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**Problem**: 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 90°CPart B 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 19°C. Assume no heat loss to the surroundings.

###### FREE Expert Solution

$\mathbf{-}{\mathbf{q}}_{\mathbf{water}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{q}}_{\mathbf{dry}\mathbf{}\mathbf{ice}}$

Step 1

${\mathbf{q}}_{\mathbf{water}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{}\mathbf{mc}\mathbf{\u2206}\mathbf{T}\phantom{\rule{0ex}{0ex}}{\mathbf{q}}_{\mathbf{water}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{(}\mathbf{15}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{L}\mathbf{\times}\frac{\mathbf{1}\mathbf{}\mathbf{g}}{\mathbf{1}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{}\mathbf{L}}\mathbf{)}\mathbf{(}\mathbf{4}\mathbf{.}\mathbf{18}\mathbf{}\frac{\mathbf{J}}{\mathbf{g}\mathbf{\xb7}\mathbf{\xb0}\mathbf{C}}\mathbf{)}\mathbf{(}\mathbf{19}\mathbf{\xb0}\mathbf{C}\mathbf{}\mathbf{-}\mathbf{}\mathbf{90}\mathbf{\xb0}\mathbf{C}\mathbf{)}\phantom{\rule{0ex}{0ex}}{\mathbf{q}}_{\mathbf{water}}\mathbf{}\mathbf{=}\mathbf{4451700}\mathbf{}\mathbf{J}\mathbf{}\mathbf{\times}\frac{\mathbf{1}\mathbf{}\mathbf{kJ}}{{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{J}}$

###### Problem Details

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the following equation: CO_{2} (s) → CO_{2} (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 90°C

Part B 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 19°C. Assume no heat loss to the surroundings.

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