Problem 41 - Chemistry: The Central Science

Question

The dipole moment and bond distance measured for the highly reactive gas phase OH molecule are \(1.78 \mathrm{D}\) and \(0.98 \AA\), respectively. (a) Given these values calculate the effective charges on the \(\mathrm{H}\) and \(\mathrm{O}\) atoms of the OH molecule in units of the electronic charges \(e\). (b) Is this bond more or less polar than the \(\mathrm{H}-\mathrm{Cl}\) bond in an \(\mathrm{HCl}\) molecule? (c) Is that what you would have expected based on electronegativities?

Step-by-Step Solution

Answer

The effective charge separation on the H and O atoms of the OH molecule is calculated to be \(q_e \approx 0.577\) units of electronic charges. The OH bond is more polar than the H-Cl bond, which is expected based on the electronegativity differences: \(3.44 - 2.20 > 3.16 - 2.20\).

Step 1: Calculate the effective charge separation

We are given the dipole moment (μ) and bond distance (d) for the OH molecule. We can use the formula: μ = q * d Where μ is the dipole moment, q is the effective charge separation, and d is the bond distance. We need to find q using the given values: μ = 1.78 D d = 0.98 Å = 0.98 * 10^(-10) m (converting Å to meters) Rearrange the formula to solve for q: q = μ / d Now, insert the given values: q = 1.78 D / (0.98 * 10^(-10) m)

Step 2: Convert the effective charge separation to units of electronic charge

To find the effective charges on the H and O atoms in units of electronic charges (e), we need to convert the D (Debye) charge separation unit to Coulombs (C). The conversion factor is: 1 D = 3.336 * 10^(-30) C·m So, q in Coulombs is: q = 1.78 D * (3.336 * 10^(-30) C·m/D) / (0.98 * 10^(-10) m) Now, we need to find the number of electronic charges (using the fact that one elementary charge e is equal to 1.602 * 10^(-19) C): q_e = q / e We finally find q_e: q_e = (1.78 * 3.336 * 10^(-30)) / (0.98 * 10^(-10) * 1.602 * 10^(-19))

Step 3: Compare the OH bond polarity to the H-Cl bond polarity

To compare the bond polarity of the OH molecule to the H-Cl bond, we need to determine the dipole moment of the H-Cl bond. Since we are only interested in a qualitative comparison (more or less polar), we can simply compare electronegativity values for the two bonds. Electronegativity values are: - H: 2.20 - O: 3.44 - Cl: 3.16 The greater the difference in electronegativity values, the more polar the bond. Since the H-O bond has a greater electronegativity difference compared to the H-Cl bond (3.44 - 2.20 > 3.16 - 2.20), we can conclude that the OH bond is more polar than the H-Cl bond.

Step 4: Determine if the observed polarity aligns with the expected polarity

Based on the electronegativity values, we would expect the bond with the greater difference in electronegativity to be more polar. Our results show that the OH bond is indeed more polar than the H-Cl bond, which aligns with the expected polarity based on electronegativity values.

Key Concepts

Electronegativity

Electronegativity refers to the ability of an atom to attract and hold onto electrons within a bond. It's a fundamental property that influences how different atoms connect and form molecules. The higher the electronegativity, the more an atom wants to pull electrons towards itself.
In the periodic table, electronegativity generally increases across a period from left to right and decreases down a group. For instance, oxygen has a high electronegativity of 3.44, meaning it strongly attracts electrons. On the other hand, hydrogen, with an electronegativity of 2.20, is less effective at pulling electrons. This difference plays a key role in defining the characteristics of various chemical bonds.
Understanding electronegativity helps predict bond behavior, like polarity and the strength of interaction between atoms.

Bond Polarity

Bond polarity arises when there is a difference in electronegativity between two bonded atoms. If one atom attracts the shared electrons more strongly, the bond becomes polar, creating a dipole moment. A "dipole moment" is when one end of the bond is slightly negative, and the other end is slightly positive.
The difference in electronegativity directly influences how polar a bond is. In our OH molecule, the difference between oxygen and hydrogen's electronegativity (3.44 - 2.20) indicates a significant bond polarity. This polarity means electrons are unequally shared, favoring the more electronegative atom.
Recognizing bond polarity can help predict the physical and chemical properties of molecules, like solubility and reactivity.

Effective Charge Separation

Effective charge separation in a molecule refers to the distribution of electrical charges due to differences in electronegativity between the bonded atoms. This separation creates areas of partial negative and positive charges, often represented by the symbol δ (delta).
In a polar molecule like OH, the disparity in electronegativity means that electrons are pulled more towards oxygen, giving it a partial negative charge (δ-), while hydrogen ends up with a partial positive charge (δ+). The effective charge separation is also quantified by measuring the dipole moment.
Understanding this concept is essential for analyzing molecular interactions, as the effective charge separation influences how molecules interact with electric fields and each other.

Debye Unit

The Debye unit (D) measures the dipole moment of a molecule, which reflects the strength of the separation of charges. It's a key unit in molecular chemistry, particularly when assessing bond polarity.
One Debye is equivalent to approximately 3.336 × 10^{-30} Coulomb-meters. In our exercise, the OH molecule's dipole moment of 1.78 D indicates significant charge separation, showing the high polarity of the bond.
Using the Debye unit allows chemists to quantify and compare the polarity between different molecules, providing insight into how substances behave under various conditions. It's a useful tool in both theoretical calculations and practical applications in chemistry.

Elementary Charge

The elementary charge (e), valued at approximately 1.602 × 10^{-19} Coulombs, is the basic unit of electric charge carried by a single proton or electron. In chemistry, it helps express the charge distribution within molecules.
When calculating the effective charge separation in the OH molecule, the result is often expressed in terms of elementary charges. This conversion makes the values more relevant and easier to understand for those studying chemical principles.
Incorporating the elementary charge into dipole moment calculations aids in understanding the extent of charge separation and can also help relate molecular behavior to other areas of physics and chemistry.