Who took a proton from the proton jar? The bumbling biochemist is on the case and her prime suspect is the base! And hopefully she can also help clear up the case of H⁺ and OH- that seem to fly into equations out of nowhere!

text from November 2020, pH video added 10/13/21

More details below, but here’s the TLDR gist: We usually think of water as a charge-neutral molecule consisting of 2 hydrogens and an oxygen (H₂O). But those H’s like to come and go. And when they do, they usually leave behind their (negatively-charged) electron because the O “wants it more” (is more electronegative). So instead of thinking of water as H₂O we can think of it as a mixture of H₂O, H⁺, & OH⁻.

pH is a measure of how many protons (H⁺) are floating around. We call pH 7 “neutral” – above it (fewer protons) & we call a solution BASIC or ALKALINE – lower than 7 (so more protons) and we call it ACIDIC 

Some molecules (which we call bases) can steal protons as they go about their travels. And, kinda like how you might feel guilty taking a cookie if there are only a couple left in to jar but you’d happily take one if the cookie jar’s full, molecules will more readily accept protons (become protonated) if there are more protons available. And (just to confuse us) this corresponds to a low pH. It’s not really to confuse us it’s because pH is the inverse log of the proton concentration. 

On the flip side there are molecules we call acids which fill that cookie jar – they donate protons. But they’ll only do so if the jar’s not already full. We talk about “acids” and “bases” but these are just temporary roles that molecules take on – it’s their “job” not their “identity” and they go back and forth between their “conjugate acid” & “conjugate base” forms because once an acid gives one up it can take one (act as a base) and vice versa. Different molecules have different proton greedinesses which we can describe using a value called pKa.

Some more details: Atoms (like the hydrogens & oxygens) have smaller parts called protons (+ charged), neutrons (neutral), & electrons (- charged). The # of protons defines an element (e.g. hydrogen *always* has 1 & oxygen *always* has 8) but the number of electrons & neutrons can vary. 

Since neutrons aren’t charged, you can add or remove them without changing the overall charge of the atom (though you might change its stability – stuff too many in & you can get an unstable form that decays to a more stable form, letting off radiation as it does so). We call versions of the same element with different #s of neutrons nuclear isotopes, and the decay-happy ones radioactive isotopes (radioisotopes). An example is P32 which is a radioactive form of phosphorus that we use to label RNA probes, etc. more on that here: http://bit.ly/2lb0O9U 

Since electrons *are* charged, if you change the # of electrons of a neutral atom you un-neutralize it , giving you a charged particle (aka ION) -> adding electrons makes it negative (ANIONIC) & removing electrons makes it positive (CATIONIC).

Hydrogen is the “simplest” element – it only has a single proton, so its neutral form has a single electron. So if it leaves oxygen with that electron it becomes a proton. So we often use the terms proton & H⁺ interchangeably. And, even more at-first-confusingly, we also often use these terms interchangeably with H₃O⁺. H₃O⁺ is aka a HYDRONIUM ION. We usually speak of H⁺ for simplicity BUT in reality, “free” H⁺ don’t exist in water –  instead they immediately latch onto one of the many abundant surrounding H₂O molecule to form HYDRONIUM ions (H₃O⁺)

In undergrad we had to take general chemistry before biology and I remember going from chemistry class, where there was a big emphasis on “balancing equations” so that you accounted for where every molecule came from and ended up, making sure that no atoms were magically appearing or vanishing – to biology, where molecules seemed to “fly into equations” out of nowhere. Especially protons (H⁺) and hydroxide ions (OH⁻).

But these charged particles (ions) weren’t really coming from nowhere – they were often coming from the water the molecules are dissolved in. We usually think of water as a charge-neutral molecule consisting of 2 hydrogens and an oxygen (H₂O). But those H’s like to come and go. And when they do, they usually leave behind their electron because the O “wants it more” (is more electronegative). So instead of thinking of water as H₂O we can think of it as a mixture of H₂O, H⁺, & OH⁻.

