Answer
The E,Z configurations of compounds are:
(a) Z configuration
(b) Z configuration
(c) E configuration
(d) Z configuration
Work Step by Step
(a) The priority order of the groups attached to the double bonds are to be determined on the left hand side of the double bond, $CH_{2}OH$ has a higher priority than $CH_{3}$. On the right hand side of the double bond, the $CH_{3}$ group has a higher priority than $H$ atom.
Therefore, the compound has a Z configuration since the higher priority groups are on the same side of the double bond.
(b) The priority order of the groups attached to the double bonds are to be determined on the left hand side of the double bond,
$CO_{2}H$ has a lower priority than the $Cl$ atom. On the right hand side of the double bond, the $OCH_{3}$ group has a higher priority over the hydrogen atom.
Therefore, the compound has a Z configuration since the higher priority groups are on the same side of the double bond.
(c) The priority order of the groups attached to the double bonds are to be determined on the left hand side of the double bond, $NC$ group has a higher priority than $CH_{3}CH_{2}$ group. On the right hand side of the double bond, the $CH_{3}$ group has a lower priority than the $CH_{2}OH$ group.
Therefore, the compound has an E configuration since the higher priority groups are on the opposite sideS of the double bond.
(d) The priority order of the groups attached to the double bonds are to be determined on both sides of the double bond. On the left hand side of the double bond, two carbons are attached to the doubly bonded carbon; which is a tie. So we look at the next atoms attached to those carbons. For the upper carbon atom, it is OOC and for the lower carbon atom, it is OOH. Therefore, $CO_{2}CH_{3}$ group has a higher priority than $CO_{2}H$ group. On the right hand side of the double bond, the same method is followed. The upper carbon atom is attached to CCH and the lower carbon atom is attached to CHH. Therefore, $CH=CH_{2}$ group has a higher priority than the $CH_{2}CH_{3}$ group.
Therefore, the compound has a Z configuration since the higher priority groups are on the same side of the double bond.