By heating, you distinguish them by whether they release carbon dioxide gas that affects limewater or a flame.

Direct answer

  • Baking powder (sodium hydrogencarbonate, NaHCO₃) decomposes on heating to give carbon dioxide, water, and sodium carbonate. The gas:
    • Extinguishes a burning matchstick, or
    • Turns clear limewater milky when bubbled through it (due to formation of calcium carbonate).
  • Washing soda (sodium carbonate decahydrate, Na₂CO₃·10H₂O) on heating only loses water of crystallization and does not give off carbon dioxide, so:
    • It does not extinguish a flame by gas evolution.
    • It does not turn limewater milky on heating alone.

Simple stepwise test (heating method)

  1. Take a small sample of the unknown powder in a dry test tube.
  1. Heat it gently.
  1. Immediately:
    • Bring a burning matchstick near the mouth of the tube, or
    • Pass the evolved gas (if any) into limewater.
  1. Observation:
    • If the flame goes out or limewater turns milky → the substance is baking powder (NaHCO₃) evolving CO₂.
 * If there is no flame effect and limewater remains clear → the substance is **washing soda** (Na₂CO₃·10H₂O).

In textbook-style exam language:
“On heating, baking powder gives off carbon dioxide which turns limewater milky, whereas washing soda does not evolve carbon dioxide on heating, so it shows no such effect.”

TL;DR: Heat both, pass any gas into limewater; the one that turns limewater milky (or puts out a flame) is baking powder, while washing soda shows no such change.

Information gathered from public forums or data available on the internet and portrayed here.