Problem 76 - Chemistry The Molecular Science

Question

In the gas phase, positive and negative ions form ion pairs that are like molecules. An example is \(\mathrm{KF}\), which is found to have a dipole moment of \(28.7 \times 10^{-30} \mathrm{C} \mathrm{m}\) and a distance of separation between the two ions of \(217.2 \mathrm{pm} .\) Use this information and the definition of dipole moment to calculate the partial charge on each atom. Compare your result with the expected charge, which is the charge on an electron, \(-1.602 \times 10^{-19} \mathrm{C}\). Based on your result, is KF really completely ionic?

Step-by-Step Solution

Answer

KF is not completely ionic; the partial charge is less than that of an electron.

Step 1: Understand the formula to use

The dipole moment \( \mu \) is given by the formula \( \mu = q \times r \), where \( q \) is the charge and \( r \) is the distance of separation between the charges.

Step 2: Convert units to consistent values

Convert the separation distance from picometers to meters: \( 217.2 \text{ pm} = 217.2 \times 10^{-12} \text{ m} \).

Step 3: Rearrange the formula to find the charge

Rearrange the dipole moment formula to solve for the charge \( q \): \( q = \frac{\mu}{r} \).

Step 4: Insert values into the formula

Substitute the known values into the formula: \( q = \frac{28.7 \times 10^{-30} \text{ Cm}}{217.2 \times 10^{-12} \text{ m}} \).

Step 5: Perform the calculation

Calculate \( q = \frac{28.7 \times 10^{-30}}{217.2 \times 10^{-12}} \approx 1.32 \times 10^{-19} \text{ C} \).

Step 6: Compare with the expected charge

The expected charge is the charge of an electron, \(1.602 \times 10^{-19} \text{ C}\). Compare this with the calculated charge \(1.32 \times 10^{-19} \text{ C}\).

Step 7: Determine if KF is completely ionic

Since the calculated charge (\(1.32 \times 10^{-19} \text{ C}\)) is less than the charge of an electron (\(1.602 \times 10^{-19} \text{ C}\)), \( \text{KF} \) is not completely ionic because the charge transfer is not complete.

Key Concepts

Ion Pairs

In the gas phase, atoms can form molecules by pairing up as positive and negative ions. Think of these pairs as friends holding hands: one is positively charged, while the other is negatively charged. This combination is known as an ion pair. They are held together by electrostatic forces, which are the same forces that cause static cling between clothes in the dryer. When these ion pairs form, they often resemble the structure of a molecule and can even exhibit molecular properties such as a dipole moment. In our example with \(\mathrm{KF}\), the potassium ion (K⁺) and fluoride ion (F⁻) create an ion pair that behaves like a molecule. This concept is crucial in understanding how ionic compounds can exist in the gas phase and have measurable properties, such as the distance between ions, which is essential for calculating the dipole moment.

Partial Charge Calculation

To calculate the partial charge on each atom in an ion pair like \(\mathrm{KF}\), we need to understand their dipole moment, given by the formula \( \mu = q \times r \). Here, \(q\) is the charge, and \(r\) is the distance between the ions. The dipole moment \(\mu\) tells us how much separation exists between the positive and negative charges. For \(\mathrm{KF}\), we know the dipole moment is \(28.7 \times 10^{-30} \,\mathrm{C} \mathrm{m}\), and the distance is \(217.2 \mathrm{pm}\), which converts to \(217.2 \times 10^{-12} \mathrm{m}\).
By rearranging the dipole formula to \( q = \frac{\mu}{r} \,\), we substitute the known values: \( q = \frac{28.7 \times 10^{-30}}{217.2 \times 10^{-12}} \,\). This lets us find the partial charge, approximating \(q\) to \(1.32 \times 10^{-19} \,\mathrm{C}\). This charge is not the full charge of an electron, which implies not all the electron's charge is transferred or shared completely between the ions.

Ionic Bond Character

Ionic bond character refers to how completely electrons are transferred in the bond between atoms. In a completely ionic bond, one atom fully transfers an electron to another, resulting in ions with full charges. However, in most real-world scenarios, bonds exhibit varying degrees of ionic character. For example, \(\mathrm{KF}\) doesn't completely transfer electrons from potassium to fluoride. This means it's not 100% ionic.
The character of ionic bonds is assessed by the calculated partial charge. For \(\mathrm{KF}\), the calculated charge is \(1.32 \times 10^{-19} \,\mathrm{C}\,\), compared to the expected full electron charge of \(1.602 \times 10^{-19} \,\mathrm{C}\). Since \(\mathrm{KF}\)'s charge is less, it indicates partial charge transfer, making its bond partially ionic, not fully. Knowing whether a compound is completely ionic or not helps predict its properties like solubility, melting point, and even electrical conductivity in solution.