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 88 C.

Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation. (The Hf for CO2(s) is - 427.4kJ/mol).

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 27 C. Assume no heat loss to the surroundings.

Explanation / Answer

Amount of water = 15.0 L

Density of water = 1..0 g / ml

Therefore 15.0 L water = 15.0 kg of water

1 .00 kg = 1000 g

heat needed to raise one gram water, one degree celsius = 4.18J

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

Temperature difference= 88 C - 27 C

= 61C

62.7 kJ / C * 61C = 3824.7 kJ needed from CO2

The Hf for CO2(s) is - 427.4kJ/mol

Molar mass CO2 = 44g/mol = 22.73 moles/kg

427 kJ/mol * 22.73 moles/kg
= 9704.5 kJ/kg

3824.7 kJ / 9704.5 kJ/kg

= 0.394 kg of CO2 needed

= 394 g of CO2 needed

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