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What is the common name of (a) $ NaHC{O_3} $ and (b) $ N{a_2}C{O_3}.10{H_2}O $ ?

Answer
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Hint :As we know that the organic compounds are named by the IUPAC system of naming. The IUPAC name of $ NaHC{O_3} $ is Sodium hydrogen carbonate and it is used in the kitchen. $ N{a_2}C{O_3}.10{H_2}O $ is Sodium carbonate decahydrate.

Complete Step By Step Answer:
(A)We already know that the Sodium hydrogen carbonate is commonly called BAKING SODA or cooking soda and its chemical name is Sodium bicarbonate. We also know that Sodium bicarbonate is actually a weak base as the negative charge present on the oxygen atom is involved in the resonance with the pi-bond and that is why negative charge distributes.
Now, we are also aware of the uses of Baking soda. It helps in reducing the acidity of the stomach. It belongs to the group of medicines called antacid. It helps in treating heartburn. It is also used as an alternative to mouthwash. It is also a home remedy for whitening teeth. A popular supplement among athletes. Baking soda may also help in the cancer treatment.
(B) Then we have $ N{a_2}C{O_3}.10{H_2}O $ which is commonly known as WASHING SODA and the chemical name of $ N{a_2}C{O_3}.10{H_2}O $ is Sodium Carbonate decahydrate. And the use of this organic compound involves its cleansing action. It is also used for making glass, soap borax and paper. It also removes the hardness from the water. And it is used as a laboratory agent.

Additional Information:
We should know that when $ NaHC{O_3} $ which is Baking soda is heated at $ 80^\circ C $ , it results in the formation of $ N{a_2}C{O_3} $ , $ C{O_2} $ and $ {H_2}O $ . Then again $ N{a_2}C{O_3} $ so formed reacts with $ 10 $ molecules of water and hence results in the formation of $ N{a_2}C{O_3}.10{H_2}O $ which is washing soda.

Note :
The common name of $ NaHC{O_3} $ is baking soda and the common name of $ N{a_2}C{O_3}.10{H_2}O $ is washing soda. The formation of washing soda takes place with the help of Baking soda itself when considering it as a basic reactant.