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. 

Empirical and Molecular Formula Problems, 3

Category: Chemical Engineering Math

"Published in Vacaville, California, USA"

Analysis of a sample of ibuprofen, the active ingredient of Advil, shows that the sample contains 7.568 g of carbon, 0.881 g of hydrogen, and 1.551 g of oxygen. Use these data to calculate the empirical formula of ibuprofen.

Solution:

Moles of each components:

         Moles of carbon is

         Moles of hydrogen is
 

         
         Moles of oxygen is
 

 

From the number of moles of each component, we need to divide all of them by their least number of moles which is oxygen in order to get the number of atoms in a sample.
  
         Number of carbon in a sample is

         Number of hydrogen in a sample is

         Number of oxygen in a sample is
 

Since the number of atoms for carbon is a fraction which is 6.5, then we need to multiply all the atoms by 2 so that the number of atoms for empirical formula are all whole numbers. Therefore, the empirical formula for ibuprofen is