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Write the balanced chemical equation of the Chlor-alkali process?

Answer
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Hint:When electricity is passed through an aqueous solution of sodium chloride (called brine), it decomposes to form sodium hydroxide. The process is termed as chlor alkali process. The chemical equation is as follows: $2NaCl\,\left( aq \right)\,+\,2{{H}_{2}}O\,\left( l \right)\,\to \,2NaOH\,\left( aq \right)\,+\,C{{l}_{2}}\,(g)\,+\,{{H}_{2}}\left( g \right)$. The balanced chemical equation is obtained as discussed below.

Complete step-by-step answer:Step 1. Write skeletal chemical equation
In the chlor-Alkali process electrolysis of aqueous sodium chloride gives sodium hydroxide, chlorine and hydrogen gas. The skeletal equation for the same is given below:
$NaCl\,+\,{{H}_{2}}O\,\to \,NaOH\,+\,C{{l}_{2}}\,+\,{{H}_{2}}$
Step 2: Balance the chlorine atoms.
From the above skeletal equation, it can be seen that there are $2$$Cl$ atoms on the RHS and $1\,Cl$ atoms on the LHS. So, to balance the chlorine atom, we will add $2$ in front of $NaCl$. The reaction is shown below
$2NaCl\,+\,{{H}_{2}}O\,\to \,NaOH\,+\,C{{l}_{2}}\,+\,{{H}_{2}}$ …$\left( i \right)$
Step $3$: Balance the sodium atoms.
From equation $\left( i \right)$we see that the RHS is short of one sodium molecule. Hence, in order to balance $Na$ we will add $2$in front of $NaOH$. The reaction is given below:
$2NaCl\,+\,{{H}_{2}}O\,\to \,2NaOH\,+\,C{{l}_{2}}\,+\,{{H}_{2}}$
Step 4: Balance the hydrogen atoms.
To balance the hydrogen atoms, we will add $2$in front of ${{H}_{2}}O$, as LHS is short by two hydrogen atoms. The equation is represented below:
$2NaCl\,+\,2{{H}_{2}}O\,\to \,2NaOH\,+\,C{{l}_{2}}\,+\,{{H}_{2}}$
After following the above three steps we see that, oxygen atoms get automatically balanced. And hence, as a result the entire reaction of the Chlor-Alkali process gets balanced.

Note: In balancing a given equation, always write the skeletal equation first and start balancing the individual atoms one by one. After balancing check the result by counting whether individual atoms are same at LHS and RHS or not. If they are the same, then the reaction is accurately balanced.