H⁺ are constantly hopping around from place to place (latching onto an OH⁻ to make H₂O or joining up with H₂O to make H₃O⁺). This is called the auto-ionization of water. And water’s happiest when the concentration of H⁺ ([H⁺]) multiplied by the concentration of OH⁻ ([OH⁻]) = 1.0×10⁻¹⁴ M², a number we call the ION PRODUCT OF WATER, Kw. 

[H⁺][OH⁻] = 1.0×10⁻¹⁴ 

nomenclature note: [ ] just means “concentration of” and “M” stands for Molarity, which is mol/L, where mol is 6.02 x 10^23 of something (it’s just a lump number for counting kinda like a huge dozen)

This is a dynamic equilibrium -> H⁺ can still go from molecule to molecule but there’s no net movement (i.e. for every H⁺ that settles down there’s another one heading out). But because they can move around so easily they can get snatched up by other molecules too so they can seem to “magically appear” in equations describing reactions taking place in water (aqueous solutions).

Fiddle around with the equation a bit and you can see that 

[H⁺] = 1.0×10⁻¹⁴ / [OH⁻] 


[OH⁻]  = 1.0×10⁻¹⁴ /[H⁺] 

So the more H⁺, the less OH⁻ & vice versa. 

For water to be neutral overall, the concentration of H⁺ ([H⁺]) has to equal the concentration of OH⁻ ([OH⁻]). And for those conditions to be met and that equilibrium value to be reached, those concentrations each have to be 10⁻⁷M. That’s a pretty awkward # to work with – sure scientific notation helps (i.e. it’s nicer to work with 10⁻⁷ than 0.0000001) but it’d be nicer to avoid exponents too – so we bring in the negative log (base 10) to get the pH. If you take the negative log (base 10) of 10⁻⁷ you get 7. And this is where “neutral pH = 7” comes from 

When H⁺ can be grabbed up on their journeys by other molecules, the equilibrium gets disrupted, so water starts giving or taking to compensate. And it can get help from other molecules donating too. So the pH changes to get back to that [H⁺][OH⁻] = 1.0×10⁻¹⁴.

The proton grabbers are called BASES and the donators are called ACIDS. Water (H₂O) is secretly an acid & a base in disguise –  it can ionize into hydroxide ions (OH⁻) (base part) & H⁺ (acid part)

But in reality all acids are just bases waiting to be born and vice versa. Giving away protons is *always* acting as an acid and once something acts as an acid it has to act as a base and take a H⁺ before it can give it up again. So acid and base are 2 sides of the same coin (whose faces we call the conjugate acid & conjugate base), But some really prefer to do one or the other and the more they like to do one (take or give), the more they hate to do the other because it’s not the *process* of giving up or taking a proton they like, they’re just happier having or not having it. 

Stronger acids will add cookies when there aren’t many in the jar but weaker acids wait until the jars running low. How to measure?

pH is a measure of how full the cookie jar is – the pH of a solution depends on what molecules are inside and how greedy or generous they are. (Like how you might have a full cookie jar and then you invite over some cookie-loving friends and they take a bunch of them – or, conversely, you have a baker friend show up with a fresh batch for you).

So, pH is a property of the solution overall (which comes from contributions from all the molecules it’s made up of). If we want to know about contributions from different molecules, we can “work backwards” from the pH, which’ll help us factor in the “guilt factor” for the molecules, but we need a measure of their greediness.

For each molecule that has a donatable proton, we can assign a quantity called pKa which is like how low the cookie jar has to get before 1/2 of the copies of that molecule will add a cookie to it. The lower the pKa the stronger the acid. And the higher the pKa, the stronger the base (hungrier the cookie monster) – pH is measuring the acid-ness, but since base-ness is the opposite having a higher pKa is saying it’s a weaker acid so it prefers to act as a base. 

pKa is the pH @ which 1/2 of the acid molecules have given up a H⁺. It’s a measure of “how extreme” (i.e. basic/alkaline) conditions must be in order for an acid to give up its H⁺ 

  • at any pH above an acid’s pKa, any particular molecule of that acid is more likely to be deprotonated than protonated (cookie jar’s running low so cookie monsters donate or at least don’t steal)
  • at any pH below an acid’s pKa, any particular molecule of that acid is more likely to be protonated than deprotonated (cookies galore!)

