Calculating the pH of a Solution Given Hydroxide Ion Concentration

Understanding the relationship between pH, pOH, and hydroxide ion concentration is crucial in chemical calculations, particularly in aqueous solutions. This article explains how to calculate the pH of a solution when the hydroxide ion (OH-) concentration is given.

Step-by-Step Calculation

To find the pH of a solution from the given hydroxide ion concentration, follow these steps:

Calculate the pOH: The pOH is given by the formula:

pOH -log[OH^-]

Substitute the given concentration of OH- into the formula:

pOH -log(6.2 × 10-7) approx; 6.21

Use the relationship between pH and pOH: The relationship between pH and pOH is:

pH pOH 14

Substitute the calculated pOH into the formula to find pH:

pH 14 - pOH approx; 14 - 6.21 approx; 7.79

Other Examples

Let's consider a few additional examples involving different concentrations of OH-.

Example 1

Given [OH-] 6.0 × 10-5

Calculate the pOH: Using the pOH formula:

pOH -log[OH^-] -log(6.0 × 10-5) approx; 4.22

Use the relationship between pH and pOH: Using the formula pH pOH 14:

pH 14 - pOH 14 - 4.22 approx; 9.78

Example 2

Given [OH-] 6.9 × 10-2

Calculate the pOH: Using the pOH formula:

POH -log[OH^-] -log(6.9 × 10-2) approx; 1.16

Use the relationship between pH and pOH: Using the formula pH pOH 14:

pH 14 - POH 14 - 1.16 approx; 12.84

Formulas and Key Relationships

Understanding the key formulas and their applications can simplify these calculations. Here are some important formulas:

Calculation of pOH: POH -log[OH-] For [OH-] 6.9 × 10-2, POH approx; 1.16 Calculation of pH using pH and POH relationship: pH POH 14 For POH approx; 1.16, pH approx; 12.84 Key pH Calculations: pH -log[H ] POH -log[OH-] H 10-pH OH- 10-POH Kw 1.0 × 10-14 Ka 10-pKa Kb 10-pKb pKa × pKb 14 Henderson-Hasselbalch Eq. for a buffer solution: pH pKa log([conjugate base] / [acid]) POH pKb log([base] / [acid])

Remember, the pH and pOH of pure water at 25°C are both 7. Therefore, the sum of pH and pOH is always 14 for any aqueous solution.

Understanding these key concepts and formulas will help in solving a variety of pH and pOH calculations in chemistry.

Conclusion

C hihe understanding of the relationship between pH and pOH, along with the use of appropriate formulas, is essential in various chemical calculations. This article provides a step-by-step guide and several examples to help you master these calculations and enhance your problem-solving skills in chemistry.