The bumbling biochemist received a call for help with CHEMICAL EQUATIONS and how to balance them – hopefully she can make some *cents* of it! If you put a dollar into a (no-fee) change-making machine and it gave you back 50 pennies you’d be mad, right?! It took half your money! Similarly, when chemists see chemical equations where the number of each type of atom on each side of the equation doesn’t match, they get mad. So, just like you might count the monetary value you put in & get out, chemists count the atoms, to see if alas, there isn’t conservation of mass.

One of the things I love thinking about is that the atoms inside of us were once inside dinosaurs. Atoms are kinda like the fundamental LEGO building blocks of everything. I talk a lot about biochemical “building blocks” like amino acids (protein “letters”) and nucleotides (DNA/RNA “letters”) – but really these are just “pre-packed” groupings up, smaller, more fundamental building blocks called atoms. Atoms themselves have smaller pieces (protons, neutrons, & electrons) but those pieces are “generic” and we define elements based on the number of protons.

Atoms can be grouped together in different ways but they *can’t* be made or destroyed or interconverted (we’re not gonna go into radioactive stuff here but that’s an exception where atoms can actually change elements because they change # of protons – but still conserve mass!)

Just like you can build a lot of different things from a set of LEGO pieces, and take them apart and remake them different ways, you can build a lot of different things from a set of molecules – or at least the molecules can make different things…

We can make conditions favorable for them to remake themselves in different ways, but we’re not really “at the wheel” – we “see” what goes in (reactants) and then put an arrow representing all that rearranging and then – voila- on the other side of the equal sign we “see” some products. We can add some further “flair” with little annotations telling you what “form” each thing is in (e.g. (g) for gaseous, (l) for liquid, (s) for solid, & (aq) for aqueous (dissolved in water)). 

TADA! A chemical equation – but is it balanced??? A lot of the time it isn’t… And to help explain what I mean, let’s bring back our change-making machine!

Say you have a dollar you put in a change-making machine. That dollar has 100 cents worth of value. We’ll call cents ¢ (don’t confuse this for C, which is the abbreviation for carbon). If you put that dollar into a penny-making machine, it would give you 100 pennies, each penny worth 1 cent, so you’d have 100¢. Coming from the US, I’m used to pennies, nickels, & dimes, but what if you’re not?

How do we know each penny is worth 1 cent? We look to the SUBSCRIPT (mini number) after the ¢. What do we see – nothing! If there’s no subscript it means a 1 is implied even though not spied. 

We *do* see a number IN FRONT of the ¢ – an “adult-size” one. “100” is the STOICHIOMETRIC COEFFICIENT – it tells us how many pennies we have. Similarly, if you see “2He” it tells you you have 2 “He’s” and each He has one helium atom. As a noble gas, helium likes to go it alone, so each of those He is its own molecule, you just have 2 of them.

But atoms of other elements like to group up, and when they do so by sharing electrons, they form strong covalent bonds and we call them molecules. Some molecules are made up of just 1 type of element – like H₂ (the “diatomic” (2-atom) form hydrogen likes to hang out as). Other molecules are made up of more than 1 type of element – like H₂O (water)

In our current currency analogy, we’re just dealing with the “single element” scenario, with our “element” being “the cent.” And our “money molecules” are just “groups of cents.” Each 1 dollar bill is 100 cents (¢₁₀₀). What about nickels (the coins not the metal!)? We can represent each nickel as ¢₅ (1 “group” worth 5 cents). Following this notation, dimes would be ¢₁₀ and quarters ¢₂₅

So going back to making change – say I want to buy a pencil that costs 25¢. I can’t just tear a dollar bill into 4 parts and hand it to the clerk – they’d think I was a jerk! So even though that dollar is worth 100 cents we don’t get to change how those cents are grouped. That dollar still has 4-quarter-giving potential, but converting them requires our change-making machine.

Similarly, the key thing about molecules is that they “come as a group” and “regrouping” them (like – like water splitting into H+ & OH-) requires changing chemical bonding which *we* the balancers, can’t do – instead the atoms in the molecules have to redistribute their electrons.

