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Gay Lussac's Law, Avagadro's Law

If you are gi...

Question

If you are given Avogadro's number of atoms of a gas 'X'. If half of the atoms are converted into $X_{(g)}^{+}$ by energy $Δ H$ . The IE of X is

A

\frac{2 Δ H}{N_{A}}

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B

\frac{2 N_{A}}{Δ H}

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C

\frac{Δ H}{2 N_{A}}

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D

\frac{N_{A}}{Δ H}

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Solution

The correct option is A $\frac{2 Δ H}{N_{A}}$
Given number of atoms=Avogadro's number of atoms $= N_{A} = 6.023 \times 10^{23}$
Given that $\frac{N_{A}}{2}$ atoms are ionised, i.e.,
Ionsation energy of $\frac{N_{A}}{2}$ atoms of gas $X = Δ H$
$∴$ Ionisation energy of one atom of gas $X = \frac{Δ H}{(\frac{N_{A}}{2})} = \frac{2 \times Δ H}{N_{A}}$
Hence, ionisation energy of gas X is $\frac{2 \times Δ H}{N_{A}}$

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