When a 0.5 M solution of hydrochloric acid (HCl) is mixed with a 0.5 M solution of sodium hydroxide (NaOH), they undergo a neutralization reaction. The balanced chemical equation for this reaction is:

$HCl\left(aq\right)+NaOH\left(aq\right)\to NaCl\left(aq\right)+2_{}O\left(l\right)\backslash text\{HCl\}(aq)\; +\; \backslash text\{NaOH\}(aq)\; \backslash rightarrow\; \backslash text\{NaCl\}(aq)\; +\; \backslash text\{H\}\_2\backslash text\{O\}(l)$HCl(aq)+NaOH(aq)→NaCl(aq)+H2​O(l)

In words, hydrochloric acid reacts with sodium hydroxide to produce sodium chloride (NaCl) and water (H2O).

Explanation:

• Hydrochloric acid (HCl) dissociates in water to give hydrogen ions (H+) and chloride ions (Cl-).
• Sodium hydroxide (NaOH) dissociates in water to give sodium ions (Na+) and hydroxide ions (OH-).
• In the reaction, hydrogen ions from HCl combine with hydroxide ions from NaOH to form water (H2O).
• Sodium ions from NaOH combine with chloride ions from HCl to form sodium chloride (NaCl), which remains dissolved in the aqueous solution.

This reaction is a classic example of acid-base neutralization, where an acid and a base react to form a salt and water.