The chances of cookie donation increase the further above pKa you are (e.g. 1% deprotonated @ 2 pH units below pKa & 99% deprotonated @ 2pH units above pKa 

Different acids have different “willingness thresholds” 

  • STRONGER acids are more generous & have LOWER pKas – even a slight deficit of H⁺ in their surroundings & they’ll give one up
  • WEAKER acids are “greedier” –  they have HIGHER pKas meaning they won’t give up an H⁺ until there’s a big deficit 

For example, say you have 3 acids: X w/pKa of 3, Y (pKa of 7), & Z (pKa of 9)

  • @ neutral pH (7), most of X will be deprotonated, 1/2 of Y will be deprotonated & almost none of Z will be deprotonated
  • But if we raise the pH (so there’s less free H⁺ available) even the stingy Z will give up its H⁺ 

⚠️ Don’t confuse pKa w/pH! pH is a measure of the *total* concentration of protons ([H⁺]) from *any* source. This includes:

  • water itself: H₂O ⇌ H⁺ + OH⁻
  • AND/OR acid(s)(HA) dissolved in it: HA ⇌ H⁺ + A⁻

⚠️ pKa & pH are different: pKa is a (constant) property of a *molecule* while pH is a (changeable) property of a *solution*

The two are different BUT directly related, as described by the HENDERSON—HASSELBALCH equation: pH = pKa + log[A-]/[HA], where HA is an acid and A- is that acid’s conjugate base. 

Since pH is a property of the solution, which depends on what molecules are inside and what their pKas are, if you change what molecules are in there you can change the pH. Add an acid and the pH will decrease – as it does, you get closer and closer to that acid’s pKa (and then surpass if) so the pH will change more slowly. And eventually will reach an equilibrium where it’s happy. the cookie donators (acids) are filling the cookie jar at the same rate as the cookie-takers (bases) are taking them. So the number of cookies stays constant (number of free protons doesn’t change so pH doesn’t change. 

But what if you add a base? (invite a greedy, cookie-less friend over)? – it takes protons so there are fewer there so that once-stable pH gets higher. And it’ll reach a new, higher equilibrium. 

What if that’s not what you want? You can use a buffer. A buffer is a solution with about the same number of givers and takers at the pH you’re aiming for (so the desired pH is near the pKa). So if you add a giver there are plenty of takers standing by and vice versa. Eventually it will get overwhelmed, so there’s a “buffering range” it’s useless outside of so you can’t add *too much* or pH *will* change. http://bit.ly/2X4Yhz7

We care about the pH because proton availability affects how molecules, including proteins, act. For example, one of the aminos (protein letters), Histidine (His, H) has a pKa near physiological (bodily) pH, so it can be present in deprotonated (and neutral) or prototonated (and positive) states in the proteins it’s part of and is sensitive to slight changes in pH. 

This can have huge biological importance. At how, at low pH, a His in the oxygen-carrying protein hemoglobin, gets protonated, which allows for charge-based attractions to form and stabilize the protein in a shape that favors oxygen dumping. Since increased levels of CO₂ lead to lower pH: 

CO₂ + H₂O  ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻

tissues rich in CO₂ and in need of oxygen are able to convince hemoglobin to release oxygen where it’s needed. This is called the Bohr effect, and you can learn a lot more about it here:  http://bit.ly/39p5RqW

note: the proton giving/taking is the Bronsted way of defining acids & bases. There’s also the Lewis definition, which is in terms of electron pair givers (Lewis bases) & takers (Lewis acids). And if you want to learn about that: http://bit.ly/nucleophilesandbases

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 http://bit.ly/2OllAB0

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