Answer :
From the information available in the question, the concentration of H3O^+ is 4 × 10^-13 M.
What is equilibrium constant?
The equilibrium constant is a value that shows the extent to which reactants are converted to products.
We can set up the ICE table as follows;
(CH3)2NH(aq) + H2O(l) ⇄ (CH3)2NH2+(aq) + OH^-(aq)
I 1.2 0 0
C - x +x +x
E 1.2 - x x x
Given that Kb = [ (CH3)2NH2+] [OH^-]/[(CH3)2NH]
5.4 x 10–4 = [x]^2/ 1.2 - x
5.4 x 10–4 (1.2 - x) = [x]^2
6.48 × 10^-4 - 5.4 × 10^-4x = x^2
x^2 + 5.4 × 10^-4x - 6.48 × 10^-4= 0
x=0.025 M
Now;
[OH^-] [H3O^+] = 1 × 10^-14
[H3O^+] = 1 × 10^-14/[OH^-]
[H3O^+] = 1 × 10^-14/0.025 M
[H3O^+] = 4 × 10^-13 M
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