Explain why using a base such as baking soda is effective in cleaning up a spill of acid, such as vinegar, in the kitchen

This is because the base will react with the acid spill to form water and salt that is easier to clean. When a base is mixed with an acid, the basic reaction is;

Acid + Base -  Salt + Water

The salt dissolves in the water (and exists in aqueous form) and washes off with ease.