The balanced equation for the reaction of stearic acid and sodium hydroxide is:

CH₃(CH₂)₁₆COOH + NaOH → CH₃(CH₂)₁₆COONa + H₂O

Here's a breakdown of the reaction:

* Stearic acid (CH₃(CH₂)₁₆COOH) is a long-chain fatty acid.

* Sodium hydroxide (NaOH) is a strong base.

* Sodium stearate (CH₃(CH₂)₁₆COONa) is the salt formed from the reaction, which is a soap.

* Water (H₂O) is produced as a byproduct.

This reaction is a neutralization reaction where the acidic stearic acid reacts with the basic sodium hydroxide to form a salt (sodium stearate) and water. This is a common method for producing soap.