The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 kJ mol –1 . The number of valence electrons in the element is :

Solution

Chemistry ma’am · 3 steps

Look for the one huge jump. Electrons removed before it are the valence electrons.

1. Why a jump appears. Each successive ionisation enthalpy is larger, because the ion left behind is more positive. Once the valence shell is empty, the next electron must come from an inner, noble-gas-like core, so the energy needed shoots up sharply.

   Ionisation	Value (kJ mol⁻¹)	Ratio to previous
   Δᵢ H₁	800	first value
   Δᵢ H₂	2427	about 3.0
   Δᵢ H₃	3658	about 1.5
   Δᵢ H₄	25024	about 6.8, the big jump
   Δᵢ H₅	32824	about 1.3

2. Read the jump. From Δᵢ H₃ to Δᵢ H₄ the value rises by about 21 400 kJ mol⁻¹, far more than any other step. So the first three electrons are outer electrons and the fourth comes from the core. These values match boron, 1s² 2s² 2p¹.
3. So. The element has 3 valence electrons, which is option (b).

The idea to keep. In a list of successive ionisation enthalpies, find the step where the value jumps several times over. The number of electrons removed before that jump equals the number of valence electrons.

Answer from the NTA final answer key. Solution by PrepWiser.