How to calculate 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 [H3O+].

chem.purdue.edu - Calculating_pHandpOH

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pH, pOH, pK a , and pK b

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) = 2.60 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

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 10-5 M?

pOH = - log [4.82 x 10-5] = - ( - 4.32) = 4.32 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).

Relationship Between pH and pOH

The pH and pOH of a water solution at 25oC are related by the following equation.

pH + pOH = 14

If either the pH or the pOH of a solution is known, the other can be quickly calculated.

Example: A solution has a pOH of 11.76. What is the pH of this solution?

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pH = 14 - pOH = 14 - 11.76 = 2.24 Top

Calculating pK a

The pK a is calculated using the expression:

pK a = - log (K a )

where "K a " is the equilibrium constant for the ionization of the acid.

Example: What is the pK a of acetic acid, if K a for acetic acid is 1.78 x 10-5?

pK a = - log (1.78 x 10-5) = - ( - 4.75) = 4.75 Top

Calculating K a from the pK a

The K a for an acid is calculated from the pK a by performing the reverse of the mathematical operation used to find pK a . K a = 10-pKa or K a = antilog ( - pK a ) Example: Calculate the value of the ionization constant for the ammonium ion, K a , if the pK a is 9.74.

9.74 = - log (K a )

-9.74 = log (K a )

K a = 10-9.74 = 1.82 x 10-10

On a calculator calculate 10-9.74, or "inverse" log ( - 9.74).

Calculating pK b

The pK b is calculated using the expression:

pK b = - log (K b )

where K b is the equilibrium constant for the ionization of a base.

Example: What is the pK b for methyl amine, if the value of K b for methyl amine is 4.4 x 10-4?

pK b = - log (4.4 x 10-4) = - ( - 3.36) = 3.36 Top

Calculating K b from pK b

The K b for an acid is calculated from the pK b by performing the reverse of the mathematical operation used to find pK b . K b = 10-pKb or K b = antilog ( - pK b ) Example: Calculate the value of the ionization constant, K b , for aniline if the pK b is 9.38.