What happens when C17H35COO-, a soap, reacts with an acidic solution? My book says that-


  In acidic water, the negative fatty acid ions become fatty acids. 


However, they did not include a chemical equation to demonstrate this, so I made my own:

$$\ce{C17H35COO- (aq) + HCl (aq) -&gt; C17H35COOH (aq) + Cl- (aq)}$$ 

But according to this equation, the fatty acid ion is a base, since it gets a proton. So this must be wrong. Can anyone point out my mistakes (if any), and explain what happens when a negative fatty acid ion comes in contact with acidic water, and becomes a fatty acid?
Your equation is correct. Hydrochloric acid ($\ce{HCl}$) is a stronger acid than stearic acid ($\ce{C17H35COOH}$),i.e. it is dissociated into $\ce{H+}$ and $\ce{X-}$, the anionic rest, to a greater degree. Therefore, it protonates the stearate ion. One can also say that the conjugated base of stearic acid (the stearate ion) is a stronger base than chloride, the conjugated base of hydrochloric acid.