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Understanding hydronium ion concentration is key to grasping pH calculations. The concentration of hydronium ions \([\text{H}_3\text{O}^+]\) refers to the number of hydronium ions present in a unit volume of solution, typically measured in moles per liter (M). For example, in the given problem, the concentration is \(2.5 \times 10^{-12}\) M. This small number indicates that ammonia is a basic solution because it has a very low concentration of hydronium ions. Remember, the more hydronium ions present, the stronger the acidity of the solution. Conversely, fewer hydronium ions indicate a more basic (alkaline) solution.

Logarithms play a crucial role in chemistry, especially when dealing with exponential scales like pH. The pH formula uses the base-10 logarithm (log), which helps in transforming the small hydronium ion concentrations into manageable numbers. For the pH, the formula is: \[ \text{pH} = -\text{log}[\text{H}_3\text{O}^+] \] This means you take the logarithm of the hydronium ion concentration and then multiply it by -1. For instance, in the exercise when calculating \(\text{log}(2.5 \times 10^{-12})\), you split it into \( \text{log}(2.5) \) and \( \text{log}(10^{-12}) \), find their values separately, and add them together. This calculation simplifies interpreting the concentration into the pH value.

The pH formula is a simple yet powerful tool in chemistry: \[ \text{pH} = -\text{log}[\text{H}_3\text{O}^+] \] This equation relates the acidity or basicity of a solution to its hydronium ion concentration. To use it:

• Identify the hydronium ion concentration in moles per liter (M).
• Insert this value into the logarithm function.
• Multiply the result by -1.

For the given example with \(2.5 \times 10^{-12}\) M, we substitute into the formula: \[ \text{pH} = -\text{log}(2.5 \times 10^{-12}) \] After finding \( \text{log}(2.5) + \text{log}(10^{-12}) \), which is \(0.39794 - 12 \), we get \( -11.60206 \). Multiplying by -1 yields a pH of 11.60206, indicating a basic solution. Practicing these steps helps in efficiently and accurately determining the pH of various solutions.