Given for the following equilibrium taking place in 1 L flask at 300 K. `PC1_(5)(g)hArrPC1_(3)(g) + C1_(2)(g)` , `K_(c) = 4` Thus, degree of dissociations of `PC1_(5)` (g) is

Options

A. `2[sqrt(2)-1]`
B. `(2sqrt(2)-1)`
C. `2[sqrt(2)+1]`
D. `-2[sqrt(2)+1]`

Answer

A

Explanation

`{:(,PCl_(5)(g),hArr,PCl_(3)(g),+,Cl_(2)(g)),("Let",,,,,),("Initial moles",1,,0,,0),("At equilib",(1-x),,x,,x),("Active masses",(1-x)/1,,x/1,,x/1"mol"L^(-1)):}`
`K_(C) = ([PC1_(3)][C1_(2)])/([PC1_(5)]) =(x^(2))/((1-x)) =4`
`x^(2) + 4x - 4 = 0`
`x = (-4 + sqrt(16+16))/(2) = (-4+4sqrt(2))/(2)`
`x = 2[sqrt(2) -1]`