Question

What are the formal charges on the atoms in the \(\mathrm{HCl}\) molecule? What are the actual charges on the atoms in this molecule? Are formal charges the same as actual charges?

Short answer

The formal charges on both hydrogen and chlorine in HCl are zero. However, due to chlorine's higher electronegativity, the actual charges are that chlorine bears a partial negative charge and hydrogen bears a partial positive charge. Formal charges and actual charges are not the same.

Step-by-step solution

Determine the Formal Charges

The formal charge (FC) on an atom in a molecule is calculated with the formula: FC = (Valence electrons) - (Non-bonding electrons) - (1/2 * Bonding electrons). For hydrogen (H), with 1 valence electron, no lone pairs, and contributing 1 electron to the bond: FC(H) = 1 - 0 - (1/2 * 2) = 0. For chlorine (Cl), with 7 valence electrons, 6 non-bonding electrons, and contributing 1 electron to the bond: FC(Cl) = 7 - 6 - (1/2 * 2) = 0. Both atoms have a formal charge of 0.

Consider the Electronegativities for Actual Charges

The actual charge is influenced by the electronegativity difference between the atoms. Chlorine is more electronegative than hydrogen, which means it will attract the shared electrons in the bond more strongly. As a result, chlorine will have a partial negative charge, and hydrogen will have a partial positive charge.

Compare Formal and Actual Charges

Formal charges are a bookkeeping method that assign whole charges to atoms based on their valence electrons, bonding, and lone pairs. Actual charges, on the other hand, take into account the distribution of electron density in a molecule resulting from differences in electronegativity. They are usually partial charges and are not the same as formal charges. In the case of HCl, while the formal charges are zero, the actual charges are partial charges due to the difference in electronegativity.

Key concepts

Formal Charge Calculation

Understanding the formal charge of an atom within a molecule is critical for grasping how molecules interact and react with one another. Formal charge is a theoretical charge that is calculated based on an atom's number of valence electrons, the electrons it owns in non-bonding pairs, and those electrons it shares in bonding pairs.

To calculate the formal charge, we use the formula:
\[ \text{Formal Charge (FC)} = (\text{Valence electrons}) - (\text{Non-bonding electrons}) - \frac{1}{2} \times (\text{Bonding electrons}) \]
This formula allows us to see how electrons are distributed in a molecule and whether an atom is electron-rich or deficient compared to its neutral state. For instance, within an \(\mathrm{HCl}\) molecule, the hydrogen atom has one valence electron and shares a pair of electrons in a bond, while chlorine has seven valence electrons and also shares in that bonding pair. Their formal charges are calculated to be zero because they're seen as sharing the electrons equally in this bookkeeping system.

Electronegativity in Molecules

Electronegativity is a measure of an atom's ability to attract and hold onto electrons in a chemical bond. It plays a significant role in determining the actual charge distribution within a molecule. When two atoms in a molecule have different electronegativities, the shared electrons tend to be closer to the more electronegative atom, creating a polarity.

In \(\mathrm{HCl}\), chlorine has a higher electronegativity compared to hydrogen, which means chlorine will pull the shared bonding electrons closer to itself. This unequal distribution of electron density results in a partial negative charge (\(\delta-\)) on the chlorine atom and a partial positive charge (\(\delta+\)) on hydrogen. These partial charges depict the true polar nature of the molecule which impacts properties such as solubility, reactivity, and intermolecular forces.

Actual vs Formal Charge

While formal charge is a valuable tool in predicting the structure and stability of molecules, it is important to distinguish between formal and actual charges. Formal charges are merely a bookkeeping method that often simplifies the complex nature of electron sharing and does not always reflect the real electron distribution in a molecule.

Actual charges arise from the real-world scenario of atoms with different electronegativities engaging in bonds. In the \(\mathrm{HCl}\) molecule, even though both atoms have a formal charge of zero, the electronegativity difference means that chlorine pulls the bonding electrons closer, adopting a partial actual charge. This discrepancy is crucial because while formal charges can help predict molecular geometry and reactivity, actual charges offer insight into a molecule's behavior in different environments, such as its polarity, intermolecular forces, and how it may interact with other chemical species.