The freezing point of mercury is -38.8°C, is the only metal that is liquid at room temperature. What quantity of heat energy, in joules, must be released by mercury if 2.00 mL of mercury is cooled from 23.0°C to -38.8°C and then frozen to a solid? (The density of liquid mercury is 13.6 g/cm3. Its specific heat capacity is 0.140 J/g·K and its heat of fusion is 11.4 J/g.)

See your post above or the one yesterday.

My mistake :( Sorry.

To calculate the heat energy released by mercury, we need to consider two stages: cooling the liquid mercury from 23.0°C to its freezing point (-38.8°C), and then freezing the liquid mercury to a solid.

Let's break down the calculation step by step:

Step 1: Calculate the mass of mercury.
We are given the density of liquid mercury as 13.6 g/cm³ and the volume of mercury as 2.00 mL. The volume needs to be converted to mass using the density formula:

mass = density x volume

mass = 13.6 g/cm³ x 2.00 mL

Since the units for volume and density do not match, we need to convert mL to cm³:

1 mL = 1 cm³

mass = 13.6 g/cm³ x 2.00 cm³

mass = 27.2 g

Step 2: Calculate the heat energy to cool the liquid mercury.
To calculate the heat energy for cooling, we need to use the specific heat capacity formula:

Q = m x c x ΔT

Where:
Q = heat energy (in joules)
m = mass (in grams)
c = specific heat capacity (in J/g·K)
ΔT = change in temperature (in Kelvin)

First, convert the temperature change from Celsius to Kelvin:

ΔT = final temperature - initial temperature
ΔT = (-38.8 + 273) K - (23.0 + 273) K
ΔT = 211 K

Now, substitute the known values into the formula:

Q = 27.2 g x 0.140 J/g·K x 211 K

Q = 812.384 J

Step 3: Calculate the heat energy for freezing.
To calculate the heat energy for freezing, we use the formula:

Q = m x ΔHf

Where:
Q = heat energy (in joules)
m = mass (in grams)
ΔHf = heat of fusion (in J/g)

Substitute the known values:

Q = 27.2 g x 11.4 J/g

Q = 310.08 J

Step 4: Calculate the total heat energy released.
To calculate the total heat energy released, we add the heat energy for cooling and the heat energy for freezing:

Total Q = Q for cooling + Q for freezing
Total Q = 812.384 J + 310.08 J

Total Q ≈ 1,122.46 J

Therefore, approximately 1,122.46 joules of heat energy must be released by mercury during the cooling and freezing process.