Question

BH⁺ClO₄^- is a salt formed from the base B (K_b= 1.00×10^-4)and perchloric acid. It dissociates into BH⁺, a weak acid, and ClO₄^-, which is neither an acid nor a base. Find the pH of 0.100 M BH⁺ClO₄^-.

Short answer

The pH of 0.100 M BH⁺ClO₄^-is 5.50.

Step-by-step solution

Definition of salt, weak acid and weak base and pH.

Salt is an ionic compound that contains a base (cation) and acid (anion).

Example- NaCl, KCl

Weak acids are the acid substances that do dissociate in the constituent ions when dissolve in water.

Example- CH₃COOH

Weak base are the basic substances that do not completely ionize in water.

Example- NH₃

pH is defined as a quantitative measure of acidity and basicity. Compound having pH more than 7 is acidic in nature while pH when shown above than 7 is called as basic in nature. When pH comes 7, compound is said to be neutral.

Disassociation of salt.

A salt BH⁺ClO₄^- is formed from the base B (with K_b= 1.00 × 10^-4) and perchloric acid. When we consider that BH⁺ClO₄^- disassociates into BH⁺ and ClO₄^-, we will find the pH of 0.100 M BH⁺ClO₄^-.

Calculating Ka.

The reaction of dissociation of BH⁺as follows:

$$\begin{gathered} {\mathrm{BH}}^{+}\stackrel{}{\stackrel{}{\rightleftarrows }}\mathrm{B}+{\mathrm{H}}^{+} \\ \left[{\mathrm{BH}}^{+}\right]=0.100-\mathrm{x} \\ \left[\mathrm{B}\right]=\left[{\mathrm{H}}^{+}\right]=\mathrm{x} \end{gathered}$$

where,

$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}}={\mathrm{K}}_{\mathrm{w}}/{\mathrm{K}}_{\mathrm{b}} \\ =(1\times {10}^{-14})/(1\times {10}^{-4}) \\ =1\times {10}^{-10} \end{gathered}$$

 Step 4: Calculate the value of x.

$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}}=\frac{{\mathrm{x}}^2}{0.1-\mathrm{x}} \\ 1\times {10}^{10}=\frac{{\mathrm{x}}^2}{0.1-\mathrm{x}} \\ \mathrm{x}=3.16\times {10}^{-6}\mathrm{M} \end{gathered}$$

Calculate the pH.

Since [B] = [H⁺] = x,

The pH of solution will be

$$\begin{gathered} \mathrm{pH}=-\log \left[{\mathrm{H}}^{+}\right] \\ =-\log (3.16\times {10}^{-6}) \\ =5.50 \end{gathered}$$

Result:

The pH of 0.100 M BH⁺ClO₄^- is 5.50.