In the reaction given
`Mg(s)+NO_(3)^(ɵ)+H_(2)OtoMg(OH)_(2)(s)+overset(ɵ)(O)HO(aq.)+NH_(3)(g)` 20 " mL of " sample of `NO_(3)^(ɵ)` solution is treated with Mg. The `NH_(3)^(g)` was passed into 50 " mL of " 0.1 M HCl. The excess HCl requried 30 " mL of " 0.1 M KOH for its neutralisation calculate the molarity of `NO_(3)^(ɵ)` ions in the original sample?

Explanation

To solve the problem step by step, we will follow the chemical reaction and the stoichiometry involved.

### Step 1: Understand the Reaction
The reaction is:
\[ \text{Mg}(s) + \text{NO}_3^{-} + \text{H}_2\text{O} \rightarrow \text{Mg(OH)}_2(s) + \text{OH}^- + \text{NH}_3(g) \]

### Step 2: Calculate Milliequivalents of NH3
We know that the ammonia (NH3) produced will react with hydrochloric acid (HCl).
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