The pH Scale (Leaving Cert Chemistry): Revision Notes

The pH Scale

What is the pH scale?

The pH scale is a numerical system used to measure how acidic or basic a solution is. It runs from 0 to 14, where values below 7 indicate acidic solutions, 7 represents neutral solutions, and values above 7 indicate basic (alkaline) solutions. Understanding the pH scale is essential for chemistry students as it appears throughout acid-base chemistry topics.

The pH scale is logarithmic, meaning each unit change represents a ten-fold change in acidity. For example, a solution with pH 3 is ten times more acidic than a solution with pH 4.

Development of the pH scale

The pH scale was developed in 1909 by Danish chemist Søren Sørensen while working for a brewery. He needed a simpler way to express hydrogen ion concentrations in solutions, as these numbers were often very small and cumbersome to work with (like 0.0001 or $10^{-4}$ moles per litre).

Instead of using these tiny decimal numbers or negative powers, Sørensen created the pH system to make these values easier to handle and communicate.

Mathematical definition of pH

The pH of a solution is defined mathematically as:

$\text{pH} = -\log_{10}[\text{H}^+]$

Where $[\text{H}^+]$ represents the hydrogen ion concentration measured in moles per litre.

This definition means that:

• The "p" in pH stands for "power" (referring to the power of 10)
• The negative sign ensures that as hydrogen ion concentration increases, pH decreases
• Higher hydrogen ion concentrations result in lower pH values (more acidic)
• Lower hydrogen ion concentrations result in higher pH values (more basic)

Relationship between hydrogen ion concentration and pH

There is a direct relationship between hydrogen ion concentration and pH values.

Key relationships to remember:

• pH 3: $[\text{H}^+] = 1 \times 10^{-3}$ mol/L (acidic)
• pH 6: $[\text{H}^+] = 1 \times 10^{-6}$ mol/L (acidic)
• pH 7: $[\text{H}^+] = 1 \times 10^{-7}$ mol/L (neutral at 25°C)
• pH 9: $[\text{H}^+] = 1 \times 10^{-9}$ mol/L (basic)
• pH 12: $[\text{H}^+] = 1 \times 10^{-12}$ mol/L (basic)

Notice how each change of 3 pH units represents a 1000-fold change in hydrogen ion concentration.

Temperature dependence of pH

An important concept that many students miss is that the neutral pH of pure water is not always 7. The neutral pH only equals 7 at 25°C. At other temperatures, the neutral pH changes because the water dissociation constant ($K_w$) changes with temperature.

Key temperature effects:

• At 0°C: Pure water has pH 7.47 (appears basic, but is actually neutral)
• At 25°C: Pure water has pH 7.00 (neutral)
• At 100°C: Pure water has pH 6.14 (appears acidic, but is actually neutral)

This happens because as temperature increases, water molecules dissociate more readily, producing more $\text{H}^+$ and $\text{OH}^-$ ions. However, equal amounts of both ions are still produced, so the water remains neutral despite the lower pH.

Measuring pH

There are several methods to measure pH in laboratory and everyday situations:

pH sensors and digital metres

Modern pH measurement often uses electronic pH sensors connected to digital metres or data-logging equipment. These provide accurate, precise readings and can monitor pH changes continuously.

Universal indicators

Universal indicator paper or solution changes colour depending on the pH of the solution being tested. Different colours correspond to different pH ranges, allowing for quick estimation of pH values.

Calculations with pH

When working with pH calculations, understanding the mathematical relationships is crucial for accurate results. Here are the key conversion processes you need to master:

Key steps for successful pH calculations:

1. Converting from $[\text{H}^+]$ to pH: Use $\text{pH} = -\log_{10}[\text{H}^+]$
2. Converting from pH to $[\text{H}^+]$: Use $[\text{H}^+] = 10^{-\text{pH}}$
3. Always include units: $[\text{H}^+]$ should be in mol/L
4. Check your calculator settings: Ensure you're using $\log_{10}$ (common logarithm)

For exam success, practice these conversions until they become automatic, as pH calculations appear frequently in acid-base chemistry questions.