Why does a mixture of vinegar and baking soda blow out burning splint?

When vinegar (acetic acid, \(CH_3COOH\)) and baking soda (sodium bicarbonate, \(NaHCO_3\)) are mixed, they react to produce carbon dioxide gas (\(CO_2\)). This gas is released rapidly, causing a fizzing reaction and creating a lot of bubbles. If a burning splint is held near the mixture, the carbon dioxide gas will extinguish the flame by displacing the oxygen around it. Carbon dioxide is a heavier gas than oxygen, so it will sink to the bottom of the container and create a layer that prevents oxygen from reaching the flame. Without oxygen, the flame cannot continue to burn and will eventually go out.

The chemical reaction that takes place between vinegar and baking soda can be represented as follows:

$$CH_3COOH + NaHCO_3 → CO_2 + H_2O + CH_3COONa$$

In this reaction, the hydrogen ions from the vinegar react with the bicarbonate ions from the baking soda to produce carbon dioxide gas, water, and sodium acetate. The carbon dioxide gas is what causes the fizzing reaction and eventually extinguishes the flame.