Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublim

Question

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the following equation: CO2(s)CO2(g). When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 liters of water heated to 87 C

Calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 12 C. Assume no heat loss to the surroundings.

Explanation / Answer

15 liters H2O = 15*1000g = 15,000 grams
heat needed to raise one gram water, one degree celsius = 4.18J

4.18J * 15,000g = 62,700J = 62.7kJ needed per degree C

87 - 12 = 75C temp drop needed

62.7 kJ * 69C = 4702.5kJ needed from CO2

enthalpy of CO2 = 393.51kJ/mol
CO2 = 44g/mol = 22.73 moles/kg
393.51kJ/mol * 22.73 moles/kg
= 8,943.4 kJ/kg

4702.5kJ / 8,943.4 kJ/kg = .525 kg of CO2 needed

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