Question

The molecule bromine monofluoride has a dipole moment of \(1.42 \mathrm{D}\) and a bond length of \(176 \mathrm{pm}\). Calculate the charge on the ends of the molecule, expressed in electronic charge units \(\left(e^{-}=1.60 \times 10^{-19} \mathrm{C}\right)\). Which atom carries the positive charge?

Short answer

The magnitude of the charge on the ends of the bromine monofluoride molecule is approximately \(0.168 e^{-}\) and the bromine atom carries the positive charge.

Step-by-step solution

Convert Dipole Moment to Coulomb-meters

First, convert the dipole moment of bromine monofluoride from Debye (D) to Coulomb-meters (Cm) which is the SI unit. Use the conversion factor where 1 D = 3.33564 x 10^(-30) Cm. The conversion can be calculated as follows: \( 1.42 \, \text{D} \times 3.33564 \times 10^{-30} \, \text{Cm/D} = 4.73641 \times 10^{-30} \, \text{Cm} \).

Convert Bond Length to Meters

Next, convert the bond length of bromine monofluoride from picometers (pm) to meters (m) by using the conversion factor where 1 pm = 1 x 10^(-12) m. The conversion is calculated as follows: \( 176 \, \text{pm} \times 1 \times 10^{-12} \, \text{m/pm} = 1.76 \times 10^{-10} \, \text{m} \).

Calculate the Charge on the Ends of the Molecule

Use the formula for the dipole moment, \( p = q \times d \), where \( p \) is the dipole moment, \( q \) is the magnitude of the charge, and \( d \) is the bond length. Rearrange the formula to solve for \( q \), the charge, as follows: \( q = \frac{p}{d} \). Plug in the values from Step 1 and Step 2 to get \( q = \frac{4.73641 \times 10^{-30} \, \text{Cm}}{1.76 \times 10^{-10} \, \text{m}} = 2.69 \times 10^{-20} \, \text{C} \).

Express the Charge in Units of Electronic Charge

To express the charge in electronic charge units, divide the charge calculated in Step 3 by the charge of one electron (\( e^{-} = 1.60 \times 10^{-19} \, \text{C} \)). Therefore, \( q_{\text{e}} = \frac{2.69 \times 10^{-20} \, \text{C}}{1.60 \times 10^{-19} \, \text{C/e}^{-}} = 0.168 \, \text{e}^{-} \).

Determine Which Atom Carries the Positive Charge

Bromine (Br) is less electronegative than Fluorine (F), meaning that F will pull the shared electrons closer towards itself and thus will carry a partial negative charge. Consequently, Br will have a partial positive charge.

Key concepts

Understanding Chemical Bonding

Chemical bonding is the force that holds atoms together in molecules and compounds, forming the basis of all substances around us. At the heart of chemical bonding is the quest for stability, where atoms gain, lose, or share electrons to achieve a full outer shell, reminiscent of the noble gases' electron configuration.

There are mainly three types of bonds: ionic, covalent, and metallic.

• Ionic bonding occurs between metals and non-metals where electrons are transferred from one atom to another, resulting in oppositely charged ions that attract each other.
• Covalent bonding involves the sharing of electron pairs between atoms, typically non-metals, allowing them to fill their outer shells.
• Metallic bonding is characterized by a 'sea' of delocalized electrons flowing around a lattice of positive metal ions, providing the unique properties of metals such as electrical conductivity.

Understanding the type of bond and the structure of molecules is essential for predicting the properties and behavior of substances.

The Role of Electronegativity in Bonding

Electronegativity is a term used to describe an atom's ability to attract and hold onto electrons within a chemical bond. This property is pivotal because it determines how shared electrons are distributed between atoms in a molecule.

The most electronegative element is fluorine, and elements are often compared against it to determine their relative electronegativity. The greater the difference in electronegativity between two bonded atoms, the more polar the bond.

Impact on Dipole Moments

Electronegativity differences can lead to uneven electron distribution, resulting in a dipole moment—a measure of a molecule's overall polarity. In bromine monofluoride, for instance, the more electronegative fluorine atom will cause the electrons to migrate towards itself, leading to a net dipole moment that can be quantified and used to calculate the partial charges on the atoms as shown in the textbook exercise.

Molecular Polarity and Its Consequences

Molecular polarity is a key concept that describes the distribution of electrical charge over the atoms joined by the bond. A molecule is polar if it has an asymmetrical shape or atoms with different electronegativities, resulting in an unequal sharing of electrons.

Polarity influences a molecule's physical properties, such as boiling and melting points, solubility, and reactivity. For instance, polar molecules tend to have higher boiling points due to strong intermolecular forces, like hydrogen bonding. Polarity is also responsible for the interaction of molecules with electric fields, which is crucial in techniques like chromatography and spectroscopy.

Dipole Moments Reflect Polarity

The exercise with bromine monofluoride illustrates how a molecule's dipole moment can reflect its polarity. By calculating the charge on the atoms based on the dipole moment and bond length, we gain insights into the molecular separation of charge. As a result, we understand why certain molecules, like water or bromine monofluoride, have distinctive chemical properties and behave differently in physical and chemical processes.