Question

Borax is (a) \(\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{4}\right] .8 \mathrm{H}_{2} \mathrm{O}\) (b) \(\left.\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{2}(\mathrm{OH})\right)_{10}\right] \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{6}\right] .7 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{3}(\mathrm{OH})_{8}\right] \cdot 6 \mathrm{H}_{2} \mathrm{O}\)

Short answer

The correct answer is (a): \( \mathrm{Na}_2[\mathrm{B}_4\mathrm{O}_5(\mathrm{OH})_4] \cdot 8\mathrm{H}_2\mathrm{O} \).

Step-by-step solution

Understand the Composition of Borax

Borax is known to have the chemical formula of \[ \mathrm{Na}_2\left[\mathrm{B}_4\mathrm{O}_5(\mathrm{OH})_4\right] \cdot 8 \mathrm{H}_2 \mathrm{O} \]This formula consists of sodium (Na), boron (B), oxygen (O), hydrogen (H), and the attached water molecules.

Analyze Each Option

We examine each provided option to find a match with the given formula of borax:- Option (a) has the formula \[ \mathrm{Na}_2\left[\mathrm{B}_4\mathrm{O}_5(\mathrm{OH})_4\right] \cdot 8 \mathrm{H}_2 \mathrm{O} \] which matches the known borax formula.- Option (b) \[ \mathrm{Na}_2\left[\mathrm{B}_4\mathrm{O}_2\mathrm{(OH)}_{10}\right] \cdot 5 \mathrm{H}_2 \mathrm{O} \] does not match.- Option (c) \[ \mathrm{Na}_2\left[\mathrm{B}_4\mathrm{O}_5(\mathrm{OH})_6\right] \cdot 7 \mathrm{H}_2 \mathrm{O} \] does not match.- Option (d) \[ \mathrm{Na}_2\left[\mathrm{B}_4\mathrm{O}_3(\mathrm{OH})_8\right] \cdot 6 \mathrm{H}_2 \mathrm{O} \] does not match.

Conclusion

Since option (a) matches the molecular formula and hydrate count of borax, we conclude that option (a) is the correct choice.

Key concepts

Inorganic Chemistry

Inorganic chemistry is the branch of chemistry that deals with inorganic compounds, those typically not containing carbon-hydrogen (C-H) bonds. This field covers a wide variety of substances including metals, minerals, and organometallic compounds.
Unlike organic chemistry, inorganic chemistry focuses mostly on compounds that aren't based on carbon. One major aspect of inorganic chemistry is the study of metallurgical processes and the preparation of inorganic materials like borax.
Borax, also known as sodium borate, is a classic mineral used in various household products and industrial applications. It's one of many inorganic compounds that can be studied to understand the behavior of non-carbon based substances in different environments.

• Inorganic chemistry includes salt formation, the creation of alloys, and the study of minerals.
• Applications can be found in catalysis, materials science, pigments, surfactants, coatings, and medicine.

Hydrates

Hydrates are compounds that contain water molecules within their crystalline structure. In chemistry, these are typically represented by a chemical formula followed by "·nH₂O" where "n" is the number of water molecules.
Borax, for example, is a hydrated compound because it forms with eight water molecules in its chemical composition, declared as \( ext{Na}_2[ ext{B}_4 ext{O}_5( ext{OH})_4] imes 8 ext{H}_2 ext{O} \). Hydrates are significant because the number of water molecules can affect the properties of the compound, such as its solubility and stability.

• The water in hydrates is not necessarily bonded, but instead integrated into the structure.
• Heating can remove these water molecules, resulting in an anhydrous form of the compound.

Molecular Formulas

Molecular formulas provide information on the exact number and type of atoms in a molecule, giving insight into its composition and structure. For example, the molecular formula of borax is \( ext{Na}_2[ ext{B}_4 ext{O}_5( ext{OH})_4] imes 8 ext{H}_2 ext{O} \). This indicates that each molecule of borax contains two sodium (Na) atoms, four boron (B) atoms, five oxygen (O) atoms, eight hydroxide (OH) groups, and eight water (H₂O) molecules.
By analyzing molecular formulas, chemists can deduce the physical and chemical properties of compounds.

• Molecular formulas are different from empirical formulas; they show the actual number of atoms, whereas empirical formulas show the simplest ratio.
• Understanding these formulas helps to predict interactions with other substances in chemical reactions.