r a weak acid with a dissociation co assumption that the chai ssocatconstant of
ID: 303671 • Letter: R
Question
r a weak acid with a dissociation co assumption that the chai ssocatconstant of 1.00 x 10. Evaluate the equnbrium calculation by cf the weak acid can be ignored in an equilibrium with and without the calculating the hydronium ion concentration [HO'1 at [HA] listed below. assumption for initial concentrations of the weak acid (For the percent error calculation uadratic equation) as the correet' answer) value obtained without the assumption (from the HA Ratio of HA/Ka % error INa-- 1-assumption assumption 0.10 M 1.0 x 102 M 1.0x 10M 1.0 x 104 NM 1.0 x 10 M a reasonable value for the ratio of acid concentration to After filling out the table, identify equilibrium constant for the assumption to be valid.
Explanation / Answer
let the weak acid be represented as HA. It undergoes ionization in presence of water as
HA+ H2O ------------>A- + H3O+
Ka= [A-][H3O+]/[HA]= 1*10-5,
preparing the ICE table,
component initial concentration (M) Change Eq. concentration
HA M -x M-x
A- 0 x x
H3O+ 0 x x
Ka= x2/(M-x)= 1*10-5 (1)
x2 = 1*10-5*(M-x) , if x cannot be neglected
x2= 1*10-5M- 1*10-5x
x2+1*10-5x -1*10-5M = 0 (2)
this is a quadratic equaiton of the form ax2+bx+c=0 whose roots as
x= {-b+-sqrt(b2-4ac)}/2a, here a= 1, b =-1*10-5 and c= -1*10-5
the +ve root need to be considered for this quadratic equation, hence x= {-b+sqrt(b2-4ac)}/2a
x= {-1*10-5 +sqrt(1*10-10+4*10-5M}/2a (3)
when x is very very small, it is reasonable to assume that M-x is approximately equal to M.
hence Eq.1 becomes x2= 1*10-5M, x= sqrt(1*10-5M) (4)
% error = 100*(Eq.4-Eq.3)/Eq.3
x =[H3O+]
one sample calculation is shown and rest of them are tabulated. for
M= 1M, [HA]/Ka= 1/1*10-5 = 105, when [HA] =1 M
From Eq.3, x={ -1*10-5+sqrt(1*10-10+4*1*10-5M)}/2= 0.003157
from Eq.4, x= sqrt(1*10-5)= 0.00316278M
% error= 100*(0.00316278-0.003157)/0.003157=0.158
Rest of the calculations for different initial concentration of M is shown below
the data suggests that at lower concentration of M, the assumption of M-x approximatelty equal to M is not justified.
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