One can make a “dry ice bomb” by dropping a chip of dry ice (solid CO2) into a plastic 2-liter bottle of warm water and sealing the cap. The CO2 sublimates into gas, and the gas pressure ultimately blows the bottle apart. Assume that the 2.00-liter bottle is precisely three-quarters full, and the temperature of the bottle is kept at room temperature (297 K). 22 grams of dry ice are added to the bottle, and then the bottle is sealed up, so the number of moles of CO2 is constant, as is the total volume of the bottle. To solve this problem realistically, we require taking into account the fact that some of the gas is dissolved in the water. This is described by a law of chemistry called Henry’s Law, which states:
H d
k n
p
V
=
Where p is the partial pressure of the CO2 gas, nd = number of moles of gas dissolved in the water, and V is the volume of the water. For CO2 in water at room temperature, the constant kH = 29.4 L atm/mol.
a) Compute the final pressure of the gas (in atmospheres) when all the CO2 sublimates, assuming, as you did in Recitation, that you can ignore the heat capacity of the gases.
b) Repeat the calculation in (a), but do NOT ignore the heat capacity of the gases. Was our “ignore the gases” assumption a good one?