Explain why pure dry benzoic acid does not affect a litmus paper

Answer 1

The H of the COOH group of C6H5COOH need H2O to dissociate.
C6H5COOH + H2O ==> C6H5COO^- + H3O^+. It's the H3O^+ that reacts with the litmus paper.

Answer 2

Litmus paper is an indicator for the presence of an acidic solution (blue litmus => red) or alkaline solution (red litmus => blue). To understand this it is important to note that for a substance to become an acid or base two conditions must apply; that is, (1) the substance of interest must have water as a solvent which (2) effects ionization of the substance to yield hydronium ions (H₃O⁺ = H⁺) for an acidic solution or hydroxide ions (OHˉ) for an alkaline solution. Since benzoic acid in solid form is not in water, it will not ionize to deliver H⁺ ions into solution and litmus will be unable to detect H⁺ ions and change color.