Sometimes the molecules really do go into “machines” for help – Biochemical reactions often use enzymes. These are usually proteins (sometimes RNA or a mix of the 2) & they act kinda like the machines. They help out but they’re not really adding or removing anything – they’re just facilitating – kinda like the funnel that helps you put coins in and keep them together in order to do their reacting. 

Just like different machines are optimized for different tasks (e.g. our penny-producer won’t give us nickels), enzymes are optimized to assist in sorting things the same way, but it’s really the molecules themselves that have the final say (kinda like how you can lead a horse to water but can’t make it drink you can hold reactants together but can’t force it to attack!)

They can choose to “regroup” in different ways. But the key is *they* get to choose. NOT YOU! And when you’re given a chemical equation you’re seeing the choice they made. So when you’re balancing chemical equations, if they’re together you don’t get to regroup them (no changing subscripts). You can only change how many groups of them there are. And you do this by changing the stoichiometric coefficient. 

It’s like how you can put more than one dollar into the penny-making machine but it will still just give you pennies (but more of them).

The coefficient says multiply everything in the molecule that’s in front of me by me. If I have 2 pennies (2¢), and we know that each penny has 1¢, I’d have 2 X 1 = 2¢. 3 pennies (3¢) would be 3 X 1 = 3, etc. 2 nickels (2¢₅) would be 2 x 5 = 10¢, 2 dimes (2¢₁₀) would be 2 X 10 = 20¢, and 2 quarters (2¢₂₅) would be 2 X 25 = 50¢. 

So if I put 1 dollar (¢₁₀₀) into a money-changing machine I should get 1 x 100 = 100¢ worth out. But depending on what machine I put it into, those ¢ will be grouped in different ways.

penny-making machine, I should get…

¢₁₀₀ -> 100¢

Nickel making machine? Each nickel has 5 cents-worth of value, so a nickel is like c5. So, 

¢₁₀₀ -> some number of ¢₅

We know that we’re going to have to multiply 5 by some coefficient to get to 100. To find out what we can divide -> 100/5 = 20, so you’ve put in 20 nickels-worth so you get 20 nickels

What if you put that dollar into a dime-making machine? Each dime has 10 cents-worth of value, so a dime is like ¢₁₀. 100/10 = 10, so 

¢₁₀₀ -> 10 some number of ¢₁₀

¢₁₀₀ -> 10¢₁₀

Finally, if you put that dollar into a quarter-making machine, you’d get

¢₁₀₀-> 4¢₂₅

Not too bad so far – you change the coefficient so that coefficient x subscript is the same on each side. But what if you put in a less nicely-dividable amount of money? What if you put in 2 $1 (2¢₁₀₀), 1 nickel (1¢₅) and 3 pennies (3¢)

2¢₁₀₀ + 1¢₅ + 3¢ -> ????

first off, let’s figure out how many cents we have in our input (“reactants”). We do this by multiplying the coefficient (big # in front of the letter) by the subscript (little number after the letter). And remember that if there isn’t 1 of these, you can assume it’s just a 1.


2¢₁₀₀: 2 x 100 = 200¢’s

¢₅ : 1(implied) x 5 = 5¢’s

3¢: 3 x 1 (implied) = 3¢’s

so total ¢’s in reactants = 200 + 5 + 3 = 253 ¢’s.

Now, there are lots of ways you can make change out of that, but our machines aren’t gonna give us choices. 

So if we put it in our penny-producer we’re gonna get pennies. And how many pennies are we going to get? How many pennies do you need to have 253 c’s? 253!

2¢₁₀₀ + ¢₅  + 3¢ -> 253¢

But what if we put it into our nickel-producer? Things start getting trickier… Because you can’t evenly split 253 into nickels (253/5 = 50.6) and our machine only gives & takes exact change. So if you want to use the machine you’ll have to put in some multiple of 5. Often when you’re trying to balance a chemical equation you’ll have some molecule like this that’ll serve as the kinda “most annoying” one – so you often want to start with start with things that appear in only 1 group on each side and/or are most complex (have the largest # of different types of atoms).

