In this experiment, 1-2 mL of saturated sodium chloride is used to transfer the crude product after the initial distillation. Why is saturated sodium chloride, rather than pure water, used for this procedure?

Saturated sodium chloride is used to transfer the product rather than water since it is not polar and rinsing the product with water would revert any 4-methylcyclohexene back to 4-methylcyclohexanol in the Hickman Head and thus lowering the percent yield; using water would shift the equilibrium towards the reactants. Also sodium chloride removes the small amount of phosphoric acid and also a small amount of water. If one were to add water, both 4-methylcyclohexene and phosphoric acid are partially soluble making difficult to remove the water later; sodium chloride makes the water less reactive so easier to remove by making the aqueous later more polar.