Question

The trichloride ion, \(\mathrm{Cl}_{3}^{-1}\), is not very stable in aqueous solution. The equilibrium constant for the following dissociation reaction is 5.5 at \(25^{\circ} \mathrm{C}\) : $$\mathrm{Cl}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{aq})$$ (a) Draw a Lewis structure for the \(\mathrm{Cl}_{3}^{-}\) ion and predict the geometry. (b) Calculate the equilibrium concentration of \(\mathrm{Cl}_{3}^{-}\) if 0.0010 moles each of \(\mathrm{KCl}\) and \(\mathrm{Cl}_{2}\) are dissolved in water at \(25^{\circ} \mathrm{C}\) to make \(1.0 \mathrm{L}\) of solution.

Short answer

The predicted geometry of \(\mathrm{Cl}_{3}^{-}\) is linear. The equilibrium concentration of \(\mathrm{Cl}_{3}^{-}\) can be calculated by solving the given equilibrium expression.

Step-by-step solution

Draw the Lewis structure of \(\mathrm{Cl}_{3}^{-}\)

Start by counting the total number of valence electrons. Chlorine has 7 valence electrons, but since there are three, we have 21. The extra electron given by the ion charge leads to 22 electrons. As per the octet rule, each Cl atom needs 8 electrons. Hence, each of the two chlorine atoms forms a single bond with the central chlorine atom to complete its octet, taking up 4 electrons. The remaining 18 electrons are distributed as lone pairs. 12 go to the two bonding chlorine atoms (6 each), and the remaining 6 go to the central atom. Thus, the central chlorine atom has a formal negative charge, in accordance with the -1 charge of the overall ion.

Predict the geometry of \(\mathrm{Cl}_{3}^{-}\)

The geometry of a molecule/ion can be predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory that essentially posits that electron groups (including lone pair electrons and bonding electrons) tend to repel each other and will thus orient themselves as far apart as possible. In Cl3-, the central Cl has 5 electron groups (3 lone pairs and 2 atoms), implying a 'Trigonal Bipyramidal' shape for the 5 electron groups. However, when considering atoms only, they occupy 'Linear' positions.

Calculate initial concentrations

Cl3- has zero initial concentration as it has yet to form. For Cl- and Cl2, after KCl and Cl2 dissolve, their concentrations will be the amount of moles in 1 L, hence their initial concentrations are both 0.0010 M.

Write the expression for the equilibrium concentrations

Consider the dissociation reaction at equilibrium. Cl3- will form changing its initial concentration by +x. As for Cl- and Cl2, they will decrease by x each from the initial concentration. Hence, the equilibrium concentrations are x M for Cl3-, and (0.0010-x) M for both Cl- and Cl2. x is the variable we need to solve for.

Use the given equilibrium constant to solve for x

Given the equilibrium constant (K) as 5.5, we plug the equilibrium concentrations into the expression for K, which will be \([Cl^-][Cl_2]/[Cl_3^-] = K\). Substituting the concentrations gives \((0.0010-x)*(0.0010-x)/x = 5.5\). Solving this equation for x leads to an equilibrium concentration of Cl3-

Key concepts

Lewis Structure

A Lewis structure is a diagram that illustrates the bonding between atoms, as well as the lone pairs of electrons in a molecule. To construct a Lewis structure, you tally the total valence electrons and distribute them to satisfy the octet rule for all atoms involved.

• In the case of the chloride ion, \(\mathrm{Cl}_{3}^{-}\), each chlorine atom contributes 7 valence electrons, totaling 21.
• Since the ion bears a negative charge, one extra electron is added, culminating in 22 electrons.
• The central chlorine atom, bonded to two other Cl atoms, utilizes 4 electrons for bonding.
• The remaining 18 electrons are assigned as lone pairs: 12 shared between the two bonded Cl atoms (6 each), and 6 assigned to the central Cl atom, giving it a formal negative charge.

This arrangement follows the rules for Lewis structures, ensuring that each chlorine atom satisfies the octet rule, which maintains stability. The structure of \(\mathrm{Cl}_{3}^{-}\) showcases the distribution of electrons necessary for predicting molecular geometry.

VSEPR Theory

VSEPR theory (Valence Shell Electron Pair Repulsion theory) is a model that predicts the geometry of molecular structures based on electron pairs’ repulsion around the central atom. The main idea is that molecules are organized in a way that minimizes electron pair repulsions.

• For \(\mathrm{Cl}_{3}^{-}\), the central Cl atom is surrounded by 5 electron groups, 3 as lone pairs and 2 as bonds.
• According to VSEPR theory, 5 electron groups arrange into a 'Trigonal Bipyramidal' shape (considering all electron groups).
• However, lone pairs occupy more space than bonding pairs and repel bonded atoms.
• This results in the bonded atoms assuming a 'Linear' arrangement, as the electron pairs spread as far apart as possible.

VSEPR theory is a powerful tool in chemistry that allows the prediction of molecular shapes, thereby giving insight into their chemical behavior and reactivity.

Molecular Geometry

Molecular geometry refers to the three-dimensional shape of a molecule. It is significantly determined by VSEPR theory and affects many physical and chemical properties of the molecule.

• The \(\mathrm{Cl}_{3}^{-}\) ion has a 'Linear' geometry when focusing solely on the position of the atoms.
• This is because, despite the 'Trigonal Bipyramidal' electron pair geometry, the lone pairs on the central Cl atom influence the spatial distribution of the Cl atoms, forcing them to align linearly.
• A linear molecular geometry means that the atoms are directly in line with each other, creating a 180-degree bond angle.

Understanding molecular geometry is crucial as it helps predict the molecule’s interaction with other chemical species and its overall behavior in different environments.

Dissociation Reaction

A dissociation reaction is a process wherein a compound splits into two or more smaller molecules or ions. These reactions are common in aqueous solutions and are crucial for understanding equilibrium and reaction dynamics.

• For the equation \(\mathrm{Cl}_{3}^{-} \rightleftharpoons \mathrm{Cl}^{-} + \mathrm{Cl}_{2}\), we observe dissociation where the unstable \(\mathrm{Cl}_{3}^{-}\) ion separates into a chloride ion \(\mathrm{Cl}^{-}\) and a chlorine molecule \(\mathrm{Cl}_{2}\).
• The equilibrium constant \(K = 5.5\) signifies the position of the equilibrium towards the products, meaning dissociation is favored at 25°C.
• Reversibly, such equilibrium constants allow us to calculate concentrations at equilibrium, a key concept in developing solutions with desired chemical properties.

Dissociation reactions are fundamental to many areas of chemistry, providing insight into molecular stability and the formation of various compounds in a solution.