A 6.4 gm sample of methanol (CH_(3) OH) was placed in an otherwise empty 1 litre flask and heated to 227^(@)C to varpoise the methanol. Methanol vapour decomposes by following gasesous compound to effuse out of flask. Measurement shows it contains 32 times as much as H_(2) (g) as CH_(3)OH (g). Then Value of K_(C) for this reaction is :

A 6.4 gm sample of methanol (CH_(3) OH) was placed in an otherwise emp

1.	A 6.4 gm sample of methanol (CH_(3) OH) was placed in an otherwise empty 1 litre flask and heated to 227^(@)C to varpoise the methanol. Methanol vapour decomposes by following gasesous compound to effuse out of flask. Measurement shows it contains 32 times as much as H_(2) (g) as CH_(3)OH (g). Then Value of K_(C) for this reaction is :
Answer» `(16)/(25)` `(4)/(5)` `((4)/(5))^(3)` `((16)/(25))^(2)` Solution :`{:(CH_(3)OH (g),hArr,CO (g),+,2H_(2) (g),{"Given " a_(0) = (n_((CH_(3)OH)))_("initial") = (6.4)/(32) = 0.2},),(t = 0 "mole" a_(0) - a_(0) alpha,,a_(0) alpha,,2a_(0) alpha,,):}` `sum n_("eqm") = a_(0) (1 + 2 alpha)` `(r_(H_(2)))/(r_(CH_(3)OH)) = (p_(H_(2)))/(P_(CH_(3)OH)) sqrt(M_(CH_(3)OH)/(M_(H_(2)))) = (2 a_(0) alpha)/(a_(0) (1 - alpha)) sqrt((32)/(2))` `(32)/(1) = (Deltan_(H_(2)))/(Deltan_(CH_(3)OH)) = (2 alpha)/(1 - alpha) xx 4` `4 = (alpha)/(1 - alpha) rArr 4 - 4 alpha = alpha` `alpha = (4)/(5)` `K_(C) = (a_(0) alpha (2a_(0) alpha)^(2))/(a_(0) (1 - alpha)) xx (1)/(V^(2))` `K_(C) = (4 alpha^(3) xx a_(0)^(2))/(1 - alpha) xx (1)/(V^(2)) = 4 xx ((4)/(5))^(3) xx ((0.2)^(2))/(1 - (4)/(5)) = ((16)/(25))^(2)`