Sorbic acid is used to prevent mold and fungus growth in some food products, especially cheeses. The systematic name for sorbic acid is 2,4-hexadienoic acid. Draw structures for the four geometrical isomers of sorbic acid.

First, we need to write the main carbon chain of 2,4-hexadienoic acid. This compound has a six-carbon chain, with a carboxyl group (-COOH) attached to the first carbon. It has two double bonds at carbon positions 2 and 4. The rest of the carbons will have hydrogen atoms attached to them.

The double bonds are present at the second and fourth carbon positions. In drawing geometrical isomers, we will be focusing on the arrangement of groups around these double bonds.

We will now take the main carbon chain with the double bonds and arrange the hydrogen atoms and the carboxyl group in different positions across the double bonds to form the four geometrical isomers. To do this, we'll consider the following options for each double bond: - The hydrogen atoms on the same side of the double bond (cis configuration) - The hydrogen atoms on opposite sides of the double bond (trans configuration) Here are the four geometrical isomers for 2,4-hexadienoic acid (sorbic acid): 1. cis,cis-isomer: Hydrogen atoms are in the cis configuration on both double bonds. The carboxyl group is also on the same side as the hydrogen atom on the second double bond. \[CH_3-CH=CH-CH=CH-COOH\] 2. cis,trans-isomer: Hydrogen atoms are in the cis configuration on the first double bond and in the trans configuration on the second double bond. The carboxyl group is on the opposite side of the hydrogen atom on the second double bond. \[CH_3-CH=CH-CH=CH-COOH\] 3. trans,cis-isomer: Hydrogen atoms are in the trans configuration on the first double bond and in the cis configuration on the second double bond. The carboxyl group is on the same side as the hydrogen atom on the second double bond. \[CH_3-CH=CH-CH=CH-COOH\] 4. trans,trans-isomer: Hydrogen atoms are in the trans configuration on both double bonds. The carboxyl group is also on the opposite side of the hydrogen atom on the second double bond. \[CH_3-CH=CH-CH=CH-COOH\] These are the four geometrical isomers of 2,4-hexadienoic acid (sorbic acid).