Ketchup contains tomatoes, corn syrup, vinegar, sugar, water, and a variety of seasonings. A recipe for homemade ketchup involves combining the ingredients and pouring them into sterile canning jars, leaving some head space (air) at the top; covering each jar with a metal lid that has a rubber seal on its bottom side; and loosely screwing a metal band onto the threaded top of the jar to keep the lid in place while allowing steam and air to escape. The jars are immersed in boiling water for about 30 minutes and then removed; the bands are tightened to assure a tight seal between the lid and the jar contents; and the jars cool to room temperature. As long as the seal remains tight, a jar can be stored for up to a year.
Suppose the canning jar diameter is 2¼ inches, and a half-inch of headspace is left after the ketchup has been added to the jar. Room temperatureis25 degrees C. In the calculations that follow, assume that water is the only volatile component of ketchup and that the head space volume remains constant at its initial value.
(a) During this process, what is the lowest pressure (atm) in the head space of the jar?
b) Estimate the molar composition of the gas in the head space when the canning process is complete, stating all assumptions you make.
(c) Calculate the energy (kJ) transferred from the head space during the cooling process. Again, state your assumptions.
(d) Speculate on the likely reason for boiling the ketchup.
(e) When the band is removed from the top of a jar of ketchup, the lid remains firmly attached to the top of the jar and sometimes may need to be pried off. Why?
