Question

Write the formula for the oxide corresponding to the highest expected oxidation state for (a) \(\mathrm{Cd}\), (b) \(\mathrm{V}\), (c) \(\mathrm{W}\), (d) Ru.

Short answer

The oxide formulas for the elements in their highest oxidation states are: (a) \(\mathrm{CdO}\) (b) \(\mathrm{V_2O_5}\) (c) \(\mathrm{WO_3}\) (d) \(\mathrm{RuO_4}\)

Step-by-step solution

Identify the highest oxidation states for each element

For this step, we will find the highest oxidation states of the elements using their location in the periodic table and known information about their common oxidation states. (a) Cadmium (Cd) is in Group 12 of the periodic table. For elements in Group 12, the highest oxidation state is usually +2. (b) Vanadium (V) is in Group 5 (sometimes called Group 15) of the periodic table. For elements in this group, the highest oxidation state is typically +5. (c) Tungsten (W) is in Group 6 (sometimes called Group 16) of the periodic table. For this group, the highest oxidation state is generally +6. (d) Ruthenium (Ru) is in Group 8 (sometimes called Group 18) of the periodic table. Transition metals in this group typically have variable oxidation states, but for ruthenium, the highest known oxidation state is +8.

Write the formula for the oxide corresponding to the highest oxidation state for each element

Now that we have determined the highest oxidation states for each element, we can write the formula for their respective oxides by combining each element with oxygen (\(\mathrm{O}\)), which has an oxidation state of -2. (a) \(\mathrm{Cd}\) has an oxidation state of +2, and \(\mathrm{O}\) has an oxidation state of -2. The formula for cadmium oxide is then \(\mathrm{CdO}\). (b) \(\mathrm{V}\) has an oxidation state of +5, and \(\mathrm{O}\) has an oxidation state of -2. To combine these in a neutral compound, we would need 2 \(\mathrm{V}\) atoms (+5 each) and 5 \(\mathrm{O}\) atoms (-2 each). The formula for vanadium oxide is then \(\mathrm{V_2O_5}\). (c) \(\mathrm{W}\) has an oxidation state of +6, and \(\mathrm{O}\) has an oxidation state of -2. To combine these in a neutral compound, we would need 1 \(\mathrm{W}\) atom (+6) and 3 \(\mathrm{O}\) atoms (-2 each). The formula for tungsten oxide is then \(\mathrm{W_1O_3}\) or simply \(\mathrm{WO_3}\). (d) \(\mathrm{Ru}\) has an oxidation state of +8, and \(\mathrm{O}\) has an oxidation state of -2. To combine these in a neutral compound, we would need 4 \(\mathrm{Ru}\) atoms (+8 each) and 16 \(\mathrm{O}\) atoms (-2 each). The formula for ruthenium oxide is then \(\mathrm{Ru_4O_{16}}\). However, this oxide can be simplified to \(\mathrm{RuO_4}\) by dividing each subscript by the greatest common divisor (4). The oxide formulas for the elements in their highest oxidation states are: (a) \(\mathrm{CdO}\) (b) \(\mathrm{V_2O_5}\) (c) \(\mathrm{WO_3}\) (d) \(\mathrm{RuO_4}\)

Key concepts

Chemical Formulas

Understanding chemical formulas is fundamental in chemistry as they are the shorthand representations of compounds, displaying the types and numbers of atoms involved. For instance, when determining the highest oxidation states for elements such as Cd, V, W, and Ru, we must create the corresponding oxide formulas by combining the metal atoms with oxygen atoms in the right ratios.

Consider the example of vanadium (V) oxide. Vanadium can have an oxidation state of +5, and oxygen has a constant oxidation state of -2. To balance the charges and achieve a neutral molecule, vanadium oxide's formula is written as \(\mathrm{V_2O_5}\) illustrating that two \(\mathrm{V}\) atoms (each +5) balance with five \(\mathrm{O}\) atoms (each -2). Remember, the subscripts in a chemical formula must result in an overall net charge of zero for the compound.

Periodic Table Groups

The periodic table groups play a key role in determining the properties of elements, including their common oxidation states. Groups are columns of elements on the periodic table, and elements within the same group often have similar chemical behaviors. For example, Group 12 elements, like cadmium (Cd), typically exhibit a +2 oxidation state.

Knowing the group an element belongs to can provide a quick reference to predict its possible oxidation states. This understanding is crucial when writing oxide formulas, as the oxidation state will affect the ratio of metal to oxygen atoms. In academic tasks such as identifying the correct oxide formula for elements, recognizing the periodic table groups simplifies predicting chemical behavior and facilitates learning and solution discovery.

Transition Metals

In the context of oxidation states and forming compounds, transition metals, such as vanadium (V), tungsten (W), and ruthenium (Ru), are especially intriguing due to their ability to adopt multiple oxidation states. This flexibility is due to the filling of their d electron subshells and their position in the center of the periodic table, specifically in groups 3 through 12.

Variable Oxidation States

While transition metals can exhibit various oxidation states, each metal often has a maximum oxidation state it can reach, which is usually related to the number of electron orbitals it can use for bonding. For instance, ruthenium (Ru) in group 8 can reach an oxidation state of +8, which is considered very high and is less common among the transition elements. Understanding the unique properties of transition metals provides insight into the complexity and variety of compounds they can form, such as different oxides in our exercise.

Combining Elements

When combining elements to form compounds, such as oxides, it is not only about fitting pieces together; it is about understanding and applying the rules of chemistry to achieve a compound with a neutral charge. The principle of charge neutrality must always be observed, meaning the total positive charge must balance the total negative charge.

For example, when we combine ruthenium (Ru) with oxygen to form ruthenium oxide, knowing that Ru has a +8 oxidation state and oxygen has a -2 oxidation state helps us deduce the correct stoichiometric formula, which is \(\mathrm{RuO_4}\). This ensures that the overall charge is zero and the compound is stable. The processes of combining elements involve predicting reactivity, understanding electron transfer, and applying the laws of conservation of mass and charge.