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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 ...

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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 ...

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According to Martin Chaplin's Water Dissociation and pH: In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming and re-associating ions, the dissociation constant is much lower (for example at $-4~\mathrm{^\circ C}$, $K_\mathrm{w} = 2 \times 10^{-20}~\mathrm{mol^2~L^{-2}}$). So $[\ce{H+}] = 1.4 \times 10^{-10}~\mathrm{... 44 I've decided to tackle this question in a somewhat different manner. Instead of giving the chemical intuition behind it, I wanted to check for myself if the mathematics actually work out. As far as I understand, this isn't done often, so that's why I wanted to try it, even though it may not make the clearest answer. It turns out to be a bit complicated, and ... 37 The real definition of the$\text{pH}$is not in terms of concentration but in terms of the activity of a proton, $$\text{pH} = - \log a_{\ce{H+}} \ ,$$ and the activity is a dimensionless quantity. You can think of the activity as a generalization of the mole fraction that takes into account deviations from the ideal ... 34 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. 33 It is not proven that "sugar makes your body acidic"! Your body's pH is very tightly regulated by the body's internal systems; it is also different in different parts of the body - the stomach is acidic (1.0-2.5), the intestine are mildly basic (jejunem 7-9) terminal ileum 7.5 reference here. Blood pH is 7.35, and any deviation from this is indicative of ... 31 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, $$\mathrm{... 26 Water undergoes autoionization, i.e., it reacts as follows:$$ \ce{H2O + H2O <=> H3O+ + OH-} $$The equilibrium constant for this reaction at standard conditions is K_w = [\ce{H3O+}][\ce{OH-}] \approx 1.0 \cdot 10^{-14}. In pure water, [\ce{H3O+}] = [\ce{OH-}], hence [\ce{H3O+}] = \sqrt{K_w} \approx 1.0 \cdot 10^{-7}\ \textrm{M}. Suppose we ... 24 It is possible to have \mathrm{pH}<0 and you don't need to create any substance. Take a concentrated solution of one of the strong inorganic acids (i.e. one with dissociation constant above 1000 like sulfuric acid) and here you are. 23 A PRACTICAL DEMONSTRATION WITH PYTHON Nicolau answer is an excellent analysis of the function that describes the titration but I would like to follow the Ben Norris answer (that I think to tackle better the problem at its origin) using Python hoping that this could be useful to become more confident and explore titration on your own. Acidify pure water and ... 21 At first you have to think of where the protons come from. That is as you mentioned it, hydrochloric acid (for every chloride ion in solution there has to be a proton) and water (for every hydroxide ion from the autoprotolysis there also has to be a proton).$$\ce{[H+] = [OH-] + [Cl-]}$$The concentration for the hydroxide ions can be derived from the ... 19 The pH titration curve is shaped as it is because pH is a logarithmic scale. pH is the negative base ten logarithm of hydrogen ion concentration:$$\text{pH}=-\log_{10}{\ce{[H+]}}$$Thus, each change of 1 pH unit is a 10-fold change in concentration, and linear of value that 10-fold change gets smaller as the pH increases. For example, going from pH 1 to ... 19 The controversy surrounding the \mathrm{p}K_\mathrm{a} of hydronium mostly arises from the definition of K_\mathrm{a} or lack thereof. There is no IUPAC definition of \mathrm{p}K_\mathrm{a} or K_\mathrm{a}. The closest IUPAC defined term is the standard equilibrium constant, which can be denoted as K^\circ or just K. Physical chemistry ... 19 Deprotonation of the phenol and protonation of aniline result in species that easily react with a diazonium cation in the intended manner. Let's have a look at the species involved. On the one hand, there is the diazonium cation: Deprotonation of phenol yields phenolate, for which a resonance structure with a negative charge in para position to the ... 19 Since the \mathrm{pI} is the \mathrm{pH} at which the amino acid has no overall net charge, you need to average the \mathrm pK_\mathrm a values relevant to the protonation/deprotonation of the form with no net charge. Here are the acid-base equilibria for tyrosine: The form with no net charge is in red (+1 and -1 cancel out to give no net charge). It ... 18 \mathrm{pH + pOH = 14} This equation only holds true at around 25~^\circ\mathrm{C}, where the water autodissociation constant K_\mathrm{w} = 10^{-14}. Mathematically, you can write$$\begin{align} K_\mathrm{w} = [\ce{H+}][\ce{OH-}] &= 10^{-14} & &\\ \log([\ce{H+}][\ce{OH-}]) &= \log(10^{-14}) & &\text{(logarithms of both ... 