Question

Chlorine dioxide gas \(\left(\mathrm{ClO}_{2}\right)\) is used as a commercial bleaching agent. It bleaches materials by oxidizing them. In the course of these reactions, the \(\mathrm{ClO}_{2}\) is itself reduced. (a) What is the Lewis structure for \(\mathrm{ClO}_{2} ?\) (b) Why do you think that \(\mathrm{ClO}_{2}\) is reduced so readily? (c) When a \(\mathrm{ClO}_{2}\) molecule gains an electron, the chlorite ion, \(\mathrm{ClO}_{2}^{-},\) forms. Draw the Lewis structure for \(\mathrm{ClO}_{2}^{-} .\) (d) Predict the \(\mathrm{O}-\mathrm{Cl}-\mathrm{O}\) bond angle in the \(\mathrm{ClO}_{2}^{-}\) ion. (e) One method of preparing \(\mathrm{ClO}_{2}\) is by the reaction of chlorine and sodium chlorite: $$\mathrm{Cl}_{2}(g)+2 \mathrm{NaClO}_{2}(s) \longrightarrow 2 \mathrm{ClO}_{2}(g)+2 \mathrm{NaCl}(s)$$ If you allow 15.0 \(\mathrm{g}\) of \(\mathrm{NaClO}_{2}\) to react with 2.00 \(\mathrm{L}\) of chlorine gas at a pressure of 1.50 atm at \(21^{\circ} \mathrm{C},\) how many grams of \(\mathrm{ClO}_{2}\) can be prepared?

Short answer

The Lewis structure of $\mathrm{ClO}_{2}$ has a chlorine atom single-bonded to each of the two oxygen atoms and one lone pair of electrons on the chlorine atom, and three lone pairs of electrons on each oxygen atom. The chlorine atom is readily reduced because it has an incomplete octet, and the chlorite ion, $\mathrm{ClO}_{2}^{-}$, results from adding an extra electron to the ClO2 molecule. The O-Cl-O bond angle in the chlorite ion is approximately \(109.5^{\circ}\), and given the conditions stated, the reaction between NaClO2 and Cl2 yields 16.4 g of ClO2.

Step-by-step solution

Determine the Lewis structure of ClO2

Begin by counting the total number of valence electrons in the molecule. Chlorine has 7 valence electrons and each oxygen atom has 6 valence electrons. The total number of valence electrons in ClO2 is therefore \(7 + 6 \cdot 2 = 19\). Now, arrange the atoms with the least electronegative atom in the center (Cl), and connect each oxygen atom to the chlorine atom with a single bond. This accounts for a total of 4 valence electrons (2 lone pairs), leaving 15 remaining electrons. Distribute the remaining electrons to complete the octets of the outer atoms (oxygen) first. Each oxygen atom needs 6 more electrons (3 lone pairs), which accounts for the remaining 12 valence electrons. Two electrons are left, which should be placed on the central atom, chlorine, as a lone pair. This gives the Lewis structure of ClO2: Cl with a single bond to each oxygen atom, a lone pair of electrons on the chlorine atom, and 3 lone pairs on each oxygen atom.

Explain the ease of reduction of ClO2

The reduction of ClO2 is favored because, in its Lewis structure, the chlorine atom does not have a complete octet (it only has 7 electrons). This makes it highly reactive and susceptible to gaining an additional electron, completing its octet and stabilizing the molecule.

Determine the Lewis structure of ClO2- (the chlorite ion)

The chlorite ion, ClO2-, can be formed by adding an extra electron to the ClO2 molecule, which completes the octet of the chlorine atom. The Lewis structure of the chlorite ion will be the same as that of ClO2, with the addition of one more lone pair on the chlorine atom. This gives a total of 2 lone pairs on the chlorine atom and 3 lone pairs on each oxygen atom.

