Understanding the Context

pH is a measure of the acidity or alkalinity (basicity) of a solution. It represents the negative logarithm (base 10) of the hydrogen ion concentration [H⁺] in moles per liter (M). Because pH values can range from around 0 (very acidic) to 14 (very basic), scientists use a logarithmic scale to express these concentrations compactly and conveniently.

The pH Formula

The fundamental pH formula is:
pH = -log[H⁺]

Where:

• [H⁺] = concentration of hydrogen ions (in mol/L)
  
• log = logarithm (base 10)
  
• - ensures pH is always a positive number even when [H⁺] is small.

Key Insights

Decoding pH = -log(1 × 10⁻⁵)

Let’s break down the calculation step-by-step:

• We’re given pH = -log(1 × 10⁻⁵)
  
• The expression inside the log represents the hydrogen ion concentration: [H⁺] = 1 × 10⁻⁵ mol/L

Now apply the logarithm:

• log(1 × 10⁻⁵) = log(1) + log(10⁻⁵)
  
• Logarithm of 1 is 0: log(1) = 0
  
• log(10⁻⁵) = -5 because 10⁻⁵ means 1 × 10⁻⁵
  
• Therefore, log(1 × 10⁻⁵) = 0 + (-5) = -5

Final Thoughts

Now plug this into the pH formula:
pH = -(-5) = 5

Why It’s Important to Use the Negative Sign

In logical terms, taking the negative of a negative value reverses it to positive:

• log(10⁻⁵) = -5 (negative exponent gives small pH, low acidity)
  
• But since pH = -log(10⁻⁵), the outer negative turns it positive:
  pH = -(-5) = +5

This means the solution is mildly acidic — common in weak acids like vinegar or carbonated water.

Real-World Applications of pH = 5

A pH of 5 indicates a relatively acidic environment, slightly above neutral (pH 7). This value is crucial in: