I don’t understand how the neutral pH of 7 is an integer number and not arbitrarily chosen. How likely is that?
Edit: Dudes, stop explaining that negative logarithmic scale… this has nothing to do with my question. I could ask the same thing with “Why is it an integer number 14?’.
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The equilibrium constant of water at STP is 10^(-14). When water dissociates, two water molecules form one hydronium (H30^(+)) and one hydroxide (OH^(-)). When calculating equilibrium, you multiply the concentrations of the products, and because they are equal in a neutral solution, you get x^(2) = 10^(-14) or x = 10^(-7). When you take the -log10 of that, you get 7.
Now, technically at STP the dissociation coefficient of water isn’t exactly 10^(-14) it’s actually about 1.012 * 10^(-14), which would yield a pH of 6.997 but sometimes you just have to round for simplicity. Very rarely are you in a situation where the dissociation of water is the significant contributor of hydronium or hydroxide ions.
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Because pH = 7 – mV/57.14 [at 25C and 1 atm pressure]
This was intentional to make a scale that was easy to work with and not need to do log scale calculations or use millivolts all the time.
It’s the 57.14 mV when measuring voltage potentials that really matters as that relates to the actual electrochemistry of a pH electrode.
Each 57.14 mV corresponds to an order of magnitude more H ions in solution when measured through an Hydrogen selective electrode against a reference electrode within the same solution.
Some people won a nobel prize on this figuring out how (The Nernst Equation) and the really complicated membrane math about 50-60 years after we empirically figured out the 57.14mV number and created the scale (to simplify measurement / math).
pH = – log[H+]
if i recall my high school chemistry correctly, a neutral pH solution has the hydrogen ion concentration equal to 10^-7 M at 25 ºC and 1 atm, hence “7” when you apply the log (base 10) operation
neutral pH at different temperatures is not 7; pure water is pH 7.47 at 0 ºC and 6.14 at 100 ºC
Ok, so we’ve got a few things here that need to be unpacked (I’ll be using the Arrhenius definition, since it assumes aqueous solution):
pH is the negative log of the concentration of hydrogen ions (H+/protons) in neutral water. The concentration of hydrogen ions in neutral water is 1×10^-7 molar. The negative log of that number is 7. Seven is NOT arbitrarily chosen.
Because it is a made up scale. Someone made the decision that 7 was neutral. They could have made it 50 and made acids go to zero and bases to 100. It is just a scale and we have agreed upon it. It’s like kilograms vs pounds, a made up scale.
So, your edit basically says “I don’t care about the formulation of the Henderson-Hasselbalch Equation, I’m legitimately just wondering why the number is exactly 7”
And the answer is two parts:
it’s not exactly 7 at Standard Temperature and Pressure (STP) — as some people have mentioned. It’s like 6.99 and we just round to 7 because on a logarithmic scale that amount of difference is completely negligible.
As for why it is this number? It just is. There is no reason.
It’s like asking why the circumference of a circle divided by its diameter = pi. It’s just a physical property that we could probably explain in detail if we did some hardcore modeling of the individual electrochemical properties of each individual water molecule, and then expand that to a whole beaker full of water, but it doesn’t really matter. That number just relates to the neutral dissociation constant for water. Other liquids (methanol, ethanol, THF, whatever) will have different neutral pH numbers. The exact value of 7 has no underlying significant meaning, it’s just the value you get when you measure.
It isn’t quite 7 dead on. In fact, the pH amd ionization constant of pure water changes a fair amount with temperature. At 25 degrees Celsius, the ionization constant is 1.008 E-14, so the pH is really close to 7. So when we say the pH of water is seven, we really mean that pure water that’s a little warmer than room temperature is very close to pH 7.
You’ve asked a good question and there is some misunderstanding about this.
pH of water varies with temperature.
At standard temperature (25 deg C), pH of pure water is actually about 6.99948.
This is so close to 7 that the difference is not significant for laboratory purposes.
(The temperature at which it is exactly 7 is around 24.87 deg C.)
Neutral pH isn’t some lucky integer, it falls out cleanly from the definition. pH is literally defined as the negative base-10 logarithm of the hydrogen ion concentration:
pH=−log10[H+]pH = -log_{10}[H^+]pH=−log10[H+]
In pure water at 25°C, the autoionization constant gives [H+]=1.0×10−7[H^+] = 1.0 times 10^{-7}[H+]=1.0×10−7 M. Plug that into the definition: −log10(10−7)=7-log_{10}(10^{-7}) = 7−log10(10−7)=7. That’s why neutral is exactly 7 — not because it was “chosen,” but because math on a log scale naturally lands on an integer there.
The scale stretching to 14 comes from the fact that the ion product of water is 1.0×10−141.0 times 10^{-14}1.0×10−14. So when hydrogen is 10−710^{-7}10−7, hydroxide is also 10−710^{-7}10−7. If hydrogen drops to 10−1410^{-14}10−14, hydroxide rises to 10010^{0}100. That symmetric spread makes the whole range 14 units wide.
It only looks “conveniently integer-y” because base 10 logs are designed to turn powers of ten into neat whole numbers.