The pH Scale: A Measure of Acidity and Basicity
What is pH?
pH scale
The pH scale is a logarithmic measure of the concentration of hydrogen ions ($ [H^+] $) in an aqueous solution.
It is defined mathematically as:
$$ \text{pH} = -\log_{10} [H^+] $$
Here:
- $ [H^+] $ represents the concentration of hydrogen ions in moles per cubic decimeter ($ \text{mol dm}^{-3} $).
- The negative logarithm ensures that pH values are positive, as $ [H^+] $ in aqueous solutions typically ranges from $ 1 \, \text{mol dm}^{-3} $ to $ 10^{-14} \, \text{mol dm}^{-3} $.
If the $ [H^+] $ of a solution is $ 1.0 \times 10^{-3} \, \text{mol dm}^{-3} $ at 298 K, its pH is: $$ \text{pH} = -\log_{10} [H^+] = -\log_{10} (1.0 \times 10^{-3}) = 3.00 $$
This indicates the solution is acidic.
If you know the pH, you can reverse the process to calculate the $ [H^+] $ concentration using the equation:
$$ [H^+] = 10^{-\text{pH}} $$
If the pH of a solution is $ 5.0 $ at 298 K, the $ [H^+] $ is:
$$ [H^+] = 10^{-\text{pH}} = 10^{-5} = 1.0 \times 10^{-5} \, \text{mol dm}^{-3} $$
- pH is temperature-dependent and is typically quoted at 298 K (25°C).
- Changes in temperature can affect the ionization of water, altering the $[H^+]$ concentration and thus shifting the neutral pH value slightly from 7 at standard conditions.
The pH Scale: Ranges and Interpretations
- The pH scale generally ranges from $ 0 $ to $ 14 $, though values outside this range are possible for very strong acids or bases.
- Here’s how to interpret pH values:
- Acidic solutions: $pH< 7$ ($ [H^+] >[OH^-] $)
- Neutral solutions: $pH = 7$ ($ [H^+] = [OH^-] $)
- Basic (alkaline) solutions: $pH > 7$ ($ [H^+]< [OH^-] $)
pH and dilution
Measuring pH: Indicators and Probes
Using Indicators
Acid–base indicators are substances that change color based on the pH of the solution. For example:
- Litmus paper: Turns red in acidic solutions and blue in basic solutions.
- Universal indicator: A mixture of indicators that shows a spectrum of colors across the pH scale (e.g., red for pH 1, green for pH 7, violet for pH 14).
If a solution turns the universal indicator orange, its pH is approximately $ 4 $, indicating it is weakly acidic.
Using a pH Probe
- For precise measurements, digital pH meters are used.
- These devices consist of an electrode that measures $ [H^+] $ concentration and converts it into a pH value.
- Calibration with standard buffer solutions (e.g., pH $ 4.00 $, $ 7.00 $, and $ 10.00 $) is necessary for accurate readings.
Always calibrate your pH probe before use, particularly when working with solutions at extreme pH values or when high precision is required.
- Students often forget that the pH scale is logarithmic.
- A decrease of 1 unit in pH corresponds to a tenfold increase in $ [H^+] $.
- For example, a solution with pH $ 3 $ is $ 10 $ times more acidic than one with pH $ 4 $, not $ 1 $ time more.
- Another common error is failing to convert concentrations to $ \text{mol dm}^{-3} $ before calculating pH.
- Always ensure your units are consistent.
- Calculate the pH of a solution with $ [H^+] = 2.5 \times 10^{-4} \, \text{mol dm}^{-3} $ at 298 K.
- A solution has a pH of $ 8.5 $ at 298K. What is the $ [H^+] $ concentration?
- Compare the $ [H^+] $ concentrations of solutions with pH $ 3 $ and pH $ 6 $ at 298 K. How many times more acidic is the first solution?
- Why might a pH probe provide more accurate readings than a universal indicator?
