Two solid compounds A and B dissociate into gaseous products at `20^(@)C` as
a. `A(s) hArr A'(s)+H_(2)S(g)`
b. `B(s) hArr B'(g)+H_(2)S(g)`
At `20^(@)C` pressure over excess solid A is `50` mm and that over excess solid B is `68` mm. Find:
a. The dissociation constant of A and B
b. Relative number of moles of A' and B' in the vapour phase over a mixture of the solids A and B.
c. Show that the total pressure of gas over the solid mixture would be `84.4` mm.

Answer

(a) `K_(p1)=625mm^(2)`, `K_(Pz)=1156mm^(2)` (b) `(625)/(1156)`

Explanation

`A(S)hArrA'(g)+H_(2)S(g) B(s)hArrB'(g)+H_(2)S(g)`
`A(S)hArrA'(g)+H_(2)S(g) P=50mm rArr P_(H_(2)S=P_(A).=P//2=25mm`
`B(S)hArrB'(g)+H_(2)S(g) P=68mm rArr P_(H_(2)S=P_(B')=P//2=34mm`
(i) `K_(p1)=(25)^(2)=625mm^(2)`
`K_(P2)=(34)^(2)=1156mm^(2)`
(ii) Ratio of moles is same as that of partial pressure so
A`(S) hArr A,(g) + H_(2)S(g)`
`P_(1) P_(1)+P_(2)`
`B(S) hArr B'(g) + H_(2)S(g)`
`P_(2) P_(2)+P_(1)`
`K_(p1)=P_(A.)xxP_(H_(2)S=P_(1)(P_(1)+P_(2))` .....(i)
`K_(p2)=P_(B.)xxP_(H_(2)S=P_(2)(P_(1)+P_(2))` .....(ii)
`(K_(p1))/(K_(P2))=(P_(1))/(P_(2))=(625)/(1156)`
(iii) total pressure `=P_(1)+P_(2)+(P_(1)+P_(2))=P_(1)+P_(2))`
(i)+(ii)`=(p_(1)+P_(2))^(2)`
`sqrtK_(P1)+K_(P2)=P_(1)+P_(2)`
`P_(T)=2xx(sqrtK_(P1)+K_(P2))=84.4mm`.