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pH, pOH, pK
a
, and pK
b
The symbol "p" means " the negative of the logrithm of ." "p" is often used with very small or very large values. Calculating pH Calculating hydronium ion concentration from pH Calculating pOH Calculating hydroxide ion concentration from pOH The relationship between pH and pOH Calculating pKa Calculating Ka from pKa Calculating pKb Calculating Kb from pKb
Calculating pH
To calculate the pH of an aqueous solution you need to know the concentration of the hydronium ion in moles per liter (molarity). The pH is then calculated using the expression: pH = - log [H 3 O
]. Example: Find the pH of a 0.0025 M HCl solution. The HCl is a strong acid and is 100% ionized in water. The hydronium ion concentration is 0.0025 M. Thus: pH = - log (0.0025) = - ( - 2.60) = 2. Top
Calculating the Hydronium Ion Concentration from pH
The hydronium ion concentration can be found from the pH by the reverse of the mathematical operation employed to find the pH. [H 3 O
] = 10 -pH or [H 3 O
] = antilog (- pH) Example: What is the hydronium ion concentration in a solution that has a pH of 8.34?
8.34 = - log [H 3 O
]
- 8.34 = log [H 3 O
- ] [H 3 O+] = 10-8.34^ = 4.57 x 10-9^ M On a calculator, calculate 10 -8. , or "inverse" log ( - 8.34). Top
Calculating pOH
To calculate the pOH of a solution you need to know the concentration of the hydroxide ion in moles per liter (molarity). The pOH is then calculated using the expression: pOH = - log [OH
- ] Example: What is the pOH of a solution that has a hydroxide ion concentration of 4.82 x 10
M? pOH = - log [4.82 x 10
] = - ( - 4.32) = 4. Top
Calculating the Hydroxide Ion Concentration from pOH
The hydroxide ion concentration can be found from the pOH by the reverse mathematical operation employed to find the pOH. [OH
- ] = 10 -pOH or [OH - ] = antilog ( - pOH) Example: What is the hydroxide ion concentration in a solution that has a pOH of 5.70? 5.70 = - log [OH
] -5.70 = log[OH
] [OH-] = 10-5.70^ = 2.00 x 10-6^ M On a calculator calculate 10-5.70, or "inverse" log (- 5.70). Top
Relationship Between pH and pOH
The pH and pOH of a water solution at 25oC are related by the following equation. pH + pOH = 14
The pKb is calculated using the expression: pKb = - log (Kb) where Kb is the equilibrium constant for the ionization of a base. Example: What is the pKb for methyl amine, if the value of Kb for methyl amine is 4.4 x 10
) = - ( - 3.36) = 3. Top
Calculating Kb from pKb
The Kb for an acid is calculated from the pKb by performing the reverse of the mathematical operation used to find pKb. Kb = 10-pKb^ or Kb = antilog ( - pKb) Example: Calculate the value of the ionization constant, Kb, for aniline if the pKb is 9.38. 9.38 = - log (Kb) -9.38 = log (Kb) Kb = 10-9.38^ = 4.17 x 10- On a calculator calculate 10-9.38, or "inverse" log ( - 9.38). Top
