The separation of methyl alcohol (methanol) from pyroligneous acid leverages differences in the physical and chemical properties of the various components within the mixture. Pyroligneous acid is a complex aqueous mixture produced by the destructive distillation of wood. It contains, amongst other things, methanol, acetic acid, water, acetone, and various tars and other organic compounds.

Here's a breakdown of the key principles employed:

• Distillation: This is the primary separation technique. Distillation separates liquids based on their boiling points. Methanol has a significantly lower boiling point (64.7°C or 148.5°F) than acetic acid (118°C or 244°F) and water (100°C or 212°F). Thus, when pyroligneous acid is heated, methanol vaporizes more readily and can be collected and condensed separately.
• Fractional Distillation: Because pyroligneous acid is a complex mixture, simple distillation alone isn't sufficient to obtain pure methanol. Fractional distillation is used. This involves using a fractionating column, which provides a temperature gradient. As the vapor rises through the column, it cools, and components with higher boiling points condense and fall back into the distillation flask, while the methanol-rich vapor continues to rise and is collected at the top.
• Chemical Treatment (Neutralization and Esterification): Acetic acid is a major component of pyroligneous acid that interferes with methanol purification. It can be neutralized with a base (like lime or sodium hydroxide) to form a salt. These salts are less volatile and remain in the distillation residue. Alternatively, the acetic acid can be esterified with methanol to form methyl acetate, which can then be separated by distillation based on boiling point differences.
• Solvent Extraction: Sometimes, solvent extraction is used to selectively remove methanol from the aqueous mixture. A solvent that preferentially dissolves methanol but is immiscible with water is added. The methanol dissolves into the solvent phase, which is then separated. The methanol can then be recovered from the solvent by distillation.

In summary, the separation theory relies on exploiting the differences in boiling points through distillation (especially fractional distillation) and using chemical treatments or solvent extraction to deal with other components, especially acetic acid, that would otherwise contaminate the methanol product.