Dimethyl amine $(CH_3)_2NH$ is a weak base and its ionization constant is $5.4 \times 10^{-5}$. Calculate $[OH^{-}]$,$[H_3O^{+}]$,$pOH$ and $pH$ of its $0.2 \ M$ solution at equilibrium.
For a weak base,the equilibrium is: $(CH_3)_2NH + H_2O \rightleftharpoons (CH_3)_2NH_2^{+} + OH^{-}$.
Using the approximation $[OH^{-}] = \sqrt{K_b \times C}$,where $K_b = 5.4 \times 10^{-5}$ and $C = 0.2 \ M$.
$[OH^{-}] = \sqrt{5.4 \times 10^{-5} \times 0.2} = \sqrt{1.08 \times 10^{-5}} = \sqrt{10.8 \times 10^{-6}} \approx 3.286 \times 10^{-3} \ M$.
$pOH = -\log[OH^{-}] = -\log(3.286 \times 10^{-3}) \approx 2.48$.
$pH = 14 - pOH = 14 - 2.48 = 11.52$.
$[H_3O^{+}] = 10^{-pH} = 10^{-11.52} \approx 3.02 \times 10^{-12} \ M$.
Using the approximation $[OH^{-}] = \sqrt{K_b \times C}$,where $K_b = 5.4 \times 10^{-5}$ and $C = 0.2 \ M$.
$[OH^{-}] = \sqrt{5.4 \times 10^{-5} \times 0.2} = \sqrt{1.08 \times 10^{-5}} = \sqrt{10.8 \times 10^{-6}} \approx 3.286 \times 10^{-3} \ M$.
$pOH = -\log[OH^{-}] = -\log(3.286 \times 10^{-3}) \approx 2.48$.
$pH = 14 - pOH = 14 - 2.48 = 11.52$.
$[H_3O^{+}] = 10^{-pH} = 10^{-11.52} \approx 3.02 \times 10^{-12} \ M$.
Explore More
Similar Questions
The percentage dissociation of a decinormal solution of a weak acid $HA$ is: $(K_a = 4.9 \times 10^{-8})$
Difficult
View SolutionCalculate the $pH$ of a solution containing $6.0 \ g$ of acetic acid $(CH_3COOH)$ in $250 \ mL$ of water. Given: $K_a = 1.8 \times 10^{-5}$ at $298 \ K$,and atomic masses are $C = 12, H = 1, O = 16$. (in $.57$)
Medium
View Solution$K_b$ for $NH_4OH$ is $1.8 \times 10^{-5}$. The $[OH^{-}]$ of $0.1 \ M \ NH_4OH$ is
Medium
View SolutionDetermine the degree of ionization and $pH$ of a $0.05 \, M$ ammonia solution. The ionization constant of ammonia $(K_{b})$ is $1.77 \times 10^{-5}$. Also,calculate the ionization constant of the conjugate acid of ammonia.
Medium
View SolutionDerive the equation for the ionization constant $K_a$ of a weak acid $HX$.
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo