The percent dissociation of an acid in solution can be determined by first calculating the concentration of the hydrogen ions
([H+].) that are produced when the acid dissociates. The dissociation constant
(Ka) gives us a measure of the extent to which the acid dissociates in solution. For a weak acid, which only partially dissociates, the equilibrium expression can be written as:
squareHA⇌H++A−where
HA is the weak acid,
H+is the hydrogen ion, and
A−is the conjugate base. The dissociation constant,
Ka, is then given by:
Ka=‌The degree of dissociation (a) in weak acids is quite small. We can therefore assume that the change in concentration of the acid (the amount that dissociates) is relatively small and the equilibrium concentration of the acid
[HA] can be approximated as the original concentration (
C0 ) of the acid. Hence, taking
α to represent the degree of dissociation, we get:
‌[H+]=[A−]=αC0‌[HA]=C0−αC0≈C0Now we plug in these into the expression for
Ka :
‌Ka=‌‌Ka=α2C0Solving for
α, we get:
α=√‌ Now let's plug in the given values:
‌Ka=2.25×10−6‌C0=0.01M‌α=√‌‌α=√2225×10−4‌α=1.5×10−2 Now to find the percent dissociation, we convert the degree of dissociation into a percentage:
‌‌ Percent dissociation ‌=α×100%‌‌ Percent dissociation ‌=1.5×10−2×100%‌‌ Percent dissociation ‌=1.5%Therefore, the percent dissociation of the acid in its
0.01M solution is
1.5%, which corresponds to option A.