How to Calculate pOH from [OH-]: A Detailed Walkthrough

📚 Understanding pOH

pOH is a measure of the hydroxide ion concentration ($[OH^-]$) in a solution. It's analogous to pH, which measures the hydrogen ion concentration ($[H^+]$). In simple terms, pOH tells us how basic or alkaline a solution is.

📜 History and Background

The concept of pOH arose from the need to quantify the alkalinity of solutions, complementing the pH scale for acidity. Søren Peder Lauritz Sørensen, who introduced the pH scale in 1909, laid the groundwork for understanding ionic concentrations in aqueous solutions. Later, the understanding of acid-base chemistry was expanded to include pOH, providing a complete picture of a solution's properties.

⚗️ Key Principles of pOH Calculation

• 🧮 Definition of pOH: pOH is defined as the negative base-10 logarithm of the hydroxide ion concentration: $pOH = -\log_{10}[OH^-]$.
• ⚖️ Relationship between pH and pOH: In aqueous solutions at $25^{\circ}C$, the sum of pH and pOH is always 14: $pH + pOH = 14$.
• 🧪 Hydroxide Ion Concentration: $[OH^-]$ is measured in moles per liter (M).
• 💡 Calculating pOH from $[OH^-]$: To find the pOH, simply take the negative logarithm of the hydroxide ion concentration.

📝 Step-by-Step Calculation

1. Identify $[OH^-]$: Determine the hydroxide ion concentration in the solution.
2. Apply the Formula: Use the formula $pOH = -\log_{10}[OH^-]$.
3. Calculate: Use a calculator to find the logarithm and then apply the negative sign.

🧪 Real-World Examples

Let's go through some examples:

1. Example 1:

   If $[OH^-] = 1 \times 10^{-5} M$, then:

   $pOH = -\log_{10}(1 \times 10^{-5}) = -(-5) = 5$

2. Example 2:

   If $[OH^-] = 3.2 \times 10^{-2} M$, then:

   $pOH = -\log_{10}(3.2 \times 10^{-2}) = -(-1.49) = 1.49$

3. Example 3:

   If $[OH^-] = 0.0075 M$, then:

   $pOH = -\log_{10}(0.0075) = -(-2.12) = 2.12$

💡 Tips and Tricks

• 🔢 Use a Calculator: Always use a scientific calculator for accurate logarithmic calculations.
• 📝 Remember the Formula: Keep the pOH formula handy: $pOH = -\log_{10}[OH^-]$.
• 🧪 Understand the Relationship: Know that $pH + pOH = 14$ to easily convert between pH and pOH.
• 🧐 Pay Attention to Units: Ensure that the hydroxide ion concentration is in moles per liter (M).

⚗️ Practice Quiz

1. What is the pOH of a solution with $[OH^-] = 1 \times 10^{-3} M$?
2. Calculate the pOH when $[OH^-] = 6.8 \times 10^{-6} M$.
3. If $[OH^-] = 0.0001 M$, what is the pOH?
4. Determine the pOH of a solution where $[OH^-] = 2.5 \times 10^{-9} M$.
5. A solution has a hydroxide ion concentration of $9.2 \times 10^{-4} M$. Find its pOH.
6. What is the pOH if $[OH^-] = 0.75 M$?
7. Calculate the pOH for $[OH^-] = 5.0 \times 10^{-2} M$.

✅ Conclusion

Calculating pOH from hydroxide ion concentration is straightforward once you understand the basic principles and formulas. By following the steps and practicing with examples, you can easily master this concept. Remember, pOH is a valuable tool in understanding the alkalinity of solutions in chemistry.