Question

`1` mol of A in `1` litre vessel maintained at constant T shows the equilibrium
`A(g) hArr B(g) +2C(g) " " K_(C_(1))`
`C(g) hArr 2D(g)+3B(g) " " K_(C_(2))`
If the equilibrium pressure is `13/6` times of initial pressure and `[C]_(eq)=4/9[A]_(eq)`, Calculate `K_(C_(1))` and `K_(C_(2))`.

Answer 1

`{:(A(g),hArr,B(g)+,2C(g)and ,C,hArr,2D+,3B(g)),(1,,0,0,,,,),(1-a,,(a+3b),2a-b,2a-b,,2b,(a+3b)):}`
`:. Sigma` mole at equilibrium `=1-a+a+3b+2a-b+2b`
`=2a+4b+1`
Now, `P_("initial") prop 1`
`P_(eq) prop 2a+4b+1`
`:. 2a+4b+1=13/6`
or `2a+4b=7/6`
Also `[C]_(eq)=4/9 [A]_(eq)`
`2a-b=4/9xx(1-a)`
`22a-9b=4`
By equations (i) and (ii) `a=0.25, b=0.167`
`:. K_(C_(1))=([B][C]^(2))/([A])=((a+3b)(2a-b)^(2))/((1-a))`
`=([0.25+(3xx0.167)][0.5-0.167]^(2))/((1-0.25))=0.11`
`:. K_(C_(2))=([D]^(2)[B]^(2))/([C])=((2b)^(2)(a+3b)^(3))/((2a-b))`
`=([2xx0.167]^(2)[0.25+(3xx0167)]^(3))/([0.5-0.167])=0.142`