Bromine monochloride, `(BrCl)` decomposes into bromine and chlorine and reaches the equilibrium.
`2BrCl_((g))hArrBr_(2(g))+Cl_(2(g))`
For which `K_(c)=32` at `500 K`. If initially pure `BrCl` is present at a concentration of `3.30xx10^(-3) mol litre^(-1)`, what is its molar concentration in the mixture at equilibrium?

Explanation

` {:(,2BrCl (g),hArr,Br_(2)(g),+ ,Cl_(2)), ("Intial" ,3*30 xx 10^(-3)"mol"L^(-1) ,,,,), ("At eqm.",(3*30 xx 10^(-3) -x),,x//2,,x//2):}`
` K_(c) = ((x//2)(x//2))/(3*30 xx10^(-3)-x)^(2) = 32 ("Given") :. (x^(2))/(4( 3*30 xx 10^(-3)-x))=32`
or ` x/ (2 (3*30 xx 10^(-3))-x)=sqrt(32) = 5*60`
` x = 11*32 ( 3*30 xx10^(-3) -x) or 12*32 x = 11*32 xx 3*30 xx 10^(-3) or x = 3*0 xx 10^(-3) `
` :. "At eqm., " [BrCl] = ( 3*30 xx 10^(-3) - 3*0 xx 10^(-3))= 0*30 xx 10^(-3) = 3*0 xx 10^(-4) "mol"L^(-1)`