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 82?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 17?C. Assume no heat loss to the surroundings.

Express your answer using two significant figures.

Explanation / Answer

Latent Heat of CO2(dry ice) = Ld = 572.2 KJ/Kg

Heat capacity of Water = Cw = 4.2 KJ/(Kg C)

Density of Water = Dw = 0.97 Kg/Litre(approx)

Volume of water = Vw = 15 litres

Temp Change = DT = 82-17 = 65 C

Mass of dry ice = Md = ?

Therefore balancing the energy, we get

Md * Ld = Vw * Cw * Dw * DT

therefore we get , Md = 6.9 Kg (Ans)

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