Arrange the oxides in each of the following groups in order of increasing basicity: (a) \(\mathrm{K}_{2} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{BaO}\) (b) \(\mathrm{CrO}_{3}, \mathrm{CrO}, \mathrm{Cr}_{2} \mathrm{O}_{3}\)

The oxides of alkali and alkaline earth metals are known for their basic properties. Starting with alkali metals, which reside in Group 1 of the periodic table, these elements include lithium, sodium, potassium, rubidium, cesium, and francium. Their oxides are typically very basic because alkali metals easily lose one electron to form strong bases when reacting with water. For example, potassium oxide (K_2O) reacts vigorously with water to produce potassium hydroxide (KOH), a strong base.

Moving down to the alkaline earth metals of Group 2, which consists of beryllium, magnesium, calcium, strontium, barium, and radium, their oxides are also basic but slightly less so compared to the alkali metals. This group's elements have two valence electrons, therefore their oxides, such as barium oxide (BaO), react with water to form corresponding hydroxides like barium hydroxide (Ba(OH)_2), which are less soluble but still strong bases.

The reason for this high basicity in both groups is due to the metallic character and the low ionization energies of these elements which allows them to easily donate electrons, creating hydroxide ions in solution.

Amphoteric substances are fascinating as they exhibit both acidic and basic properties. The term 'amphoteric' comes from Greek, meaning 'both kinds'. In the context of oxides, this duality is seen in the behavior of the compound in reaction with acids and bases. Aluminum oxide (Al_2O_3) is a classic example of an amphoteric oxide. It can react with acids to form salts and with strong bases to produce aluminates.

The unique nature of amphoteric oxides is due to their electronic structure and the presence of both metallic and non-metallic elements. This dual behavior can be predicted by the position of a substance in the periodic table, usually around the metalloid region or with elements that have intermediate electronegativity. These substances enrich our understanding of chemical reactions as they don't fit neatly into the category of either just an acid or a base. They play versatile roles in various chemical processes, including acting as catalysts in some industrial chemical reactions.

Chromium oxides present a case study in the diversity of chemical behavior within a single element's compounds. Chromium can exhibit multiple oxidation states, which is common for transition metals, leading to different types of oxides with varying acid-base character. For instance, chromium trioxide (CrO_3) has chromium in its +6 oxidation state and is a strong oxidizing agent, reflecting its acidic character.

Comparatively, chromium(III) oxide (Cr_2O_3), where chromium has a +3 oxidation state, is less acidic and shows some amphoteric properties. Meanwhile, chromium(II) oxide (CrO) exhibits basic properties, as it has the lowest oxidation state of these three oxides. This illustrates a general rule: the higher the oxidation state of a transition metal oxide, the more acidic it tends to be. Therefore when arranging chromium oxides in terms of increasing basicity, we start with the most acidic (CrO_3), followed by the more neutral or amphoteric (Cr_2O_3), and end with the most basic (CrO). These properties of chromium oxides are not only academically intriguing but also have important industrial applications, such as in the manufacturing of stainless steel and green paints.