Question

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 placewhileallowingsteamandairtoescape.Thejarsareimmersedinboilingwaterforabout30minutesandthen removed; thebands 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?

Answer 1

(a) From Ideal Gas Law,

P = nRT / V

where P= pressure, n = number of moles of gas, R= gas constant, T= temperature, V= Volume

Consider the head space of jar as a cylinder.

Volume of cylinder is V = Pi *r²*h

r = radius= dia /2 = 2.25/2= 1.125 inch = 0.028575 m , h= height= 0.5 inch = 0.0127m

V= 3.26 x 10^-5 m³ , T = 25^oC + 273.15 = 293.15 K

For 1 mole of gas,

P = (1 x 8.314 x 293.15 ) / 3.26 x 10^-5 =747.6 Pascal

b) When the canning process is complete, the steam and air cooled off and released creating vaccum like condition inside the head space. The very little air inside mainly comes from boiling of ketchup bottle which releases the air trapped inside as air bubble.

Assuming 1 mol of air inside it mainly contains Nitrogen and Oxygen.

Since 28.97 mol of air contains 6.704 mol of oxygen

1 mol of air will contain = 6.704/ 28.97 = 0.23 mol oxygen

Similarly 28.97 mol of air contains 21.88 mol of nitrogen

1 mol of air will contain = 21.88 / 28.97 = 0.75 mol nitrogen

c) The latent heat of condensation is the energy released when water vapor condenses into water droplets.

ΔH_cond= −ΔH_vap = -2256 J⋅g−1

The energy transferred from head space during the cooling process per mole of steam = Q

= m. ΔH_cond =18.02 g × (-2256 J⋅g−1) =-40 653 J=-40.65 kJ

d) Boiling causes removal of air, trapped in the form of air bubbles inside ketchup during filling. Hot air easily escapes from loosely placed lid. After boiling, lids are tightened causing partial vacuum inside bottle. Presence of air and oxygen inside the jar may cause undesirable chemical and biological changes.Hence this process increases shelf life of ketch up.

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. It is due to partial vacuum or very little pressure inside the head space of jar and hence external atmospheric pressure make it difficult to remove.