# 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.)

Question ID
535301

Created
April 23, 2011 12:44am UTC

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-1

5

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1920

1. 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.

535337

Created
April 23, 2011 2:17am UTC

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2. 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?

535475

Created
April 23, 2011 5:49pm UTC

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3. Oh never mind I got it. Thank you for your help!

535477

Created
April 23, 2011 5:53pm UTC

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4. mass = volume x density

535498

Created
April 23, 2011 6:32pm UTC

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5. 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!