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The energy needed for Li(g) rarr Li(g)^(...

The energy needed for `Li_(g) rarr Li_(g)^(3+) + 3e` is `1. 96 xx 10^4 kJ mol ^(-1)` . If the first ionisation energy of Li is ` 520 k J mol^(-1)` . Calcuate the second ionisation energy of `Li` .
(Given : `IE_1` for ` H = 2 . 2. 18 xx 10^(-18) k J "atom"^(-1)`).

Text Solution

Verified by Experts

Given
` Li(g) rarr Li_(g)^(3+) + 3d, DeltaH = 1.96 xx 10^4 kJ "mol"^(-1) ` ….(1)
` Li_(g) rarr Li_(g)^+ +e, IE_1 = 520 kJ "mole"^(-1) ` ….(2)
`Li_(g) rarr Li_(g)^+ +e, IE_2= a kJ "mol"^(-1)` …..(3)
` Li_(g) rarr Li_(g)^(3+) +e, IE _3 =b kJ "mole"^(-1) ...(4)`
Also `b =E_1 ` for ` Li^(2+) = E_1 ` for `H xx Z^2`
` = 2. 18 xx 10^(-18) xx 3^2 xx 6. 023 xx 10^(23) J "mole"^(-1)`
`=11.81 XX 10^(6) j MOL^(1)`
` = 11. 881 xx 10^3 kJ "mol"^(-1)`
By eqs , (1) , (2) , (3) and (4),
` 1. 96 xx 10^4 = 520 + a +11.9=81 xx 10^3`.
` a= 7270 kJ "mol"^(-1)`.
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