Chemistry - Is a negative pH level physically possible?
Solution 1:
One publication for you: “Negative pH Does Exist”, K. F. Lim, J. Chem. Educ. 2006, 83, 1465. Quoting the abstract in full:
The misconception that pH lies between 0 and 14 has been perpetuated in popular-science books, textbooks, revision guides, and reference books.
The article text provides some counterexamples:
For example, commercially available concentrated HCl solution (37% by mass) has $\mathrm{pH} \approx -1.1$, while saturated NaOH solution has $\mathrm{pH} \approx 15.0$.
Solution 2:
It's certainly possible theoretically. Solve for $\ce{pH < 0}$:
$\ce{-log[H+] < 0\\ log[H+] > 0\\ [H+] > 1}$
So, as you said, a solution in which the hydrogen ion concentration exceeds one should theoretically have a negative $\ce{pH}$. That said, at those extremes of concentration, the utility and accuracy of the $\ce{pH}$ scale breaks down for various reasons.
Even acids conventionally categorized as "strong" do not in fact dissociate 100%. In reality, their dissociation is also essentially an equilibrium process, though this only becomes apparent at surpassingly high concentrations. As the solution becomes more concentrated, any additional acid cannot be as thoroughly solvated, and the chemical equilibrium begins to favor dissociation progressively less and less. Hence, as the solution becomes increasingly saturated, the extent of dissociation begins to plateau and the hydrogen ion concentration approaches some practical upper limit. Furthermore, $\ce{pH}$ measured via molar concentration as a proxy for thermodynamic activity is inherently inaccurate at the extremes of concentration. Other phenomena, such as the formation of distinct chemical species by self-ionization in a concentration-dependent manner further complicate things (e.g., generation of $\ce{H3SO4+}$ in concentrated sulfuric acid, $\ce{H2F+}$ in concentrated hydrofluoric acid, etc.).
For highly concentrated solutions of strong acids, alternatives/extensions to $\ce{pH}$ exist that are functional beyond the limits of $\ce{pH}$ (see, for example, the Hammett acidity function).
As for whether solutions of negative $\ce{pH}$ have actually been experimentally prepared or observed, the answer is yes. Here's a link to one article describing the measurement of $\ce{pH}$ in acidic mine waters, which cites a figure of $-3.6$.
Solution 3:
Any strong acid solution with concentration more than 1 mol/L has the negative pH. Think about any concentrate commonly used strong acid solution such as 3M $\ce{HCl}$, 6M $\ce{HNO3}$. Negative pH is actually very common.
Solution 4:
It is very much possible.
Let’s say you put 3 moles of $\ce{HCl}$ into 1 mole of water. $\ce{HCl}$, being a strong acid dissociates completely into $\ce{H+}$ and $\ce{Cl-}$ ions as:
$$\ce{HCl -> H+ + Cl-}$$
so after complete dissociation, $[\ce{H+}]=3~\mathrm{mol/L}$ (ignoring the very tiny contribution from water itself)
By definition, $$\mathrm{pH} = -\log[\ce{H+}]$$
therefore, $\mathrm{pH}= -\log 3= -0.48$
So it is very much possible to have solutions of strong acids whose $\ce{[H+]}$ is 1 molar or more, and thus whose pH is negative.
Solution 5:
It is possible to have $\mathrm{pH}<0$ and you don't need to create any substance. Take a concentrated solution of one of the strong inorganic acids (i.e. one with dissociation constant above 1000 like sulfuric acid) and here you are.