Solubility Product Constant Problems, 2

Category: Chemical Engineering Math

"Published in Newark, California, USA"

The pH of a saturated solution of Fe(OH)₂ is 9.30. Calculate the K_sp of Fe(OH)₂.

Solution:

If the pH of Fe(OH)₂ is 9.30, then the pOH is 

The concentration of hydroxide ion in molarity is

Take the inverse logarithm on both sides of the equation, we have

Since Fe(OH)₂ is slightly soluble in water, then the ionization of Fe(OH)₂ is 

By using mole to mole relationship of the reactants and products in a liter of solution, if

then it follows that

 

Therefore, the solubility product constant of Fe(OH)₂ is

Solving for pH of a Base Problems

Category: Chemical Engineering Math

"Published in Newark, California, USA"

Calculate the pH for

(a) 0.02 M NaOH
(b) 0.10 M NH₄OH

Solution:

pH means "power of hydrogen". Some chemists say that pH means "potential of hydrogen". It is a measurement of acidity or alkalinity of a solution and it has a scale from 0 to 14. If pH is ranging from 0 to 6, then the solution is acidic. If pH is 7, then the solution is neutral like water, for example. If pH is ranging from 8 to 14, then the solution is alkaline. The pH of any acidic solution can be calculated by using the equation, 

where [H⁺] is the concentration of hydrogen ion in molarity. 

The pOH of any basic solution is

where [OH^-] is the concentration of hydroxide ion in molarity.

Hence, the pH of any basic solution can be calculated by using the equation,

                           or

(a) For 0.020 M NaOH solution 

Since NaOH is a strong base, then it is completely ionized into sodium ion and hydroxide ion as follows 

In a liter of solution, 0.02 moles of NaOH is ionized completely into 0.02 moles of Na⁺ and 0.02 moles of OH^-. Hence, the concentration of [OH^-] is 0.02. 

The pOH of 0.02 M NaOH is

Therefore, the pH of 0.02 M NaOH is

If the pH of a base is closer to 14, then it is a strong base. 

(b) For 0.10 M NH₄OH solution

Since NH₄OH is a weak base, then it is partially ionized into ammonium ion and hydroxide ion as follows

In a liter of solution at equilibrium,  

where x is moles of NH₄OH that partially ionized. The ionization constant for NH₄OH is given by the equation 

From Table of Ionization Constants of Acids and Bases, K_b = 1.8 x 10^-5 for ammonium hydroxide. The amount of NH₄OH that partially ionized is 

Since the value of K_b is less than 1 x 10^-3, then we can neglect x at the denominator as follows 

Hence, the concentration of hydroxide ion is 

The pOH of 0.01 M NH₄OH is

Therefore, the pH of 0.01 M NH₄OH is

If the pH of a base is closer to 7, then it is a weak base.