Question

Write Lewis structures for \(\mathrm{CO}_{3}^{2-}, \mathrm{HCO}_{3}^{-},\) and \(\mathrm{H}_{2} \mathrm{CO}_{3}\). When acid is added to an aqueous solution containing carbonate or bicarbonate ions, carbon dioxide gas is formed. We generally say that carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\) is unstable. Use bond energies to estimate \(\Delta E\) for the reaction (in the gas phase) $$\mathrm{H}_{2} \mathrm{CO}_{3} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}$$Specify a possible cause for the instability of carbonic acid.

Short answer

The Lewis structures of the given compounds are: 1. \(\mathrm{CO}_{3}^{2-}\): Carbon atom double-bonded to an Oxygen atom and two singly bonded Oxygens with one extra pair of electrons on each of these two Oxygen atoms. 2. \(\mathrm{HCO}_{3}^{-}\): Carbon atom single-bonded to one Hydrogen atom, double bonded to one Oxygen atom, and singly bonded to another Oxygen atom with two lone pairs. 3. \(\mathrm{H}_{2}\mathrm{CO}_{3}\): Carbon atom single-bonded to two Hydrogen atoms, double bonded to an Oxygen atom, and singly bonded to another Oxygen atom with two lone pairs. The bond energy change, \(\Delta E\), for the reaction \(\mathrm{H}_{2}\mathrm{CO}_{3} \longrightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\) is 116 kJ/mol. A possible cause for the instability of carbonic acid is the presence of acidic conditions in the environment and/or the lower energy state of the converted products, \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

Find the Lewis structure for \(\mathrm{CO}_{3}^{2-}\)

To find the Lewis structure of \(\mathrm{CO}_{3}^{2-}\), follow these steps: 1. Determine the total number of valence electrons. Carbon has 4, Oxygen has 6 each, and there are 2 extra electrons from the charge. Total: \(4 + 3 \times 6 + 2 = 24\) electrons. 2. Place the least electronegative atom at the center, which is Carbon in this case. 3. Place the Oxygen atoms around the central Carbon atom. 4. Connect the central atom to the surrounding atoms using single bonds first. This will consume 6 of the 24 electrons. 5. Fill the remaining electrons in the surrounding atoms as lone pairs until there are no more electrons left, or every atom has a complete octet. 6. If needed, form multiple bonds to satisfy the octet rule. The final structure for \(\mathrm{CO}_{3}^{2-}\) consists of a Carbon atom double-bonded to an Oxygen atom and two singly bonded Oxygens with one extra pair of electrons on each of these two Oxygen atoms.

Find the Lewis structure for \(\mathrm{HCO}_{3}^{-}\)

To find the Lewis structure of \(\mathrm{HCO}_{3}^{-}\), follow the same steps as above: 1. Determine the total number of valence electrons. Hydrogen has 1, Carbon has 4, Oxygen has 6 each, and there is 1 extra electron from the charge. Total: \(1 + 4 + 3 \times 6 + 1 = 24\) electrons. 2. Place the least electronegative atom at the center, which is Carbon in this case. 3. Arrange the remaining atoms around the central Carbon atom. In this case, place H by C and the Oxygens around C. 4. Connect the central atom to the surrounding atoms using single bonds first. This will consume 6 of the 24 electrons. 5. Fill the remaining electrons in the surrounding atoms as lone pairs until there are no more electrons left. The final structure for \(\mathrm{HCO}_{3}^{-}\) consists of a Carbon atom single-bonded to one Hydrogen atom, double bonded to one Oxygen atom, and singly bonded to another Oxygen atom with two lone pairs.

Find the Lewis structure for \(\mathrm{H}_{2}\mathrm{CO}_{3}\)

To find the Lewis structure of \(\mathrm{H}_{2}\mathrm{CO}_{3}\), follow the same steps as above: 1. Determine the total number of valence electrons: Total: \(2(1) + 4 + 3 \times 6 = 24\) electrons. 2. Place the least electronegative atom at the center, which is Carbon in this case. 3. Arrange the remaining atoms around the central Carbon atom. In this case, place two H atoms by C and the Oxygens around C. 4. Connect the central atom to the surrounding atoms using single bonds first. This will consume 8 of the 24 electrons. 5. Fill the remaining electrons in the surrounding atoms as lone pairs until there are no more electrons left. The final structure for \(\mathrm{H}_{2}\mathrm{CO}_{3}\) consists of a Carbon atom single-bonded to two Hydrogen atoms, double bonded to an Oxygen atom, and singly bonded to another Oxygen atom with two lone pairs.

