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Write the balanced chemical equation for the following reaction:
(a) Calcium hydroxide + carbon dioxide $\to $ Calcium carbonate + water
(b) Zinc + silver nitrate $\to $ Zinc nitrate + silver
(c) Aluminium + copper chloride $\to $ Aluminium chloride + copper

Answer
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Hint: Write all the chemical formulas of all the compounds in the reaction. Then balance all the atoms other than hydrogen and oxygen. Once the other atoms are balanced, balance the oxygen and hydrogen atoms if present.

Complete step by step solution:
(a)- Calcium hydroxide + carbon dioxide $\to $ Calcium carbonate + water
The chemical formula of calcium hydroxide is $Ca{{(OH)}_{2}}$. The chemical formula of carbon dioxide is $C{{O}_{2}}$. The chemical formula of calcium carbonate is $CaC{{O}_{3}}$. The chemical formula of water is ${{H}_{2}}O$.
The reaction will be: $Ca{{(OH)}_{2}}+C{{O}_{2}}\to CaC{{O}_{3}}+{{H}_{2}}O$
There are 2 atoms other than hydrogen and oxygen are calcium and carbon. Both of them are equal and the number of hydrogen and oxygen on both sides is equal.
Hence the balanced reaction: $Ca{{(OH)}_{2}}+C{{O}_{2}}\to CaC{{O}_{3}}+{{H}_{2}}O$
(b)- Zinc + silver nitrate $\to $ Zinc nitrate + silver
The chemical formula of zinc is$Zn$. The chemical formula of silver nitrate is $AgN{{O}_{3}}$. The chemical formula of zinc nitrate is $Zn{{(N{{O}_{3}})}_{2}}$ and the chemical formula of silver is $Ag$.
The reaction will be: $Zn+AgN{{O}_{3}}\to Zn{{(N{{O}_{3}})}_{2}}+Ag$
Zinc and silver atoms are equal on both sides are the same but nitrogen is 2 on the product side and 1 on the reactant side. So, multiply 2 with $AgN{{O}_{3}}$. And now multiply 2 with $Ag$. So, the balanced equation is: $Zn+2AgN{{O}_{3}}\to Zn{{(N{{O}_{3}})}_{2}}+2Ag$.
(c)- Aluminium + copper chloride $\to $ Aluminium chloride + copper
The chemical formula of aluminium is $Al$. The chemical formula of copper chloride is $CuC{{l}_{2}}$. The chemical formula of aluminium chloride is $AlC{{l}_{3}}$ and the chemical formula of copper is $Cu$.
The reaction is: $Al+CuC{{l}_{2}}\to AlC{{l}_{3}}+Cu$.
The chlorine atom on the reactant side is 2 and on the product side is 3. So, multiply $CuC{{l}_{2}}$ with 3 and multiply $AlC{{l}_{3}}$ with 2. Now, multiply Al with 2 and Cu with 3. The balanced reaction is: $2Al+3CuC{{l}_{2}}\to 2AlC{{l}_{3}}+3Cu$.

Note: The oxygen atom is usually balanced by adding water molecules and then hydrogen is balanced by adding the hydrogen ions in an acidic medium or hydroxyl ion in the basic medium.