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Direction Cosines

The IE valu...

Question

The $I E$ value of, $A l (g) ⟶ {A l}^{+} (g) + e$ is $577.5 k J$ ${m o l}^{- 1}$ and $Δ H$ for $A l (g) ⟶ {A l}^{3 +} (g) + 3 e$ is $5140 k J$ ${m o l}^{- 1}$ . If second and third $I E$ values are in the ratio $2 : 3$ . ${I E}_{2}$ + ${I E}_{3} - 0.5$ in $k J$ ${m o l}^{- 1}$ is:

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Solution

Given that

$I E_{1}$ of $A l = 577.5 k J {m o l}^{- 1} . . . . (i)$
$[I E_{1} + I E_{2} + I E_{3}]$ of $A l = 5140 k J {m o l}^{- 1} . . . . (i i)$
Also given ${I E}_{2} = (2 / 3) {I E}_{3} . . . . . (i i i)$
solving eqs $(i), (i i), (i i i)$
${I E}_{2} = 1825 k J {m o l}^{- 1}$
${I E}_{3} = 2737.5 k J {m o l}^{- 1}$

$I E_{2} + I E_{3} = 1825 + 2737.5$

$= 4562.5 k J / m o l$

$I E_{1} + I E_{2} - 0.5 = 4562.5 - 0.5 = 4562$

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