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When excess of gas A was passed through solution B a white precipitate was obtained which turned colourless.
(a) Name A and B
(b) Name the product formed after each reaction
(c) State balanced chemical equation involved

Answer
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Hint: Try to think of a reaction in which a gas reacts with a colourless solution to form white ppt. Remember Calcium carbonate\[\left( {CaC{O_3}} \right)\]has milky appearance and Calcium bi-carbonate \[Ca(HC{O_3})\] is colourless.

Complete step by step answer:
When (\[C{O_2}\] ) carbon dioxide gas is passed through a solution of lime water the solution turns milky. This is due to the formation of\[\left( {CaC{O_3}} \right)\]Calcium carbonate. The chemical reaction is as follows:
\[C{O_2} + Ca{(OH)_2} \to CaC{O_3} + {H_2}O\]
When excess carbon dioxide (\[C{O_2}\]) is passed through a solution of Calcium carbonate \[\left( {CaC{O_3}} \right)\]the milkiness disappears. This is due to the formation of Calcium bi-carbonate\[Ca{(HC{O_3})_2}\]. The chemical reaction is as follows:
\[CaC{O_3} + {H_2}O + C{O_2} \to Ca{(HC{O_3})_2}\]
(a) Hence gas A is\[C{O_2}\] and solution B is lime water .
(b ) \[C{O_2} + Ca{(OH)_2} \to CaC{O_3} + {H_2}O\]
The product formed when Carbon dioxide reacts with Lime water is Calcium Carbonate.
\[CaC{O_3} + {H_2}O + C{O_2} \to Ca{(HC{O_3})_2}\]
The product formed when excess of Carbon dioxide (\[C{O_2}\]) is passed through a solution of Calcium Carbonate \[\left( {CaC{O_3}} \right)\] and water (\[C{O_2}\]) is of Calcium bi-carbonate (\[Ca{(HC{O_3})_2}\]).
(c) The balanced chemical equation for each step is as follows:
\[C{O_2} + Ca{(OH)_2} \to CaC{O_3} + {H_2}O\]
\[CaC{O_3} + {H_2}O + C{O_2} \to Ca{(HC{O_3})_2}\]

Note: (1) Calcium bicarbonate - Calcium bicarbonate is also known as Calcium hydrogen carbonate. Calcium bicarbonate is white in colour. It can be used as a colouring agent and in food. This term does not refer to a known solid compound because it is found only in aqueous solution. A solution is known as an aqueous solution in which the solvent is water. Calcium bicarbonate containing ions such as calcium (\[C{a^{2 + }}\]),bicarbonate (\[HCO_3^ - \]), and carbonate (\[CO_3^{2 - }\]).
(2) Calcium Carbonate - Calcium Carbonate is found on mineral rocks. Calcium Carbonate is used for refining of sugar, added to the swimming pool to maintain pH level. This is also used as antacid.