Problem 77
Question
Consider titanium metal and its two oxides, TiO and \(\mathrm{TiO}_{2}\). The oxide ion has no unpaired clectrons. (a) Which of these titanium species is diamagnetic? Fxplain your answer. (b) Which titanium species will he most attracted to a magmetic field? Fxplain your answer.
Step-by-Step Solution
Verified Answer
(a) \(\text{TiO}_{2}\) is diamagnetic. (b) TiO is most attracted to a magnetic field.
1Step 1: Determine Oxidation States
For TiO, let the oxidation state of titanium be \(x\). Since oxygen usually has an oxidation state of \(-2\), we write the equation: \[ x + (-2) = 0 \] Solving for \(x\), we find \(x=+2\). Therefore, in TiO, titanium has an oxidation state of +2.For \(\text{TiO}_{2}\), let the oxidation state of titanium also be \(x\). For two oxygen atoms, the equation becomes: \[ x + 2(-2) = 0 \] Solving for \(x\), we find \(x=+4\). Therefore, in \(\text{TiO}_{2}\), titanium has an oxidation state of +4.
2Step 2: Determine Electron Configuration
Titanium in its ground state has an electron configuration of \([\text{Ar}] 3d^2 4s^2\). For TiO, which has Ti\(^{2+}\) (\(+2\) oxidation state), the electron configuration will be: \([\text{Ar}] 3d^2\), after removing two electrons from the \(4s\) orbitals.For \(\text{TiO}_{2}\), which has Ti\(^{4+}\) (\(\text{oxidation state} +4\)), the electron configuration will be:\([\text{Ar}]\), as 4 electrons (2 from 3d and 2 from 4s) are removed.
3Step 3: Determine Magnetic Properties
A species is diamagnetic if it has no unpaired electrons, and paramagnetic if it has unpaired electrons.In \([\text{Ar}]\), which corresponds to \(\text{Ti}^{4+}\) in \(\text{TiO}_{2}\), there are no unpaired electrons. Thus, \(\text{TiO}_{2}\) is diamagnetic.In \([\text{Ar}] 3d^2\), which corresponds to \(\text{Ti}^{2+}\) in TiO, there are two unpaired electrons in the 3d orbitals. Thus, TiO is paramagnetic.
4Step 4: Analyze Reaction to Magnetic Field
Diamagnetic species are not attracted to magnetic fields, while paramagnetic species are attracted due to unpaired electrons. Since TiO (with Ti\(^{2+}\)) has unpaired electrons, it will be attracted to a magnetic field. In contrast, \(\text{TiO}_{2}\) (with Ti\(^{4+}\)) will not be affected by a magnetic field as it is diamagnetic.
Key Concepts
Oxidation StatesElectron ConfigurationDiamagnetismParamagnetism
Oxidation States
In chemistry, oxidation states help us understand how electrons are distributed in a compound. These states indicate the degree of oxidation of an atom within a chemical compound. To determine the oxidation state, we analyze the charges on atoms involved. For titanium in different compounds such as TiO and \( \text{TiO}_{2} \), oxygen, which typically has an oxidation state of \(-2\), allows us to assign a specific oxidation state to titanium.
For TiO, titanium's oxidation state is calculated using the formula:
\[ x + (-2) = 0 \] Solving this gives \( x = +2 \).
For \( \text{TiO}_{2} \), where there are two oxygen atoms, we use:
\[ x + 2(-2) = 0 \] Solving results in \( x = +4 \).
Thus, titanium has oxidation states of +2 in TiO and +4 in \( \text{TiO}_{2} \). Understanding these oxidation states provides insight into the electron loss and oxidation of titanium in these compounds.
For TiO, titanium's oxidation state is calculated using the formula:
\[ x + (-2) = 0 \] Solving this gives \( x = +2 \).
For \( \text{TiO}_{2} \), where there are two oxygen atoms, we use:
\[ x + 2(-2) = 0 \] Solving results in \( x = +4 \).
Thus, titanium has oxidation states of +2 in TiO and +4 in \( \text{TiO}_{2} \). Understanding these oxidation states provides insight into the electron loss and oxidation of titanium in these compounds.
Electron Configuration
Electron configuration reveals the distribution of electrons in an atom's orbitals. These configurations shape an atom's chemical properties and behavior. Understanding titanium's electron configuration helps predict its magnetic properties.
In its elemental form, titanium has an electron configuration of \([\text{Ar}] 3d^2 4s^2\). When titanium forms ions by losing electrons, such as in TiO with a +2 oxidation state, we adjust the configuration by removing electrons from the highest energy orbitals first.
In TiO's Ti\(^{2+}\), the electron configuration becomes:
\([\text{Ar}] 3d^2\).
In \( \text{TiO}_{2} \) where titanium's oxidation state is +4 (Ti\(^{4+}\)), the ion's configuration is:
\([\text{Ar}]\)
The absence of 3d and 4s electrons in Ti\(^{4+}\) sets up the stage for understanding magnetic properties related to unpaired electrons.
In its elemental form, titanium has an electron configuration of \([\text{Ar}] 3d^2 4s^2\). When titanium forms ions by losing electrons, such as in TiO with a +2 oxidation state, we adjust the configuration by removing electrons from the highest energy orbitals first.
In TiO's Ti\(^{2+}\), the electron configuration becomes:
\([\text{Ar}] 3d^2\).
In \( \text{TiO}_{2} \) where titanium's oxidation state is +4 (Ti\(^{4+}\)), the ion's configuration is:
\([\text{Ar}]\)
The absence of 3d and 4s electrons in Ti\(^{4+}\) sets up the stage for understanding magnetic properties related to unpaired electrons.
Diamagnetism
Diamagnetism arises in materials where all electrons are paired. These materials create a slight counter-force to an applied magnetic field, making them slightly repellent. This subtlety in electron pairing is pivotal in identifying whether a substance is diamagnetic or not.
For example, \( \text{TiO}_{2} \) is a compound where the titanium ion, Ti\(^{4+}\), has no unpaired electrons. Its electron configuration, \([\text{Ar}]\), confirms this. Consequently, \( \text{TiO}_{2} \) is diamagnetic as all its electron pairings provide no significant magnetism.
Key features of diamagnetic materials include:
For example, \( \text{TiO}_{2} \) is a compound where the titanium ion, Ti\(^{4+}\), has no unpaired electrons. Its electron configuration, \([\text{Ar}]\), confirms this. Consequently, \( \text{TiO}_{2} \) is diamagnetic as all its electron pairings provide no significant magnetism.
Key features of diamagnetic materials include:
- No unpaired electrons.
- Slight repulsion to magnetic fields.
Paramagnetism
Paramagnetism is observed in materials that have one or more unpaired electrons. These unpaired electrons generate magnetic moments, allowing the material to be attracted to an external magnetic field. The level of attraction depends on the number of unpaired electrons.
In the case of TiO, with a Ti\(^{2+}\) ion, its electron configuration is \([\text{Ar}] 3d^2\), which contains two unpaired electrons. This configuration confirms that TiO is paramagnetic, as the unpaired electrons cause magnetic attraction.
Essential characteristics of paramagnetic materials include:
In the case of TiO, with a Ti\(^{2+}\) ion, its electron configuration is \([\text{Ar}] 3d^2\), which contains two unpaired electrons. This configuration confirms that TiO is paramagnetic, as the unpaired electrons cause magnetic attraction.
Essential characteristics of paramagnetic materials include:
- Presence of unpaired electrons.
- Attraction to magnetic fields.
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