Problem: Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the 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 L of water heated to 86˚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 23˚C. Assume no heat loss to the surroundings.

FREE Expert Solution

The first thing that we have to focus on is that there is no heat loss to the surroundings. So, all the heat lost by water is gained by carbon dioxide for sublimation. We can write:

<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mo>-</mo><msub><mi>q</mi><mrow><msub><mi>H</mi><mn>2</mn></msub><mi>O</mi></mrow></msub><mo>&#xA0;</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mfenced><mn>1</mn></mfenced></math>

qCO2 is positive as CO2 gains heat in the process, while qH2O is negative because water is losing heat.


The temperature of water changes from 86 oC to 23 oC. Change of temperature is given by:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mo mathvariant="italic">&#x2206;</mo><mi>T</mi><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">=</mo><mo mathvariant="italic">&#xA0;</mo><msub><mi>T</mi><mrow><mi mathvariant="italic">f</mi><mi mathvariant="italic">i</mi><mi mathvariant="italic">n</mi><mi mathvariant="italic">a</mi><mi mathvariant="italic">l</mi></mrow></msub><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">-</mo><mpadded lspace="-1px"><mo mathvariant="italic">&#xA0;</mo><msub><mi mathvariant="italic">T</mi><mrow><mi mathvariant="italic">i</mi><mi mathvariant="italic">n</mi><mi mathvariant="italic">i</mi><mi mathvariant="italic">t</mi><mi mathvariant="italic">i</mi><mi mathvariant="italic">a</mi><mi mathvariant="italic">l</mi></mrow></msub></mpadded></math>


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Problem Details

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the 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 L of water heated to 86˚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 23˚C. Assume no heat loss to the surroundings.

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