Question

Calculate the pH of a solution prepared by mixing 100mL of 0.4M \[HCl\] with 100 mL of 0.4 M \[N{H_3}\]. Hydrolysis constant of ammonium chloride is \[5.6 \times {10^{ - 10}}\]

Answer 1

Hint: In order to find the pH of a solution which is prepared by mixing \[HCl\] and \[N{H_3}\], we must first know what a pH is. pH is a type of scale which is used to measure the acidity or basicity of an aqueous solution. The expanded form for pH is the power of Hydrogen. pH will indicate the concentration of the \[{H^ + }\] ions.

Complete Solution :
Let us first understand about pH. pH is a type of scale which is used to measure the acidity or basicity of an aqueous solution. The expanded form for pH is the power of Hydrogen.
Different types of substance will have different pH.
- pH for an acidic substance is below 7.
- pH for a basic substance will be above 7.
- pH for a neutral substance will be equal to 7.

Now let us move onto the problem given.
The aqueous solution of the ammonia is the ammonium hydroxide.
The equilibrium reaction between \[HCl\]and \[N{H_4}OH\] is given below:
\[HCl + N{H_4}OH \rightleftharpoons N{H_4}Cl + {H_2}O\]

We have to remember that as were mixing the strong acid, i.e. \[HCl\] with a weak base, i.e. \[N{H_3}\], the pH of the resulting solution will never be equal to 7. From the question we can see that equal volumes of \[N{H_3}\] and \[HCl\] are reacting, therefore the number of moles of the reactants undergoing neutralisation will also be equal.
Total volume of the liquids, i.e. \[N{H_3}\] and \[HCl\] = 100 + 100 = 200mL.
Therefore, the number of moles of \[N{H_4}Cl\] = \[\dfrac{{40}}{{200}} = 0.2M\]
The equilibrium reaction between \[NH_4^ + \] and \[{H_2}O\] is given as
\[NH_4^ + + {H_2}O \rightleftharpoons {H^ + } + N{H_4}OH\]

Now we have to look for the base dissociation constant \[{k_b}\] of \[N{H_3}\] at the room temperature.
\[{k_b} = 1.78 \times {10^{ - 5}}\]
\[pH = 7 - 0.5(p{K_b} + \log C)\]
\[pH = 7 - 0.5[5 - \log (1.78) + \log (0.2)]\]
\[pH = 4.96\]
The pH of the solution prepared by mixing \[N{H_3}\] and \[HCl\] is 4.96.

Note: We must remember that pH and pOH are different from one another. We can say that they are opposite of each other. pOH indicates the concentration of the \[O{H^ - }\] ions.
- pOH of the acidic substance is above 7, while pH will be below 7.
- pOH of the basic substance is below 7, while pH will be above 7.