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Thursday, September 25, 2014

Solving for pH of a Buffer Solution, 2

Category: Chemical Engineering Math

"Published in Newark, California, USA"

Calculate the pH of a liter of solution that contains 0.1 mole of acetic acid and 0.1 mole of sodium acetate. If few drops of concentrated hydrochloric acid is added to the solution that would make the solution 0.02 M in HCl if the buffer was not present, what is the new pH of the solution?

Solution:

A buffer solution is a solution of weak acid and its salt or a solution of weak base and its salt. The purpose of making a buffer solution is to prevent the rapid change of pH if more acid or base is added to the solution. 

Since acetic acid is a weak acid, then it is partially ionized into acetate ion and hydrogen ion as follows 



In a liter of solution at equilibrium, 




where x is moles of HC2H3O2 that partially ionized. The ionization constant for HC2H3O2 is given by the equation 


From Table of Ionization Constants of Acids and Bases, Ka = 1.8 x 10-5 for acetic acid. The amount of HC2H3O2 that partially ionized is  



If 0.1 moles of sodium acetate which is completely ionized into 0.1 moles of sodium ion and 0.1 moles of acetate ion is added to the solution, then the above equation becomes 



The acetate ion from sodium acetate will be added to the acetate ion from acetic acid. Since the value of Ka is less than 1 x 10-3, then we can neglect x at the numerator and denominator as follows  




Hence, the concentration of hydrogen ion is 


Therefore, the pH of a buffer solution is 





If few drops of concentrated hydrochloric acid is added to buffer solution, then acetate ion will react with hydrogen ion from hydrochloric acid to form acetic acid. The amount of acetic acid will increase while the amount of acetate ion will decrease. From the equation of buffer solution


if 0.02 M HCl solution or 0.02 moles of concentrated HCl is added and assuming that the increase in volume of solution is negligible, then the above equation becomes 




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




Hence, the concentration of hydrogen ion is 


Therefore, the pH of final solution is 





As you can see that there's a slight change of pH of buffer solution after the addition of few drops of concentrated hydrochloric acid. Without buffer solution, the pH of 0.02 M HCl solution is 1.70.