Calculate the pH of a 0.010M solution of NaCN. The Kb of CN- is (2.1)(10^-5)?

Question

Help. I am horribly confused.

Answer 1

OK I'll try to keep it simple

NaCN is a salt, thus it will dissociate 100% into Na+ and CN-.
Since the stoichiometry for the dissociation is 1 NaF : 1 CN- you will have "initial" concentration of CN-= concentration of NaCN= 0.010 M

Since HCN is a weak acid, the ion CN- will hydrolyze in water according to the reaction

.. .. .. .. .. .. .. CN- +H2O <=> HCN + OH-
Initial .. .. .. 0.010
React .. .. .. .x
Produce .. .. .. .. .. .. .. .. .. .. x .. .. ..x
At Equil. .. 0.010-x .. .. .. .. .. x .. .. .. x

Kb= [HCN][OH-]/[CN-] = x^2/(0.010-x)

Note that the concentration of H2O is considered constant in such problems and thus it is not included in the table and the K equation

Let's assume for simplicity that 0.010 >> x so that 0.010-x=0.010
Then the equation is simplified to
x^2/0.010= 2.1*10^-5 =>
x= squareroot (0.01*2.1*10^-5 ) =4.58*10^-4 This is < 0.10 so our assumption is marginally valid and we would get pH= 14-pOH= 14-(-logx) =14-(-log(4.58*10^-4)) = 10.66

However x is not that much smaller from 0.010 so I prefer in this case to solve the quadratic to get the correct value

x^2/(0.010-x)= 2.1*10^-5 =>
x^2= 2.1*10^-7 - 2.1*10^-5x =>
x^2 +2.1*10^-5x -2.1*10^-7 =0
x1= 0.00044788= 4.48*10^-4
x2= -0.00046888<0 rejected

so

pH= 14-pOH= 14-(-logx) =14-(-log(4.48*10^-4)) = 10.65

Answer 2

NaCN is a salt of strong base and weak acid
thus ph= 1/2 (pKw + pKa + log C) = 1/2( 14 + 4.68 + (-2) = 17.68
where pKw= log of ionic product of water
pKa = log of ionic product of acid

& c = concentration =0.010M


Actually u should have give Ka of CN rather than Kb because in the salt NaCN the base is NaOH(strong base) & acid is HCN (weak acid)

Answer 3

to discover pH you do the adverse log of your concentration, which consequently is 0.011M. to bypass out of your pH to concentration you will do the antilog(-pH). in view which you gave Kb i'm assuming you could discover Ka or something like that. the simplest equation that i understand for that's (Kb)(Ka) = Kw Kw = a million.0X10^-14