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Balancing a chemical equation ensures that the same number of each type of atom appears on both the reactant and product sides of the reaction. This concept is based on the law of conservation of mass which states that matter cannot be created or destroyed in a chemical reaction. To balance a chemical equation, it's important to follow several steps:

• Write down the number of atoms of each element in the reactants and the products.
• Compare these numbers and add coefficients to the chemical formulas to balance the atoms.
• Always start by balancing elements that appear in only one reactant and one product first.
• Continue adjusting coefficients systematically until all elements are balanced.
• Check your work to ensure that the coefficients are in the simplest possible ratio.

Using the example of the given reaction, we initially see the reactants: borane (\(\mathrm{B}_{2} \mathrm{H}_{6}\)), potassium hydroxide (\(\mathrm{KOH}\)), and water (\(\mathrm{H}_{2} \mathrm{O}\)), needing to match the products hydrogen gas (\(\mathrm{H}_{2}\)) and potassium metaborate (\(\mathrm{KBO}_{2}\)). Only after confirming the balanced state of the equation can we properly identify the unknown compounds X and Y as water and potassium metaborate, respectively.

Understanding oxidation states is crucial in figuring out how elements interact during a chemical reaction. The oxidation state, or oxidation number, of an element in a compound represents the number of electrons lost or gained by it. Here are some key points to understand about oxidation states:

• Elements in their natural state have an oxidation number of zero. For example, \(\mathrm{O}_2\) or \(\mathrm{H}_2\).
• The oxidation state of a simple ion is equal to its charge. For example, \(\mathrm{Na}^+\) has an oxidation state of +1.
• In compounds, hydrogen usually has an oxidation state of +1, and oxygen usually has an oxidation state of -2.
• Sum of oxidation states for all atoms in a neutral compound must be zero.

In our reaction, borane (\(\mathrm{B_2H_6}\)) must be evaluated by understanding its unusual hydrogen and boron states. Boron here traditionally adopts an oxidation state of +3, due to its affinity to accept outside electrons.

In chemical reactions involving borane and alkali, metaborates are often formed. A metaborate is a specific type of borate, which typically has the chemical formula \(\mathrm{BO}_2^-\). This happens due to the reaction of boranes with bases like \(\mathrm{KOH}\), resulting in the production of potassium metaborate (\(\mathrm{KBO}_2\)) as a product. Several important points regarding metaborate formation include:

• Boranes interact with bases through hydrolysis reactions where water molecules play a key role.
• During this process, hydrogen atoms from borane are typically displaced, leading to the release of hydrogen gas.
• As a part of the rearrangement, the boron atom forms bonds with oxygen, producing anionic species like \(\mathrm{BO}_2^-\).

Understanding these concepts is crucial to predict and explain why, in our reaction, water (\(\mathrm{H}_{2} \mathrm{O}\)) is converted into hydrogen gas and potassium metaborate is formed. This transformation is key to classifying the unknown substances X and Y accurately.