Chemistry
Chemistry
Problem
Chromium (Z = 24) and molybdenum (Z = 42) display experimentally determined ground-state electron configurations that differ from those predicted by a simple application of the subshell filling order. The chemistry of their ions also reflects these differences. Use the information below to analyze and explain these observations. • Atomic number: Cr = 24, Mo = 42 • First ionization energies (approximate): Cr = 653 kJ mol⁻¹; V = 650 kJ mol⁻¹ (a) Write the electron configuration that would be predicted for a chromium atom if subshells were filled strictly in order of increasing principal quantum number followed by increasing azimuthal quantum number. (b) The experimentally observed ground-state configuration of chromium is . Explain why this arrangement is lower in energy than the configuration you wrote in part (a). Your explanation should address electron–electron repulsion and exchange energy. (c) Write the ground-state electron configuration for a ion, and draw an orbital-box diagram for its 3d subshell. (d) Using qualitative Coulombic reasoning and your configurations, predict which element has the larger first ionization energy—vanadium (Z = 23) or chromium (Z = 24)—and justify your prediction.Intuitive explanation
The key insight is that half-filled and fully-filled subshells are unusually stable — more so than the aufbau principle predicts — because they minimize electron–electron repulsion and maximize exchange energy. Chromium and molybdenum both "steal" an electron from their orbital to achieve a or configuration, even though this seems to violate the filling order. This extra stability explains why their actual configurations differ from the simple aufbau prediction and why their ionization energies and ion chemistry behave unexpectedly.
Intuitive explanation
The key insight is that half-filled and fully-filled subshells are unusually stable — more so than the aufbau principle predicts — because they minimize electron–electron repulsion and maximize exchange energy. Chromium and molybdenum both "steal" an electron from their orbital to achieve a or configuration, even though this seems to violate the filling order. This extra stability explains why their actual configurations differ from the simple aufbau prediction and why their ionization energies and ion chemistry behave unexpectedly.