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Titanium metal is extensively used in ae...

Titanium metal is extensively used in aerospace industry because the metal imparts strength to structures but does not unduly add to their masses. The metal is produced by the reduction of `TiCl_(4(l))` which in turn is produced from mineral rutile `[TiO_(2(s))]`. can the following reaction for production of `TiCl_(4(l))` be carried out at `25^(@)C`?
`TiO_(2(s))+2Cl_(2(g))toTiCl_(4(l))+O_(2(g))`
Given that `H_(f)^(@)` for `TiO_(2(s)),TiCl_(4(l)),Cl_(2(g))` and `O_(2(g))` are `-944.7, -804.2,0.0,0.0 kJ mol^(-1)`. also `S^(@)` for `TiO_(2(g)),TiCl_(4(l)),Cl_(2(g))` and `O_(2(g))` are `50.3,252.3,233.0,205.1 J mol^(-1) K^(-1)` respectively.

Text Solution

Verified by Experts

The correct Answer is:
158
`DeltaH^(@)` for reaction
`=[H_(TiCl_(4))^(@)(l) + H_(O_(2))^(+)(g) - H_(TiO_(2))^(@) - H_(Cl_(2))^(@) xx 2]`
`=[804.2 + 0.0 -(944.7)-0.0]140.5` kJ
Also, `DeltaS` for reaction
`=[S_(TiCl_(4))^(@) (l) + SO_(2)^(@)(g) - S_(TiO_(2)(s))^(@) - S_(Cl_(2))^(@)(g) xx 2]`
`=-58.9 J =-0.0589 kJ K^(-1)`
Now, `DeltaG^(@) = DeltaH^(@) - T DeltaS^(@)`
`=140.5 - 298 xx (-0.0589) = 158 kJ`
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