Why does red cabbage juice change color with vinegar or baking soda?

Red cabbage juice changes color because its purple pigment, an anthocyanin, changes its chemical structure with the acidity of the liquid around it, and each structure has a different color. Vinegar is a solution of acetic acid, so it pushes the juice toward red or pink. Baking soda is alkaline, so it pushes the juice toward blue, green and then yellow. In between, in a neutral solution, the juice stays purple.

Acidity is measured on the pH scale: 7.0 is neutral, below 7.0 is acidic, above 7.0 is basic. A compound whose color tells you where a solution sits on that scale is called a pH indicator, and the color change itself is called halochromism. That is why red cabbage juice works as a homemade indicator. It also explains a kitchen surprise: cooked red cabbage normally turns blue, and cooks add vinegar or acidic fruit to the pot to keep it red.

The pigment's name is older than the experiment. In 1835 the German pharmacist Ludwig Clamor Marquart called it Anthokyan in a treatise on the colors of flowers, from the Greek words for 'flower' and 'dark blue'. Plants use the same pigments in other ways: in flowers their colors may attract pollinators, and in fruits they may attract animals that spread the seeds. Blueberries, cherries, eggplant peel and black rice are rich in them too.