The preparation of methane from anhydrous sodium ethanoate (sodium acetate) involves the reaction with soda lime (a mixture of sodium hydroxide and calcium oxide). Here's the balanced chemical equation:

CH₃COONa + NaOH + CaO → CH₄ + Na₂CO₃ + CaO

Explanation:

* CH₃COONa: Sodium ethanoate (anhydrous sodium acetate)

* NaOH: Sodium hydroxide (part of soda lime)

* CaO: Calcium oxide (part of soda lime)

* CH₄: Methane (the product)

* Na₂CO₃: Sodium carbonate

* CaO: Calcium oxide remains unchanged (acts as a catalyst and drying agent)

Mechanism:

The reaction proceeds in two steps:

1. Decarboxylation: Sodium ethanoate reacts with sodium hydroxide to form sodium carbonate and methane.

CH₃COONa + NaOH → CH₄ + Na₂CO₃

2. Dehydration: Calcium oxide acts as a dehydrating agent, removing water from the reaction mixture and preventing side reactions.

Note: The reaction is usually carried out by heating a mixture of anhydrous sodium ethanoate and soda lime in a hard glass test tube.