U2.2 · Intramolecular Force and Potential EnergyPractice · 分子内作用力与势能曲线

A higher bond order means a shorter bond (minimum farther left) and a larger bond energy (deeper minimum). $\ce{N2}$ N≡N 110 pm, 941 kJ/mol; $\ce{O2}$ O=O 121 pm, 495 kJ/mol; $\ce{F2}$ F–F 143 pm, 155 kJ/mol. Triple-bonded N₂ is the shortest and deepest, so it is Z; single-bonded F₂ is the longest and shallowest, so it is Y; O₂ is X.

The depth of the minimum is the bond energy: forming 1 mol of F–F bonds releases 155 kJ. Two F atoms make one $\ce{F2}$, so 0.250 mol of F atoms makes 0.125 mol of $\ce{F2}$, releasing 0.125 × 155 = 19.4 kJ. Multiplying 0.250 × 155 directly double-counts.

Draw the Lewis diagrams first: $\ce{CO}$ has a C≡O triple bond, $\ce{CO2}$ has two C=O double bonds, and $\ce{CH3OH}$ has a C–O single bond. Between the same two atoms, a higher bond order means more shared electrons pulling the nuclei closer, so a shorter bond: $\ce{CO}$ < $\ce{CO2}$ < $\ce{CH3OH}$.

C=C is one σ bond plus one π bond. A σ bond forms by end-on overlap, which is extensive; a π bond forms by side-by-side overlap of p orbitals, which is weaker, so the double bond is less than twice as strong as a single bond. C=C (134 pm) is actually shorter than C–C (154 pm), and breaking a bond always absorbs energy.

Far apart, the atoms don’t interact, and the potential energy is taken as 0. As they approach, each nucleus attracts the other atom’s electrons; attraction dominates and the energy falls. At 141 pm attraction and repulsion balance, giving the minimum of −366 kJ/mol, the H–Br bond energy. The drop in potential energy is released, so forming a bond releases energy.

The bond length is the distance at the lowest point of the curve: about 121 pm. The bond energy is the energy needed to climb from that minimum (about −495 kJ/mol) to zero, where the atoms are separated: about 495 kJ/mol, a positive number because breaking a bond absorbs energy. The curve crosses zero near 63 pm, which is just where the potential energy happens to be zero, not the bond length; the flat part on the right means the atoms have separated.