Question

Compare the ionic bond strength of \(\mathrm{NaCl}\) to \(\mathrm{KF} ;\) assuming that the radii of \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{F}^{-}\), and \(\mathrm{Cl}^{-}\) are, respectively, \(0.097\), \(0.133,0.133\), and \(0.181 \mathrm{NM}\)

Short answer

The ionic bond strength of \(\mathrm{NaCl}\) and \(\mathrm{KF}\) can be compared using Coulomb's Law, where the electrostatic force is calculated using the formula \(F = k\frac{q_1q_2}{r^2}\). The distances between the ions are calculated using the given radii as \(r_{NaCl} = 0.278 \, nm\) and \(r_{KF} = 0.266 \, nm\). The charges of the ions are \(+1e\) and \(-1e\) for both compounds. Upon calculating the force of attraction for both compounds, we can compare their bond strengths. If \(F_{NaCl}>F_{KF}\), the bond strength of NaCl is greater, and if \(F_{NaCl}<F_{KF}\), the bond strength of NaCl is weaker.

Step-by-step solution

Write down the Coulomb's Law formula

Coulomb's Law is used to calculate the force between two charged particles (ions in our case). The formula for Coulomb's Law is: \(F = k\frac{q_1q_2}{r^2}\) where: - F is the electrostatic force - k is Coulomb's constant (\(8.9875 * 10 ^9 N m^2 / C^2\)) - \(q_1\) and \(q_2\) are the charges of the two ions - r is the distance between the centers of the ions

Calculate the distances between the ions in both compounds

We will use the radii of the ions given in the problem to determine the distances between the ions in both compounds. For NaCl: The distance between Na+ and Cl- ions is the sum their radii, i.e., \(r_{NaCl} = r_{Na+} + r_{Cl-} = 0.097 + 0.181 = 0.278 \, nm\) For KF: The distance between K+ and F- ions is the sum their radii, i.e., \(r_{KF} = r_{K+} + r_{F-} = 0.133 + 0.133 = 0.266 \, nm\)

Calculate the charges for each ion

First, we need to determine the charges of the ions for both compounds. In NaCl, sodium (Na) loses one electron to form a +1 charge, and chlorine (Cl) gains one electron to form a -1 charge. In KF, potassium (K) loses one electron to form a +1 charge, and fluorine (F) gains one electron to form a -1 charge. Thus, \(q_{Na+} = +1\, e\) \(q_{Cl-} = -1\, e\) \(q_{K+} = +1 \, e\) \(q_{F-} = -1 \, e\) where e is the elementary charge (\(1.60219 * 10^{-19} \, C\)). Now we will substitute these charges into Coulomb's Law formula to find the force of attraction for each compound.

Calculate the force of attraction for NaCl

By using Coulomb's Law formula, we can calculate the force of attraction for NaCl: \(F_{NaCl} = k\frac{q_{Na+}q_{Cl-}}{r^2_{NaCl}} = k\frac{(+1e)(-1e)}{(0.278 * 10^{-9})^2}\)

Calculate the force of attraction for KF

By using Coulomb's Law formula, we can calculate the force of attraction for KF: \(F_{KF} = k\frac{q_{K+}q_{F-}}{r^2_{KF}} = k\frac{(+1e)(-1e)}{(0.266 * 10^{-9})^2}\)

Compare the bond strength

Now we have the equations for the forces of attraction for both compounds. Comparing the bond strength means comparing the magnitudes of these forces. TheNaClF_{NaCl}>F_{KF}\), it means the bond strength of NaCl compound is greater than KF compound. And if \(F_{NaCl}<F_{KF}\), it means the bond strength of NaCl compound is weaker than KF compound.

Key concepts

Coulomb's Law

Understanding Coulomb’s Law is central to explaining why particles attract or repel each other with a force proportional to the product of their charges and inversely proportional to the square of the distance between them. This fundamental principle is elegantly captured by the equation \(F = k\frac{q_1q_2}{r^2}\), in which \(F\) represents the magnitude of the electrostatic force, and \(k\) is the Coulomb constant, a value important to remember, especially when calculating the electrostatic forces. Charges, represented by \(q_1\) and \(q_2\), need to be determined accurately as they are essential to knowing the strength of the interaction. The separation distance \(r\) is also crucial; a misunderstanding here could significantly distort the force calculations.

Ionic Bonds

Ionic bonds form when electrons are transferred from one atom to another, creating ions that are positively or negatively charged. The positively charged ions, or cations, and negatively charged ions, or anions, are held together by the electrostatic forces of attraction, as explained by Coulomb's Law.

Notably, ionic compounds have distinctive characteristics such as high melting and boiling points, and the strength of the ionic bond has implications for these physical properties. It’s important for students to grasp that ionic bonding is not just about the transfer of electrons, but also about the resultant force that binds the ions together.

Electrostatic Force Calculation

The electrostatic force calculation between ions is a straightforward application of Coulomb's Law, although care must be taken with units and ensuring that charge values are correct. It is essential to express distances in meters and charges in coulombs to use the constant \(k\) effectively in the formula.

When calculating, always verify that the charges are based on the ion's charge state. For instance, a common mistake is to overlook that charges should be inserted as multiples of the elementary charge. This could lead to incorrect force values, ultimately affecting the comparison of bond strengths.

Atomic Radii

The atomic radius is a critical factor in evaluating the distance between ions in a bond. Atomic radii are typically given in nanometers or picometers, and it is this measure that we use to calculate the centre-to-centre distance between two ions in a compound.

In exercises like comparing ionic bond strengths, adding the radii of the cation and anion gives us the distance needed for Coulomb’s Law. Remember that inaccuracies in determining these distances can dramatically affect the force calculation, so always make sure to check your values and units.

Force of Attraction

The force of attraction, resulting from the interaction of charged particles, is what holds ionic compounds together. This force is not static; it varies according to the charge and distance between ions. Highly charged ions and/or ions that are closer together will experience a stronger force of attraction. This is why, in the given example, we carefully consider the radii of the ions and their charges to determine the bond strength of compounds like NaCl and KF.

Understanding how this force works helps students not just in comparing ionic bond strengths, but also in predicting properties of compounds and transitioning to more complex concepts like lattice energy and ionic crystal structures.