An element undergoes a reaction as shown : X + 2 e - → X 2 - , energy released = 30 .87 eV / atom . If the energy released is used to dissociate 4 gms of H 2 molecules, equally into H + and H * , wher

Question

An element undergoes a reaction as shown :

$X + 2 e^{-} \to X^{2 -}$ , energy released $= 30 .87 eV / atom$ . If the energy released is used to dissociate $4 gms$ of $H_{2}$ molecules, equally into $H^{+}$ and $H^{*}$ , where $H^{*}$ is excited state of $H$ atoms where the electron travels in orbit whose circumference equal to four times its de Broglie's wavelength. Determine the least moles of $X$ that would be required:

Given: I.E. of $H = 13 .6 eV / atom$ bond energy of $H_{2} = 4 .526 eV / molecule$ .

TestHub · Accepted Answer

Total energy requirement per molecule of $H_{2}$ :

Binding energy $=4 .526 eV$

$I .E = 13 .60 eV$

According to de Broglie's explanation of Bohr's orbit-

${2πr}_{n} = nλ$

As per question, $2πr = 4λ$

Thus, electron is excited to the 4^thBohr orbit

Excitation energy $= E_{4} - E_{1} = - 0 .85 - (- 13 .60) = 12 .75 eV$

Thus, total eenergy requirement per molecule $= 13 .60 + 12 .75 + 4 .526 ≅ 30 .87 eV$

Thus, $1$ molecule of $H_{2}$ will be dissociated by $1$ atom of $X$

Therefore, $(4 {gH}_{2}) \equiv 2$ moles of $H_{2}$ molecules will be dissociated by $2$ moles of $X$ .

Chemistry - Atomic Structure Question with Solution | TestHub

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