R3.1.9 pOH scale (Higher Level Only)

The pOH Scale and Its Relationship with pH

1. You’re testing the water quality of a local lake.
2. You’ve already measured its pH, but you find yourself wondering: what about the basicity of the water? Is there a way to quantify how many hydroxide ions $[O{H}^{-}]$ are present?

This is where the pOH scale becomes a powerful tool—it helps you analyze the basicity of a solution, complementing the information provided by the pH scale.

Understanding the pOH Scale

1. The pOH scale, like the pH scale, is logarithmic.
2. However, instead of measuring the concentration of hydrogen ions $[H^{+}]$, it measures the concentration of hydroxide ions $[O{H}^{-}]$.

The pOH of a solution is defined by the formula:

$$\text{pOH}=-{\log }_{10}[{\text{OH}}^{-}]$$

Here, $[O{H}^{-}]$ represents the molar concentration of hydroxide ions.

The pH-pOH Relationship

The pOH scale is closely linked to the pH scale through the ionic product of water ($K_w$), which describes the equilibrium constant for water's self-ionization:

$${\text{K}}_w=[H^{+}][O{H}^{-}]$$

• At 298 K (25°C), $K_w=1.00\times {10}^{-14}{\text{mol}}^2{\text{dm}}^{-6}$. Taking the negative logarithm of both sides gives:

$$\text{pH}+\text{pOH}=14\text{(at 298 K)}$$

Calculating $[O{H}^{-}]$ and $[H^{+}]$ from pOH and pH

• The pOH scale is particularly useful for basic solutions.
• Once you know the pOH, you can calculate $[O{H}^{-}]$ using the formula:

$${\text{[OH}}^{-}]={10}^{-\text{pOH}}$$

• Similarly, you can calculate $[H^{+}]$ using $K_w=[H^{+}][O{H}^{-}]$, or equivalently:

$${\text{[H}}^{+}]=\frac{K_w}{[{\text{OH}}^{-}]}$$

Using pOH and pH to Analyze Solutions

By combining pH and pOH, you can classify solutions:

• Acidic: $\text{pH}<7$, $\text{pOH}>7$
• Neutral: $\text{pH}=7$, $\text{pOH}=7$
• Basic: $\text{pH}>7$, $\text{pOH}<7$

Reflection