Two solids dissociates as follows
`A(s) rarr B(g) + C(g), K_(P_(1)) = x atm^(2)`
`D(s) rarr C(g) + E(g), K_(P_(2)) = y atm^(2)`
The total pressure when both the solids dissociate simultaneously is :

Options

A. `x^2+y^2` atm
B. (x+y)atm
C. `sqrt(x+y)` atm
D. `2sqrt(x+y)` atm

Answer

D

Explanation

`{:(A(s) hArr , B(g)+ , C(g)),(,p_1,p_1+p_2):}`
`K_p(1)=x=p_B .p_C`
or `x=p_1(p_1+p_2)` …(i)
`{:(D(s) hArr , C(g)+, E(g)),(,p_2+p_1,p_2):}`
`K_p(2)=y=p_C.p_E`
or `y=(p_2+p_1)p_2`…(ii)
Adding (i) and (ii)
`p_1(p_1+p_2)+p_2(p_1+p_2)=x+y`
`(p_1+p_2)^2=x+y`
or `p_1+p_2=sqrt(x+y)`
Total pressure = `p_B+p_C+p_E`
`=p_1+(p_1+p_2)+p_2`
`=2(p_1+p_2)`
`=2sqrt(x+y)` atm at equilibrium .