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Thermodynamic Processes

For the gaseo...

Question

For the gaseous reaction, $K + F ⟶ K^{+} + F^{-}$ , $Δ H = 19 k c a l / m o l$ under conditions when cations and anions are prevented by electrostatic separation from combining with each other. The ${I E}_{1}$ of $K$ is $4.3 e V$ .
Electron gain enthalpy of $F$ is $X$ .
Find - $X$ ( nearest integer value).

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Solution

$K + F ⟶ K^{+} + F^{-}; Δ H = 19 k c a l$
$∴ Δ H = I E + E_{{g a}_{1}} . . . . (i)$
$∴ Δ H = 19 \times 10^{3} c a l {m o l}^{- 1} = \frac{19 \times 10^{3} \times 4.18}{6.023 \times 10^{23}} J / m o l e c u l e$
$= \frac{19 \times 10^{3} \times 4.18}{6.023 \times 10^{23} \times 1.602 \times 10^{- 19}} e V$
$Δ H = 0.823 e V$
By eq. $(i)$ $0.823 = 4.3 + E_{{g a}_{1}} . . . . . . . . (i i)$
$o r E_{{g a}_{1}} = - 3.477 e V$

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