By Jack Brubaker
Updated Mar 24, 2022
When metals and nonmetals form compounds, metal atoms donate electrons to nonmetal atoms. The metal atoms become positively charged ions, while the nonmetal atoms become negatively charged ions. Opposite charges attract, a relationship quantified by Coulomb’s law:
F = k \frac{q_1 q_2}{d^2}Here, F is the force of attraction in Newtons, q_1 and q_2 are the ionic charges in coulombs, d is the distance between the ions’ nuclei in meters, and k is the Coulomb constant (8.99 × 109 N·m²/C²).
Consult a table of common ions to determine the charges of the positive and negative species in the compound. Chemical formulas list the cation first. For example, in calcium bromide (CaBr2), calcium is the cation with a charge of +2, while bromine is the anion with a charge of –1. Thus, q1 = 2 and q2 = 1 (in elementary charge units).
Multiply each charge by the elementary charge (1.602 × 10–19 C). The calcium ion carries 2 × 1.602 × 10–19 = 3.204 × 10–19 C, while the bromide ion carries 1 × 1.602 × 10–19 = 1.602 × 10–19 C.
Use a table of ionic radii to find the sizes of the ions. In solids, ions occupy positions that minimize their separation, so the distance equals the sum of the radii. For Ca2+ (≈1.00 Å) and Br– (≈1.96 Å), the nuclear separation is 1.00 + 1.96 = 3.96 Å.
Convert angstroms to meters by multiplying by 1 × 10–10. Thus, 3.96 Å = 3.96 × 10–10 m.
Insert the values into Coulomb’s equation:
F = (8.99 × 109) × (3.204 × 10–19) × (1.602 × 10–19) ÷ (3.96 × 10–10)2First square the distance: (3.96 × 10–10)2 = 1.57 × 10–19 m². Performing the multiplication and division yields F ≈ 4.1 × 10–9 N. This is the magnitude of the attractive force between the calcium and bromide ions in the crystal lattice.
Scientific notation like 1.9 × 10–19 means “one point nine times ten to the negative nineteenth power.” Input these values directly into a scientific calculator using the EE button.