Calculate the bond energy change ΔE for the reaction

To calculate the bond energy change ΔE, we need to first identify all the bonds that are breaking and those that are forming in the reaction: $$\mathrm{H}_{2}\mathrm{CO}_{3} \longrightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}$$ Breaking bonds: - 1 C=O bond in \(\mathrm{H}_{2}\mathrm{CO}_{3}\) - 1 C-O bond in \(\mathrm{H}_{2}\mathrm{CO}_{3}\) - 2 H-O bond in \(\mathrm{H}_{2}\mathrm{CO}_{3}\) Forming bonds: - 2 C=O bonds in CO2 - 2 H-O bonds in \(\mathrm{H}_{2}\mathrm{O}\) Using the given bond energies in the problem and remembering that breaking bonds requires energy input while forming bonds releases energy: ΔE = Bond energy change = Energy spent - Energy released ΔE = {[1 × C=O + 1 × C-O + 2 × H-O] - [2 × C=O + 2 × H-O]} Now, substituting the bond energy values and calculating the bond energy change: ΔE = ([-1686 - 358 - 2(467)] - [-2 × 799 - 2 × 459]) ΔE = 116, so the bond energy change for the reaction is 116 kJ/mol.

Specifying a possible cause for the instability of Carbonic Acid

The calculated bond energy change is positive, implying that the conversion of \(\mathrm{H}_{2}\mathrm{CO}_{3}\) to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\) is endothermic and not spontaneous. However, in the presence of acids acting as catalysts, the activation energy is reduced, allowing the unstable carbonic acid to decompose easily into carbon dioxide and water. Therefore, the possible cause for the instability of carbonic acid could be the presence of acidic conditions in the environment and / or the lower energy state of the converted products, \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\).

Key concepts

Lewis Dot Structures

Understanding Lewis dot structures is essential for determining the electron arrangement in molecules and ions. They are diagrams that represent the valence electrons of an atom as dots. These dots are placed around the elemental symbol, illustrating the electrons that may participate in bonding.

In creating Lewis dot structures, we aim to represent molecules such that atoms achieve a full valence shell, most commonly the octet rule for many elements. This approach allows us to predict the connectivity between atoms and the distribution of electrons in a molecule. For species like \( \mathrm{CO}_3^{2-} \) and \( \mathrm{HCO}_3^{-} \) understanding the Lewis dot structure informs us of the resonance structures, which are different possible configurations of the same molecule, showing that some molecules have flexible bonding patterns that contribute to stability.

Valence Electrons

Valence electrons are the electrons located in an atom's outermost shell and are crucial in the formation of chemical bonds. As we saw in the exercise, when drawing Lewis structures, calculating the total number of valence electrons is the first step. This total dictates how the atoms within a molecule will share electrons to achieve stable electron configurations.

For example, the carbonate ion has a total of 24 valence electrons to be distributed among its atoms. These electrons are what makes it possible for carbonate to bond in various ways, with some oxygens double bonded to carbon, while others are single bonded. Thus, valence electrons are not just numbers but are the actual participants in bonding, dictating molecular structure and reactivity.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. The valence-shell electron-pair repulsion (VSEPR) theory helps us predict this geometry by considering the repulsions between electron pairs. Valence electrons, whether in bonds or as lone pairs, will arrange themselves to be as far apart as possible from each other.

For instance, a tetrahedral molecular geometry is common when a central atom is bonded to four other atoms with no lone pairs, like methane (\( CH_4 \)). In the case of \( \mathrm{CO}_3^{2-} \) the molecule exhibits trigonal planar geometry, with 120-degree angles between the bonded oxygen atoms. Understanding molecular geometry is not just related to shapes but also to the functional behavior of molecules, like reactivity, polarity, and intermolecular interactions.

Bond Energies

Bond energies are measures of the strength of chemical bonds and are defined as the average energy required to break one mole of bonds in the gas phase, at constant temperature and pressure. They are essential for estimating the changes in energy during chemical reactions, as demonstrated in the calculation of the bond energy change \( \Delta E \) for the decomposition of carbonic acid.

Every type of bond between atoms possesses a characteristic bond energy, which is taken into account when predicting the feasibility of chemical reactions. For example, double bonds typically have higher bond energies than single bonds, indicating that more energy is required to break them. By analyzing these energies, we gain insight into the energetic aspects that contribute to molecular stability and reactions.

Chemical Stability

Chemical stability pertains to a compound's resilience against change under given conditions. It is an inherent property that dictates a molecule's propensity to maintain its structure and resist decomposition or unwanted reactions. In the problem we've looked at, carbonic acid (\( \mathrm{H}_2\mathrm{CO}_3 \) is described as unstable, and we used bond energies to identify why.

Stable molecules usually have a lower potential energy and do not spontaneously decompose. Unstable molecules, such as \( \mathrm{H}_2\mathrm{CO}_3 \) under certain conditions, tend to transition to a more stable state, even without external energy, releasing carbon dioxide and water. The instability can be due to various factors, including molecular structure, external conditions like temperature or pH, and the potential energy relative to decomposition products.