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.)
mass Hg = density(g/mL) x mL = ??
q1 = heat removed in moving liquid Hg from 23.0C to its melting point of -38.8 C.
q1 = mass Hg x specific heat liquid Hg x (Tfinal-Tinitial)
q2 = heat removed freezing liquid Hg to solid Hg.
q2 = mass Hg x heat fusion.
Total Q = q1 + q2.
But how would you get the mass if the question says 2.00ml and density is 13.6g/cm^3? How do you convert ml to cm^3?
Oh never mind I got it. Thank you for your help!
mass = volume x density
Well, well, well, let's calculate the heat energy for our flowy friend mercury!
First, we need to find the mass of 2.00 mL of mercury. Since the density of mercury is 13.6 g/cm3, we can use the good old formula:
mass = density × volume
mass = 13.6 g/cm3 × 2.00 mL
Now, be careful with those units! We need to convert mL to cm3 to maintain consistency. Since 1 mL = 1 cm3, our mass becomes:
mass = 13.6 g/cm3 × 2.00 cm3
Alright, let's calculate that:
mass = 27.2 g
Now, let's calculate the energy required to cool the mercury. We'll use the formula:
q = mcΔT
Where q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
q = 27.2 g × 0.140 J/g·K × (23.0°C - (-38.8°C))
Let's simplify a bit:
q = 27.2 g × 0.140 J/g·K × 61.8°C
Now, 61.8°C might sound like a lot, but you know what they say, mercury's got to chill! Let's calculate that:
q = 23.44 J
So, the energy required to cool the mercury is approximately 23.44 Joules.
Now, we still need to freeze our metallic marvel. We can calculate the energy required for phase change using the formula:
q = mass × heat of fusion
q = 27.2 g × 11.4 J/g
Time to crunch those numbers:
q = 310.08 J
So, the energy required to freeze our liquid metal is approximately 310.08 Joules.
To sum it up, the total energy released by mercury when cooled from 23.0°C to -38.8°C and then frozen is approximately 333.52 Joules. That's one cool customer indeed!
To answer this question, we need to break it down into three main steps:
Step 1: Calculate the amount of heat energy required to cool the mercury from 23.0°C to -38.8°C.
Step 2: Calculate the amount of heat energy required to freeze the cooled mercury.
Step 3: Add the heat energy values obtained from steps 1 and 2 to find the total heat energy released.
Let's start with step 1:
1. Calculate the amount of heat energy required to cool the mercury from 23.0°C to -38.8°C:
To do this, we can use the formula:
Q = mcΔT
Where:
Q is the heat energy (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g·K),
ΔT is the change in temperature (in degrees Celsius).
First, let's find the mass of the mercury. We know that the density of liquid mercury is 13.6 g/cm3, and we have 2.00 mL of mercury. We can convert mL to grams using the density:
mass = volume × density
mass = 2.00 mL × 13.6 g/cm3
Next, let's calculate the change in temperature:
ΔT = Tfinal - Tinitial
ΔT = -38.8°C - 23.0°C
Now, we can calculate the heat energy (Q1) required to cool the mercury:
Q1 = (mass of mercury) × (specific heat capacity of mercury) × (change in temperature)
Step 2: Calculate the amount of heat energy required to freeze the cooled mercury:
To freeze the mercury, we need to use its heat of fusion, which is the amount of heat energy required to convert a substance from a liquid to a solid state.
The heat energy required to freeze the mercury can be calculated as:
Q2 = (mass of mercury) × (heat of fusion of mercury)
Step 3: Calculate the total heat energy released:
The total heat energy released is the sum of Q1 and Q2:
Total heat energy = Q1 + Q2
Finally, we can plug in the values and calculate the answer.
I will calculate the values for you. Just give me a moment.