The addition of a small crystal of sodium acetate to a dilute solution of acetic acid will cause the pH to increase. This is because sodium acetate is a salt that is derived from a weak acid (acetic acid) and a strong base (sodium hydroxide). When sodium acetate dissolves in water, it dissociates into its ions: acetate ions (CH3COO-) and sodium ions (Na+).
The acetate ions (CH3COO-) are the conjugate base of acetic acid (CH3COOH), and they can react with any excess hydronium ions (H3O+) present in the solution. This reaction consumes H3O+ ions and shifts the equilibrium towards the production of more water and undissociated acetic acid molecules. As a result, the concentration of H3O+ ions decreases, which leads to an increase in pH.
In summary, the addition of sodium acetate helps buffer the solution and reduce its acidity, causing the pH to increase.