Solving for pH of a Mixture of Acid and Base Problems, 2

Category: Chemical Engineering Math

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What is the pH of the resulting solution made by mixing 5 mL of 0.2178 M HCl and 15 mL of 0.1156 M NH₄OH? K_b = 1.8 x 10^-5 for NH₄OH.

Solution:

If an acid is mixed with a base, then the resulting product is a salt. If you mix a strong acid with a strong base, then the resulting product is a neutral salt. If you mix a weak acid with a weak base, then the resulting product is a neutral salt. However, if you mix a strong acid with a weak base, then the resulting product is an acidic salt. If you mix a weak acid with a strong base, then the resulting product is a basic salt. 

The pH of any neutral salt is usually equal to 7. The pH of an acidic salt is less than 7 and the pH of a basic salt is greater than 7. 

In the given problem, if HCl is mixed with NH₄OH, then the resulting product is
 

Since NH₄Cl is an acidic salt, then the pH is less than 7. From the given amount and concentration of the reactants, let's see if the resulting solution is acidic or basic as follows
 

 

 

Since the number of moles of NH₄OH is greater than with the number of moles of HCl, then the resulting mixture is basic. Well, let's see.

Hence, the resulting concentration of NH₄OH is
      

 

 

Since NH₄OH is a weak base, then its ionization is written as follows
 

The concentration of [OH^-] is 

Since the value of K_b is very small, then we can neglect x at the denominator as follows 

The pH of NH₄OH is

The resulting concentration of NH₄Cl which is their product is

The ionization of NH₄Cl is written as follows
 

 

 

Since [H⁺] is the product of the ionization process, then we need to convert K_b into K_a as follows

The concentration of [H⁺] in NH₄Cl is

Since the value of K_a is very small, then we can neglect x at the denominator as follows 

 

The pH of NH₄Cl is

Therefore, the pH of the overall resulting solution is