17 Standard pKa measurements pKa is, as you mentioned, commonly measured in water. This worked well initially, but as chemists got more ambitious in their measurements, they began to come up against the levelling effect, whereby the acidity/basicity of the compound being measured was limited by the acid/base properties of the solvent being used to measure it.... 16\mathrm{pH}$is the aqueous concentration of$\ce{H3O+}$or$\ce{H+}$ions in soution. I would not say that ice lacks$\ce{H3O+}$and$\ce{OH-}$ions as ice's structure would allow for such, however, since the ions are not in aqueous solution, the material cannot rightfully have a "$\mathrm{pH}$" as we know it. 16 Significant amount of geminal diol of benzaldehyde exists in an aqueous solution of benzaldehyde at 25 °C because$\mathrm{p}K_{\text{hyd}} = 2$(Ref. 1) The$\mathrm{p}K_{\mathrm a}$of benzyl alcohol is listed as 15.40 (Wikipedia). Thus, one can reasonably assume that the given value of$\mathrm{p}K_{\mathrm a}$14.9 represents a composite equilibrium ... 16 Interesting analytical chemistry problem. Currently, it is not possible to accurately determine pH in a remote fashion. Spectroscopy is the technique of choice for remote sensing, but the H$^+$is not that spectroscopy friendly i.e., it is a quiet ion. It will respond to radiofrequency in a powerful magnetic field but the sensitivity is quite poor in an NMR ... 15 Let me add a bit more to the answers already given. As has been said,$\mathrm{pH}$is nothing but a measure of the activity of protons ($\ce{H+}$) in a solvent -$\displaystyle\mathrm{pH} = -\log_{10} \ce{\ a_{H_{\text{solvated}}^{+}}}$. In dilute solutions, a solute's activity is approximately equal to its concentration, and so you can get away with saying ... 15 Sure enough, such extreme pKa values can't be determined in water for the very reason you've specified (the so-called leveling effect). Now, pretty much every textbook containing the phrase "leveling effect" would also provide a word of explanation as to how can we move beyond the common pH range of water. Even the link above does that; please, read it till ... 15 The textbook is precisely correct. The equilibrium constant$K$which the logarithm is taken of is dimensionless, and includes activities or fugacities, and not concentrations and pressures. In practice this is achieved by using standard states which refer to the pure materials: standard concentration$c^⦵$and standard pressure$p^⦵$. One must be very ... 14 You have to analyze the reaction mechanism behind the self-ionization of water to understand better what happen. In fact is not strictly self but a matter of "couple-ionization": you know the water atoms have different electronegativity, the more electronegative oxygen attracts the less electronegative hydrogen of another water molecule forming an hydrogen ... 14 Consider the choices. Since it's acetic acid, you can rule out any pH values that indicate a basic or neutral solution. Knowing that acetic acid is a weak acid and that vinegar is a fairly dilute solution, you can also rule out any pH values that would indicate either a strong acid or a highly concentrated solution. Eliminating those impossible values leaves ... 14 At a particular temperature, the$K_{\text{eq}}$for the following reaction (yes, it's the auto-protolysis of water): $$\ce{H2O(l) <=> H+(aq) + OH-(aq)}$$ will be constant. Note that$K_\mathrm{w}=K_{\text{eq}}\times[\ce{H2O}]=\ce{[H+(aq)][OH-(aq)]}$is called the auto-protolysis constant of water. It is considered a constant because concentration of ... 14 In acid-base titrations, synthetic indicators are exclusively used to find accurate end-point determinations because they always have a highly defined color change at certain pHs. For example, phenolphthalein ($\mathrm{p}K_\mathrm{a} = 9.7$at$\pu{25 ^{\circ}C}$) is colorless in acidic solutions (precisely$0 \lt \mathrm{pH} \lt 8.2$), but it is pink in ... 13 It's not as intuitive as it seems and your questions are all legitimate questions, but sometimes even good arguments can't be used as evidence in chemistry.$\ce{NaHCO3 -> Na+ + HCO3-}$, but that one doesn't involve water at all Look at this reaction: $$\ce{NaCl <=>Na+ +Cl-}$$ Even this reaction doesn't "involve" water in the schematics but is ... 12 The tap water is likely "hard," i.e., contains some dissolved mineral salts, most likely (primarily) calcium and magnesium carbonates and bicarbonates. The anions of these salts are slightly basic, consuming$\ce{H^+}\$ ions and thereby raising the pH. Carbonates (with the obvious exception of alkali metal salts) are only sparingly soluble in water, while ...

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