Explain why borax beads produce different colors with certain basic radicals under oxidizing and reducing flame conditions.

When borax ($\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O}$) is heated, it first loses its water of crystallization and swells. Upon further heating, it decomposes to form a transparent glassy bead consisting of sodium metaborate and boric anhydride.

$$\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O}(\text{s}) \xrightarrow{\text{heat}} \text{Na}_2\text{B}_4\text{O}_7(\text{s}) + 10\text{H}_2\text{O}(\text{g})$$ $$\text{Na}_2\text{B}_4\text{O}_7(\text{s}) \xrightarrow{\text{heat}} 2\text{NaBO}_2(\text{l}) + \text{B}_2\text{O}_3(\text{l})$$

When a metal salt is introduced into the bead and heated, the metal oxide (formed from the decomposition of the salt) reacts with the boric anhydride ($\text{B}_2\text{O}_3$) to form a colored metal metaborate. For example, with copper(II) oxide:

$$\text{CuO}(\text{s}) + \text{B}_2\text{O}_3(\text{l}) \xrightarrow{\text{heat}} \text{Cu(BO}_2)_2(\text{l})$$

In the outer, oxidizing flame, the metal ion is typically in its higher oxidation state. For copper, this is $\text{Cu}^{2+}$, which forms copper(II) metaborate. This compound gives a characteristic blue color when hot and cold.

$$\text{Cu(BO}_2)_2(\text{l}) \quad (\text{blue bead in oxidizing flame})$$

In the inner, reducing flame (rich in carbon monoxide), the higher oxidation state metal ion is reduced to a lower oxidation state. For copper, $\text{Cu}^{2+}$ is reduced to $\text{Cu}^{+}$ (copper(I)) or even to metallic copper. Copper(I) metaborate ($\text{CuBO}_2$) is typically green, and elemental copper appears opaque red.

$$2\text{Cu(BO}_2)_2(\text{l}) + \text{C}(\text{s}) \xrightarrow{\text{reducing flame}} 2\text{CuBO}_2(\text{l}) + \text{B}_2\text{O}_3(\text{l}) + \text{CO}(\text{g})$$ $$\text{CuBO}_2(\text{l}) \quad (\text{green bead in reducing flame})$$

This change in oxidation state, driven by the flame conditions, results in two different colored beads for the same basic radical.