Three hypothetical main-group elements X, Y

CHEMISTRY · Multi-part · AP · Chemistry · Atomic Structure and Properties · Atomic Structure and Properties

Problem

Three hypothetical main-group elements X, Y, and Z each have a single valence electron in an

s

subshell, but their principal quantum numbers differ. Relevant measured properties are shown.

Property	X	Y	Z
Average distance of valence electron from nucleus, $r$ (pm)	110	140	200
Effective nuclear charge experienced by valence electron, $Z_{\text{eff}}$	3.2	2.6	2.5
Experimental first ionization energy, $I_1$ (kJ mol $^{-1}$ )	1610	1000	481

Chemists sometimes use the proportionality

I_1 \propto \dfrac{Z_{\text{eff}}}{r^2}

as a crude model. (a) Using only the data for X and Y, calculate the ratio

\dfrac{I_{1,\text{pred}}(\text{X})}{I_{1,\text{pred}}(\text{Y})}

predicted by the proportionality model. Show all steps. (b) Determine the corresponding experimental ratio

\dfrac{I_{1,\text{exp}}(\text{X})}{I_{1,\text{exp}}(\text{Y})}

and compare it to the predicted value. (c) Discuss two possible reasons why the proportionality model does not exactly reproduce the experimental ratio. (d) Without performing further calculations, predict whether the proportionality model is likely to overestimate or underestimate

I_1

for element Z. Support your prediction with qualitative reasoning.

Related theory

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