The logarithmic pH scale of eq 1 is open-ended, allowing for pH values below 0 or above 14. Nevertheless, there is much confusion about the permissible range of the pH scale (e.g., 1–16). The misconception that pH lies between 0 and 14 has been perpetuated in popular-science books (1–3), textbooks (4–8), revision guides (9), and reference books (10–16).

Although many chemistry texts state or infer that negative pH values are possible, typically no examples are given. This may be because negative pH values are difficult to measure experimentally (17, 18) and there has been a lack of suitable buffer standards for pH < 1. It is easier to report H₃O⁺ concentrations or total acid concentrations in the 10⁰–10¹ mol L^-1 range than imprecise negative pH values. Furthermore, most texts have a diagram of a pH scale similar to Figure 1A. Comparison of the typical textbook diagram (without arrows on the pH-scale axis) to mathematical-textbook diagrams (e.g., 19, 20, 21), suggests that the pH scale is a closed line interval rather the open-ended scale shown in Figure 1B.

Figure 1. Two pH scales: (A) a typical textbook diagram; (B) arrows on the axis show that pH is measured on an open-ended scale.

The misconception might be minimized by using pH scale diagrams similar to Figure 1B and listing examples of solutions, with pH outside the 0–14 range, in textbooks. For example, commercially available concentrated HCl solution (37% by mass) has pH ≈ -1.1, while saturated NaOH solution has pH ≈15.0 (22). Hot springs near Ebeko volcano, with naturally occurring HCl and H₂SO₄, have estimated pH values as low as –1.7 (23, 24). Waters from the Richmond Mine at Iron Mountain, CA, have pH = -3.6 (25, 26).

Acknowledgment

KFL thanks Phillip Ponder (Penleigh and Essendon Grammar School, Keilor East, Australia) and Jeanne Lee () for encouraging and helpful discussions.

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