidifying the mercury at its melting point
To calculate the heat energy released during solidification, we use the equation:

q2 = ΔH * n

Where:
q2 is the heat energy released (in joules)
ΔH is the enthalpy of fusion (in J/mol)
n is the number of moles of mercury

Given:
Enthalpy of fusion (ΔH) = 2.29 kJ/mol = 2.29 * 10^3 J/mol
Number of moles of mercury (n) can be calculated using:

n = m / (molar mass) = 29.7 g / 200.59 g/mol

Substituting the values into the equation, we get:

q2 = ΔH * n = 2.29 * 10^3 J/mol * (29.7 g / 200.59 g/mol)

Finally, to calculate the total heat energy released, we add q1 and q2:

Total heat energy released = q1 + q2

I hope this explanation helps you understand the calculation process. Remember to substitute the values accurately and perform the proper unit conversions to get the correct answer.

q1 = heat released in cooling Hg from +25C to its melting point which is -83.3C.

q1 = mass Hg x specific heat Hg x (Tfinal-Tinitial)
Tfinal is -83.3. Ti is 25C.

q2 = heat released on freezing Hg.
q2 = mass Hg x heat fusion..
Total q = q1 + q2.
You have given specific heat in kJ/mol and J/mol; therefore, you must convert grams Hg to mols Hg.mol = grams/molar mass.