Predict the O-Cl-O bond angle in the chlorite ion

The chlorite ion has an AX2E2 molecular geometry, with two bond pairs (O-Cl bonds) and two lone pairs on the central atom (Cl). According to the VSEPR theory, the bond pairs and lone pairs will repel each other and arrange symmetrically around the central atom. In the case of AX2E2 molecules, the geometry corresponds to a bent shape with an ideal O-Cl-O bond angle of approximately 109.5°.

Calculate the mass of ClO2 produced from the reaction between NaClO2 and Cl2

First, determine the moles of NaClO2 and Cl2 used in the reaction. For NaClO2: \(\text{moles of NaClO}_{2}=\frac{15.0\,\text{g}}{90.45\,\text{g/mol}}=0.166\,\text{mol}\) For Cl2, use the ideal gas law: \(PV=nRT\Rightarrow n=\frac{PV}{RT}\) \(\text{moles of Cl}_{2}=\frac{(1.50\,\text{atm})(2.00\,\text{L})}{(0.0821\,\text{L}\cdot\text{atm/mol}\cdot\text{K})(294\,\text{K})}=0.122\,\text{mol}\) Now, determine the limiting reactant by comparing the mole ratio to the stoichiometry of the balanced equation: \(\frac{\text{moles of Cl}_{2}}{\text{moles of NaClO}_{2}}=\frac{0.122}{0.166}=0.736\) Since the stoichiometry of the balanced equation requires 1 mol of Cl2 to react with 2 mol of NaClO2, the ratio should be 0.5. This means that Cl2 is the limiting reactant. To find the mass of ClO2 produced, use the stoichiometry of the balanced equation: \(\text{moles of ClO}_{2}=(0.122\,\text{mol Cl}_{2})\cdot\frac{2\,\text{moles ClO}_{2}}{1\,\text{mole Cl}_{2}}=0.244\, \text{mol}\) \(\text{mass of ClO}_{2}=(0.244\,\text{mol})\cdot(67.45\,\text{g/mol})=16.4\,\text{g}\) Thus, 16.4 g of ClO2 can be prepared from the given amounts of reactants.

Key concepts

Oxidation and Reduction

Oxidation and reduction are chemical processes that involve the transfer of electrons between atoms or molecules. These processes are collectively known as redox reactions. In an oxidation reaction, an atom or molecule loses electrons, thereby increasing its oxidation state. Conversely, during a reduction reaction, an atom or molecule gains electrons and decreases its oxidation state.

Chlorine dioxide (ClO2) acts as an oxidizing agent because it has a strong tendency to gain electrons and become reduced. The very property that makes ClO2 a good oxidizing agent is its high electronegativity and an incomplete octet in its valence shell, as illustrated in the textbook exercise. This incomplete octet indicates that ClO2 is electron-deficient and can easily accept an extra electron to become the chlorite ion (ClO2-), thus undergoing reduction.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It postulates that the geometric arrangement of terminal atoms and electron pairs around a central atom in a molecule is determined primarily by the repulsion between electron pairs in the valence shell of the central atom.

According to VSEPR theory, the structure of the ClO2- ion is predicted to have a 'bent' shape, as the Cl atom is surrounded by two bond pairs and two lone pairs of electrons. These electron pairs repel each other, aiming to be as far apart as possible, which results in the bond angle that is slightly less than 109.5 degrees due to the repulsion being greater for lone pairs compared to bonding pairs.

Stoichiometry

Stoichiometry is the section of chemistry that involves calculations relating to the masses of reactants and products in chemical reactions. It is based on the law of conservation of mass and the understanding that chemical reactions are described by balanced chemical equations, which provide the ratios in which reactants and products interact and form.

In the provided exercise, the stoichiometric coefficients from the balanced chemical equation of chlorine (Cl2) reacting with sodium chlorite (NaClO2) were used to determine the mass of chlorine dioxide (ClO2) that could be produced. The calculations involved finding the limiting reactant (Cl2 in this case) and using its amount to calculate the molar mass of ClO2 that can be formed. Stoichiometry is essential in ensuring that chemical reactions are conducted efficiently and predictably in both laboratory and industrial settings.