What am I doing wrong in this titration problem? Calculate the ph at the equival
ID: 870907 • Letter: W
Question
What am I doing wrong in this titration problem?
Calculate the ph at the equivalence point for the following titration 0.20M HCl versus 0.20M methylamine (CH3NH2). The Ka of methylammonium is 2.3x10^-11.
First I have to divide .20M methylamine by 2 (Why?) to get .10M
Then, I set up the equilibrium:
(2.3 x 10^-11) = x^2 / .10M
Since the ka is SO small, I just multiplied .10 with (2.3 x 10^-11) to get 2.3x10^-12, which is wrong.
Why is this wrong? Since the Ka is small, the approxiamation method should work and I won't need to do the quadratic. Instead, I am told that the x value is 1.5x10^-6 from the quadratic.
Explanation / Answer
Equivalence point:
Mol acid = Mol Base
M1*V1 = M2*V2
Assume V1 = V2 since there is no extra data, they should be in the same solution
M1 = M2 which makes sens since 0.2 = 0.2
In equilibrium
CH3NH2 + HCl ---> CH3NH3+ and Cl-
This will form an equilibrium
CH3NH3+ and H2O <---> H3O+ and CH3NH2
Recall the equilibrium
Ka = [H3O+][CH3NH2]/[CH3NH3+]
Since you have H3O+ ions, expec acidic solution
Ka = 2.3*10^-11
[H3O+] = [CH3NH2 ] = x
[CH3NH3] = 0.2 - x
Substitute in Ka expression
2.3*10^-11 = x*x / (0.2-x)
As you said, assume "-x" is so samll compared to 0.2
2.3*10^-11 = x^2 / 0.2
(2.3*10^-11)*0.2 ) = X^2
4.6*10^-12 = x^2
x = sqrt(4.6*10^-12) = 2.14*10^-6
NOTE: I don't know why you divided 0.2 by two... may be because the volume increased by 2 (i.e. 25 ml of acid and 25 ml of base, when adding will be 50 ml, recalculating concentrations you will have a diluted concnetration by a factor of 2x)
NOTE2: you are forgetting to take the square root of 2.3x10^-12
I mean: 2.3x10^-12 = x^2 as you said... you are forgetting to solve for x...
For your value... I got = 1.51*10^-6 which is exactly the value you got
NOTE: since this is exactly the value, I'm pretty sure you have same volumes of acid and base, so you have a double volume... thats why you are dividing by 2... its the only thing that makes sense to me
good luck, please let me know if oyu need more help