Vinegar contains acetic acid, a weak acid that is partially dissociated in aqueo

Question

Vinegar contains acetic acid, a weak acid that is partially dissociated in aqueous solution. CH3CO2H (aq) --><-- H+ (aq) + CH3CO2- (aq). What is the value of Kc if the extent of dissociation in 1.0 M CH3CO2H is 0.42%?

Explanation / Answer

Now lets say a substance that dissociates into two ions happens to be y% dissociated. This means at equilibrium there will be y% times the initial amount. Lets denote the initial amount using M. A====>B+C Then at equilibrium the concentration of B is M x y% but from our balanced equation we can see that for every molecule of B produced one molecule of C is also produced so the equilibrium concentration of C is also M x y%. So far we know that [B]= M x y% and [C]=M x y% Now we need to find out what [A] is. Well we know that for every molecule of B and C produced one molecule of A and since M=initial concentration of A then the equilibrium concentration of A will be [A]=M-(M x y%) which means we subtract the concentration of B or C from the initial concentration of A to get the equilibrium concentration of A. Now to sum things up we know that. [A]=M-(M x y%) [B]= M x y% [C]=M x y% and KC=[B][C]/[A] replace [A], [B] and [C] with what we found above to get Kc=[Mxy%][Mxy%]/[M-(Mxy%)] and this is your formula except they don't use y%, they just use % so lets get rid of y and write it like the do. Kc=[M x %][M x %]/[M-(M x%)] Now notice that we have the same thing two times in the numerator? That's why it's squared because [M x %][M x %]=[M x %]

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