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Understanding oxidation states helps us determine how electrons are distributed in a molecule. First, let's look at \(\text{NaBH}_4\). Sodium (\text{Na}) is in Group 1 and has an oxidation state of \(+1\). Hydrogen (\text{H}) has an unusual oxidation state of \(-1\) in metal hydrides. Since the compound is neutral, the sum of oxidation states must be zero. We calculate Boron's (\text{B}) state as follows: \(1 + x + 4(-1) = 0\), which simplifies to \(x = +3\).
In \(\text{Al(BH}_4)_3\), Aluminum (\text{Al}) typically has an oxidation state of \(+3\). We already know the \(\text{BH}_4^-\) anion’s states from previous calculations: Boron (\text{B}) \(+3\) and Hydrogen (\text{H}) \(-1\). Thus, for neutrality, the sum is \(+3 + 3(-1) = 0\).
Lastly, for \(\text{LiAlH}_4\). Lithium (\text{Li}) in Group 1 has an oxidation state of \(+1\). Using similar logic, we get \(1 + x + 4(-1) = 0\) for Aluminum (\text{Al}) which results in \(+3\). Understanding this is fundamental to exploring the electronic structure of these compounds.

The Lewis structure is a visual representation of a molecule's valence electrons. For \(\text{BH}_4^-\), we first calculate the total valence electrons: Boron (B) has 3, each Hydrogen (H) has 1, which gives 4 from H atoms, and we add 1 for the extra negative charge. This total is \(3 + 4 + 1 = 8\) valence electrons. We place B at the center, surrounded by four H atoms. Each H forms a single bond with B, utilizing 8 electrons. This creates a stable structure by applying the octet rule, showing how electrons are shared within the molecule. Such visualizations can solidify your understanding of molecular shapes and interactions.

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shape of a molecule based on repulsion between electron pairs. In \(\text{BH}_4^-\), we have four bonding pairs around the central Boron (B) atom, with no lone pairs. VSEPR theory tells us these pairs will position themselves as far apart as possible to minimize repulsion. This concept is crucial as it explains many molecular geometries and their associated chemical properties. By understanding VSEPR, you get insights into molecular angles and shapes, which can be applied broadly across diverse chemical compounds. Breaking down complex shapes into simple electron pair interactions makes them less daunting and more intuitive.

A tetrahedral geometry occurs when a central atom is surrounded by four substituents positioned as the corners of a tetrahedron. In \(\text{BH}_4^-\), Boron (B) forms such a structure with its four Hydrogen (H) atoms, resulting in bond angles of approximately 109.5°. This shape minimizes electron pair repulsion as per VSEPR theory. Recognizing tetrahedral structures is quite vital, as they're common in organic and inorganic chemistry. Such geometries impact the molecule's reactivity, stability, and overall behavior. Visualizing molecules in three dimensions enhances comprehension and can be pivotal when predicting or rationalizing molecular interactions.

Reduction agents like \(\text{NaBH}_4\), \(\text{Al(BH}_4)_3\), and \(\text{LiAlH}_4\) donate electrons to other substances, reducing them. These complex hydrides are potent reducing agents due to their ability to donate hydride ions (\text{H}-). These agents play crucial roles in synthetic chemistry, enabling selective reductions that are otherwise difficult or impossible. For example, \(\text{NaBH}_4\) can reduce ketones to secondary alcohols selectively. Such applications are invaluable in fields ranging from pharmaceuticals to materials science. Understanding the role and mechanisms of these reducing agents provides a fundamental toolset for any budding chemist aiming to master synthesis techniques.