Pennies are really nice because they’re just 1 so if you can add as many as you want each time changing by 1 cent – But each time you add a nickel you’re adding 5 cents. So if I want to make quarters out of nickels I’ll need to have multiples of 5 nickels – unless I have cents coming from someplace else. Similarly, when you’re balancing equations, you want to save “freebies” like pennies for last. Start with the most complex groups and then use the smaller ones to “make up the difference”

Speaking of complex, in these cases we’ve only been dealing with 1 “element” – the cent (¢). But usually in chemical equations you’re dealing with multiple elements. So let’s complicate things a bit. What if the machine also takes & sorts euros? It can’t “currency exchange” in the traditional “better check the dollar-euro exchange rate) – in our machine, there’s no way to go back & forth between money & tokens – they’re 2 different things just like carbon and hydrogen are 2 different things. 

What it *can* change is how it groups them – but the machine – NOT YOU – chooses the grouping. And what you’re given is the results of its choice. Then it’s up to you to balance it. It’s a lot easier to tell if something is balanced (count atoms now that we’ve seen how to do that) than it is to figure out how to make it balanced if it isn’t. 

If you put in 2 pennies grouped together and a euro it could (depending on the machine) give you a euro grouped to a penny and a free penny, or all of them grouped together, or all of them separate but you’re still gonna end up with 2 cents and 1 euro on each side. And since that euro only appears once on each side it can be a good place to start trying to balance things. Because the coefficient affects everything in the molecule it’s in front of. So if you put a 2 in front of your euro+penny group you’re gonna get 2 euros & 2 pennies (and that other penny). 

Similarly, , in H₂O you have 2 H & 1 O. Put a 2 in front of the whole thing (2 H₂O) and now you have 2 of those “2H & 1O” -> 2 x 2 = 4, so you now have 4H. And 2X1 = 2, so you now have 2O. Put a 3 in front and’s you’d have 3X2=6 H & 3X1 = 3 O, etc. The key thing to remember is that the coefficient changes everything you see until you see a + or an = or nothing (end of equation)

As we saw above, we get a lot more from double a quarter than a penny. Similarly, we get more oxygen atoms when we double diatomic oxygen (O₂) than we do when we double water (H₂O). But when we double water we also double hydrogens and they already each had 2. So when it comes to balancing equations, there’s a lot of trial, error, & playing around, even for the “pros”. You can find a lot of great practice sets and videos online. Sorry I’m not very helpful in this regard… But hopefully some of this is at least useful

It’s NOT always simple but what *should* be “simplified” is the final version – you shouldn’t be able to evenly divide everything by the same coefficient (unless it’s a 1 because anything divided by 1 is itself). Kinda like how the change-machine would say it gives you 100 pennies for every dollar. If you put in 2 dollars, it will give you 200 pennies, but it doesn’t say that. 

you’d write ¢₁₀₀ -> 100¢ NOT 2¢₁₀₀ -> 200¢ because both sides can get evenly divided by 2.

And speaking of simplifying, often what you see is the overall reaction equation – the initial initial reactants and the final final products. But a lot of the time, especially with biochemical reactions, things happen in steps where you generate intermediate products that get used as reactants in the next step and “disappear” from the equation. 

Like if instead of going straight from dollars to pennies it’s like you go from dollars to quarters to nickels to pennies. 

you see 

¢₁₀₀ -> 100¢


¢₁₀₀ -> 4¢₂₅

4¢₂₅ -> 20¢₅

20¢₅ -> 100¢

A note on CHEMICAL EQUATIONS vs. BIOCHEMICAL EQUATIONS. With chemical equations, you worry about balancing everything including charge. and so you have to write out all the charged (ionic) things – like magnesium (Mg2+) which hangs out with the negatively-charged ATP in your cells. But when we write biochemical equations, we just write “ATP” to represent the “sum of species” – free ATP, ATP complexed to Mg², etc. 

And same often goes for hydrogens. Because, as we saw with our acid/base talk, they like to come & go & you have an equilibrium of protonated & deprotonated forms. And this is the case with ATP – depending on how protonated it is you have ATP⁴⁻, HATP³⁻, H₂ATP²⁻, MgHATP⁻, & Mg²⁺ATP. 

So biochemical equations don’t always balance charge, H, or Mg, but they should balance all the other stuff. 

In the pictures, let’s look at a real-world example – one involving fireworks! (more on how fireworks work: )

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 

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