Which oxide, \(\mathrm{Mn}_{2} \mathrm{O}_{3}\) or \(\mathrm{Mn}_{2} \mathrm{O}_{7}\), is more basic in water? Why?

Understanding oxidation states is crucial when discussing manganese oxides. The oxidation state indicates the degree of oxidation of an atom in a compound. It's represented by integers, which can be positive, negative, or zero. For instance, in \(\text{Mn}_2O_3\), each oxygen has an oxidation state of -2. Since the total charge must equal zero, we can calculate the oxidation state of Mn as follows: \[2 \times x + 3 \times (-2) = 0\] Solving for x, we get: \[2x - 6 = 0 \implies x = +3\] Similarly, in \(\text{Mn}_2O_7\), since there are 7 oxygens: \[2 \times x + 7 \times (-2) = 0\] Solving for x: \[2x - 14 = 0 \implies x = +7\] Thus, the oxidation states of Mn are +3 in \(\text{Mn}_2O_3\) and +7 in \(\text{Mn}_2O_7\).

Metal oxides are compounds formed by metals combined with oxygen. They can exist in various oxidation states, influencing their physical and chemical properties. Manganese oxides demonstrate this, with \(\text{Mn}_2O_3\) being manganese(III) oxide and \(\text{Mn}_2O_7\) being manganese(VII) oxide. The properties of these oxides, such as basicity and acidity, are closely tied to the oxidation state of the metal. Higher oxidation states generally result in more acidic oxides, whereas lower oxidation states often produce more basic oxides.

The basicity and acidity of metal oxides depend on the oxidation state of the metal. Oxides with metals in lower oxidation states are more basic. Conversely, oxides with metals in higher oxidation states are more acidic. In an aqueous solution:

• Manganese(III) oxide (\(\text{Mn}_2O_3\)) with Mn in a +3 oxidation state tends to be basic.
• Manganese(VII) oxide (\(\text{Mn}_2O_7\)) with Mn in a +7 oxidation state tends to be acidic.

This is due to the higher positive charge causing a higher attraction to oxygen's electrons, creating a greater likelihood of attracting hydrogen ions (H⁺) and therefore behaving acidic.

Chemical formulas represent the composition of molecules using symbols for each element and numbers indicating their ratios. For example:

• \(\text{Mn}_2O_3\) means there are 2 manganese atoms and 3 oxygen atoms.
• \(\text{Mn}_2O_7\) indicates 2 manganese atoms and 7 oxygen atoms.

Knowing how to interpret these formulas helps understand the different characteristics of each compound, such as their basicity or acidity. For manganese oxides, \(\text{Mn}_2O_3\) signifies a lower oxidation state (+3) compared to \(\text{Mn}_2O_7\) (+7), directly influencing their behavior in water as more basic or more acidic respectively.