Question

A 0.10 M solution of a base is 2.0% hydrolzed $\left(\alpha =0.020\right)$Find${\mathbf{K}}_{\mathbf{b}}$

Short answer

The value of ${\mathrm{K}}_{\mathrm{b}}=4.1\times {10}^{-5}$.

Step-by-step solution

Step : Consider a reaction

Let the given base be B.

The reaction of base B with water is as shown below:

$$\begin{gathered} \mathrm{B}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{BH}}^{+}+{\mathrm{OH}}^{-} \\ \left[\mathrm{B}\right]=0.1-\mathrm{x} \\ \left[{\mathrm{BH}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]=\mathrm{x}) \end{gathered}$$

Calculation of the value of x

$$\begin{gathered} \mathrm{\alpha }=\frac{\mathrm{x}}{\mathrm{F}} \\ \mathrm{x}=\mathrm{\alpha }\times \mathrm{F} \\ =0.02\times 0.1 \\ =0.002 \end{gathered}$$

Calculate  

$\begin{array}{l}K=\frac{x^3}{0.1-x}\\ =\frac{{\left(0.002\right)}^2}{0.1-0.002}\\ =4.1\times {10}^{-5}\end{array}$

Hence, the value of K_b is$4.1\times {10}^5$ .