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The balance equation for reaction of ethyl alcohol with Na is :
\[{{\text{C}}_2}{{\text{H}}_5}{\text{OH}} + {\text{Na}} \to {{\text{C}}_2}{{\text{H}}_5}{\text{ONa}} + \dfrac{1}{2}{{\text{H}}_2}\]
A. True
B. False

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Answer
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Hint: On the reactant and product sides of a balanced chemical equation, there are equivalent numbers of atoms for each element involved in the reaction. This is a condition that the equation must meet in order to be consistent with the conservation of matter law.

Complete answer:
As a small piece of sodium is lowered into ethanol, it slowly reacts to produce hydrogen gas bubbles and a colourless sodium ethoxide solution. An alkoxide is the anion component. When the solvent is carefully evaporated to dryness, sodium ethoxide is left as a white solid.
The organic compound with the abbreviation NaOEt is sodium ethoxide, also known as sodium ethylate. While impure samples appear yellow or brown, it is a white solid. In polar solvents like ethanol, it dissolves. It's often seen as a stronger base.
When you dissolve sodium ethoxide in water, you get a colourless solution with a high pH. Since ethoxide ions are Brnsted-Lowry bases, they strip hydrogen ions from water molecules to release hydroxide ions, which raise the pH of the solution.
 \[{{\text{C}}_2}{{\text{H}}_5}{\text{OH}} + {\text{Na}} \to {{\text{C}}_2}{{\text{H}}_5}{\text{ONa}} + \dfrac{1}{2}{{\text{H}}_2}\]
The equation is already balanced here.

Hence option A is correct.

Note:
A nucleophile is a chemical that has a negative or partial negative charge and attacks positive centres of other molecules or ions. You may have come across the reaction between a halogenoalkane (also known as a haloalkane or alkyl halide) and sodium hydroxide solution since hydrogen ions are strong nucleophiles. The halogen atom is replaced by hydroxide ions.