The `K_(c)` for `A_(2(g))+B_(2(g))hArr2AB_((g))` at `100^(@)C` is `50`. If one litre flasks containing one mole of `A_(2)` is connected with a two litre flask containing `2 "mole"` of `B_(2)`, how many mole of `AB` will be formed at `100 ^(@)C`?

Explanation

`{:(,,A_(2(g)),+,B_(2(g)),hArr,2AB_((g))),(,"Initial mole",1,,2,,0),(,"Final mole at equilibrium",(1-x),,(2-x),,2x):}`
Total volume of both containers on joining becomes `3 litre`.
`:.` At equilibirum
`[A_(2)]=((1-x))/(3)`, `[B_(2)]=((2-x))/(3)`, `[AB]=(2x)/(3)`
`:. K_(c)=([AB]^(2))/([A_(2)][B_(2)])=(4x^(2))/(9((1-x)/(3))*((2-x)/(3)))`
`=(4x^(2))/((2-3x+x^(2))=50`
`:. 4x^(2)=100-150x+50x^(2)`
or `46x^(2)-150x+100=0`
`x=0.93` and `2.326` which is not valid since `xgt2`
`:. "Mole of" AB=2x=2(0.93)=1.86 "mole"`