Problem 42 - Chemistry The Central Science

Question

Select the more acidic member of each of the following pairs: (a) \(\mathrm{Mn}_{2} \mathrm{O}_{7}\) and \(\mathrm{MnO}_{2}\), (b) \(\mathrm{SnO}\) and \(\mathrm{SnO}_{2}\), (c) \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\), (d) \(\mathrm{SiO}_{2}\) and \(\mathrm{SO}_{2}\), (e) \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) and \(\mathrm{In}_{2} \mathrm{O}_{3},\) (f) \(\mathrm{SO}_{2}\) and \(\mathrm{SeO}_{2}\).

Step-by-Step Solution

Answer

The more acidic members of the given pairs are: (a) \(\mathrm{Mn}_{2} \mathrm{O}_{7}\), (b) \(\mathrm{SnO}_{2}\), (c) \(\mathrm{SO}_{3}\), (d) \(\mathrm{SO}_{2}\), (e) \(\mathrm{Ga}_{2} \mathrm{O}_{3}\), and (f) \(\mathrm{SO}_{2}\).

Step 1: Pair (a): \(\mathrm{Mn}_{2} \mathrm{O}_{7}\) and \(\mathrm{MnO}_{2}\)

Manganese heptoxide (\(\mathrm{Mn}_{2} \mathrm{O}_{7}\)) is a compound in which manganese has an oxidation state of +7, while manganese dioxide (\(\mathrm{MnO}_{2}\)) has manganese in the +4 oxidation state. Higher oxidation states generally result in a more acidic compound because the central atom is more electronegative and can stabilize the conjugate base better. Therefore, \(\mathrm{Mn}_{2} \mathrm{O}_{7}\) is the more acidic member of this pair.

Step 2: Pair (b): \(\mathrm{SnO}\) and \(\mathrm{SnO}_{2}\)

For tin monoxide (\(\mathrm{SnO}\)), tin has an oxidation state of +2, while for tin dioxide (\(\mathrm{SnO}_{2}\)), the oxidation state is +4. As discussed in the previous pair, compounds with higher oxidation states are generally more acidic. Therefore, \(\mathrm{SnO}_{2}\) is the more acidic member of this pair.

Step 3: Pair (c): \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\)

Sulfur dioxide (\(\mathrm{SO}_{2}\)) has sulfur in the +4 oxidation state, while sulfur trioxide (\(\mathrm{SO}_{3}\)) has sulfur in the +6 oxidation state. Due to the higher electronegativity and oxidation state in \(\mathrm{SO}_{3}\), it is more acidic than \(\mathrm{SO}_{2}\).

Step 4: Pair (d): \(\mathrm{SiO}_{2}\) and \(\mathrm{SO}_{2}\)

Silicon dioxide (\(\mathrm{SiO}_{2}\)) has silicon in the +4 oxidation state, while sulfur dioxide (\(\mathrm{SO}_{2}\)) has sulfur in the +4 oxidation state. Though both central atoms have the same oxidation state, sulfur is more electronegative than silicon. Thus, \(\mathrm{SO}_{2}\) is more acidic than \(\mathrm{SiO}_{2}\).

Step 5: Pair (e): \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) and \(\mathrm{In}_{2} \mathrm{O}_{3}\)

Gallium oxide (\(\mathrm{Ga}_{2} \mathrm{O}_{3}\)) has gallium in the +3 oxidation state, as does indium oxide (\(\mathrm{In}_{2} \mathrm{O}_{3}\)) for indium. They are in the same group in the periodic table, so we must compare their electronegativities. Gallium is more electronegative than indium, so \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) is the more acidic member of this pair.

Step 6: Pair (f): \(\mathrm{SO}_{2}\) and \(\mathrm{SeO}_{2}\)

Sulfur dioxide (\(\mathrm{SO}_{2}\)) has sulfur in the +4 oxidation state, and selenium dioxide (\(\mathrm{SeO}_{2}\)) has selenium in the +4 oxidation state. Both are in the same group in the periodic table, so we must compare their electronegativities. Sulfur is more electronegative than selenium, so \(\mathrm{SO}_{2}\) is the more acidic member of this pair.

Key Concepts

Oxidation States

In chemistry, the oxidation state of an element indicates the degree of oxidation, or loss of electrons, that an atom has undergone. This concept is crucial when evaluating the acidic nature of compounds. For instance, compounds with higher oxidation states are often more acidic. This is because higher oxidation states typically mean that the central atom can better stabilize the conjugate base.

Consider the exercise involving \(\mathrm{Mn}_{2}\mathrm{O}_{7}\) and \(\mathrm{MnO}_{2}\). Manganese in \(\mathrm{Mn}_{2}\mathrm{O}_{7}\) has a +7 oxidation state, whereas in \(\mathrm{MnO}_{2}\), it is +4. The higher oxidation state in \(\mathrm{Mn}_{2}\mathrm{O}_{7}\) makes it more acidic, proving how the oxidation state directly influences acidity.

• *Remember*: Higher oxidation numbers often correlate with increased acidity.

Electronegativity

Electronegativity describes an atom's ability to attract and hold onto electrons. It's a key factor in determining the acidity of oxides. In pairs where the central atoms have the same oxidation state, such as in sulfur dioxide (\(\mathrm{SO}_{2}\)) and selenium dioxide (\(\mathrm{SeO}_{2}\)), electronegativity becomes the decisive factor for acidity.

The higher electronegativity of sulfur compared to selenium implies that \(\mathrm{SO}_{2}\) is more acidic than \(\mathrm{SeO}_{2}\). This is because sulfur, being more electronegative, can stabilize the electrons better after donating protons.

• *Keep in mind*: Higher electronegativity often enhances acidic character.

Periodic Table Trends

The periodic table provides valuable insights into the properties of elements, including their acidity. Trends such as the increase in electronegativity from left to right and the general increase in oxidation states in higher periods are important in predicting acidic behavior.

For example, comparing \(\mathrm{Ga}_{2}\mathrm{O}_{3}\) and \(\mathrm{In}_{2}\mathrm{O}_{3}\), we find that gallium is more electronegative than indium. Despite both elements being in group 13 with a +3 oxidation state, the trend of increasing electronegativity going upwards in the group means \(\mathrm{Ga}_{2}\mathrm{O}_{3}\) is more acidic.

• *Tip*: Analyze periodic trends to quickly determine potential differences in acidity among oxides.