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 \(\Delta H\) 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 for CO32-, HCO3-, and H2CO3 are: CO32-: ``` O \\ 𝚺 C - O- // O ``` HCO3-: ``` H | O - C - O- \\ O ``` H2CO3: ``` H O C - O- \\ O ``` The change in enthalpy (ΔH) for the gas-phase reaction H2CO3 → CO2 + H2O is 83 kJ/mol. The instability of carbonic acid can be attributed to the weak O-H bond and its relatively high energy, making it easier for the molecule to release CO2 gas and form water. The positive ΔH value indicates that the reaction is endothermic, meaning it absorbs energy from its environment during the breakdown process, making it more favorable under certain conditions.

Step-by-step solution

CO32-#

To draw the Lewis structure, first, count the total number of valence electrons. Carbon has 4, each oxygen atom has 6, and there are 2 extra electrons due to the 2- charge. So, the total valence electrons are: \[4+(3 \times 6)+2=24\] Create the Lewis structure by placing the carbon atom at the center since it is the least electronegative and the oxygen atoms around it. Then, connect each oxygen with a single bond to the carbon atom to create a total of 8 electrons used. Distribute the remaining 16 electrons among the oxygen atoms (5 electrons in each oxygen atom and one oxygen atom with 6 electrons). The Lewis structure of CO32- looks like this: ``` O \\ 𝚺 C - O- // O ```

HCO3-#

Calculating the valence electrons: Carbon has 4, each oxygen atom has 6, hydrogen has 1, and there is 1 extra electron due to the 1- charge. So, the total valence electrons are: \[4+(3 \times 6)+1+1=24\] Follow the same logic as before, place the carbon atom at the center and distribute these around it: 3 oxygen atoms and 1 hydrogen atom. Then, distribute the remaining electrons among the oxygen atoms (5 electrons in each oxygen atom and one oxygen atom with 6 electrons) and connect the hydrogen atom to one of the oxygens. The Lewis structure of HCO3- is: ``` H | O - C - O- \\ O ```

H2CO3#

Calculating the valence electrons: Carbon has 4, each oxygen atom has 6, and hydrogen has 1. So, the total valence electrons are: \[4+(3 \times 6)+(2 \times 1)=24\] Connect one hydrogen atom with each of the spare electrons on two oxygen atoms, resulting in the following Lewis structure of H2CO3: ``` H O C - O- \\ O ``` #Step 2: Estimating ΔH using Bond Energies#

Computing ΔH#

To calculate ΔH for the reaction: H2CO3 → CO2 + H2O, we need to find the energy change involved in breaking the bonds in H2CO3 and forming the bonds in CO2 and H2O. ΔH = (Σ bond energies of products) - (Σ bond energies of reactants) Bond energies are as follows: \[C=O\: double\: bond: 799 \:kJ/mol\] \[C-O\: single\: bond: 358\: kJ/mol\] \[O-H\: bond\: in\: water: 467\: kJ/mol\] For H2CO3, we have 1 C=O double bond, 2 C-O single bonds, and 2 O-H bonds: Energies in H2CO3: 1(799) + 2(358) + 2(467) = 2449 kJ/mol. For the products, CO2 has 2 C=O double bonds, and H2O has 2 O-H bonds: Energies in CO2 and H2O: 2(799) + 2(467) = 2532 kJ/mol. Now, we can calculate ΔH: ΔH = 2532 - 2449 = 83 kJ/mol #Step 3: Explaining the Instability of Carbonic Acid#

Instability Reason#

Carbonic acid's instability is attributed to the ease with which it breaks down into carbon dioxide and water. This breakdown occurs due to the weak O-H bond and its relatively high energy, making it easier for the molecule to release CO2 gas and form water. The positive ΔH value indicates that the reaction is endothermic, which means that it absorbs energy from its environment during the breakdown process, making it more favorable under certain conditions.

Key concepts

Valence Electrons

Valence electrons play a crucial role in chemical bonding and are essential for drawing Lewis structures. These electrons are found in the outermost shell of an atom and are the ones involved in forming bonds. For example, in carbonate ion (\( \text{CO}_3^{2-} \)), each oxygen atom has six valence electrons, carbon has four, and the additional two electrons come from the overall negative charge. This makes a total of 24 valence electrons.

In chemical bonding, atoms will share or transfer valence electrons to achieve a stable electron configuration, often resembling noble gases with full outer shells. Oxygen generally forms bonds by sharing two electrons each, while carbon usually makes four bonds to fill its valence shell.

• Counting valence electrons is the first step in drawing Lewis structures.
• Distributing these electrons wisely ensures accurate representation of the molecule or ion.

Understanding valence electrons and their role in Lewis structures helps in predicting molecule shape and reactivity.

Bond Energies

Bond energy is the amount of energy required to break one mole of a particular bond in a molecule in the gas phase. It is a crucial factor in determining the stability of a molecule and predicting the outcome of a chemical reaction.

For example, in studying the decomposition reaction of carbonic acid (\( \text{H}_2\text{CO}_3 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \)), we look at the different types of bonds involved and to calculate the enthalpy change (ΔH):

• C=O bond in carbon dioxide is a strong double bond with high bond energy (799 kJ/mol).
• C-O single bond in carbonic acid has a lower bond energy (358 kJ/mol).
• O-H bond in water is moderate with bond energy (467 kJ/mol).

By comparing the energies needed to break the bonds in the reactants and those released when forming the products, we can determine the overall energy change and the reaction's thermodynamic feasibility.

Carbonic Acid Instability

Carbonic acid (\( \text{H}_2\text{CO}_3 \)) is often described as unstable due to its tendency to decompose rapidly into carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)). This is mainly because of the weak nature of the bonds within the molecule. The breakdown into \( \text{CO}_2 \) and water is facilitated by the ease of breaking the weak O-H bonds.

Carbonic acid's instability is beneficial in biological systems, aiding in processes like respiration where carbon dioxide must be exhaled efficiently. The reaction:\( \text{H}_2\text{CO}_3 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \) is a quick equilibrium, making carbonic acid an effective buffer in blood pH regulation.

• The instability arises from the molecular structure, allowing quick loss of \( \text{CO}_2 \).
• Its decomposition is fast, influencing its role in biochemical pathways.

Understanding carbonic acid's instability helps in various fields, from environmental science to medicine.

Endothermic Reaction

An endothermic reaction is a chemical reaction that absorbs energy from its surroundings, resulting in a net intake of energy. In the case of carbonic acid decomposition to carbon dioxide and water, the positive value of ΔH (83 kJ/mol) indicates an endothermic reaction.

This means that energy is required to break the bonds in carbonic acid, and this energy is absorbed from the surrounding environment.

• Endothermic reactions are characterized by a positive ΔH.
• Such reactions usually feel cold to the touch since they absorb heat from the surroundings.

Understanding whether a reaction is endothermic or exothermic helps in predicting its behavior and feasibility under different conditions. This insight is critical in chemical engineering, environmental science, and everyday processes such as cooking and refrigeration.