Balancing Complex Chemical Equations

Last week I posted on the three methods to balance chemical equations. My quick google search seems to point towards Method 1 (by inspection or trial-error-method) and Method 2 (writing down atom counts) being the most popular methods when it comes to balancing equations. Most of the students I have worked with only knew Method 1 from their high school science/chemistry class. There’s nothing wrong with that, but I think it gets a little daunting when it comes to having to keep track of multiple numbers of atoms (like 5 or more) and it will prolong the process unnecessarily. I mean, who wants to spend 30 minutes trying to balance ONE equation??? Seriously, that 30 minutes is probably better-spent doing other things like watching YouTube, checking out latest posts in FB, Instagram, Twitter, uploading pictures to Snapchat, level up in that favorite game of yours or doing other things that will increase your happiness.

So, imagine if you have a real complex equation like this: K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 →  Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + K2SO4 + KNO3

which has 8 types of atoms in the equation: K, Fe, S, C, N, Cr, O and H. How long do you think it will take to balance it?

I tried balancing it using Method 1. I started with K since it’s the first atom I encounter from the left. Looks like I have 6 K altogether. Ok…what about on the right? Looks like a total 3 K on the right. First question, how should I balance K? I know I’ll need to “double” the K counts on the right, but which term should I start with – K2SO4 or KNO3? Not sure. Never mind…leave K alone for now. Let’s move on to Fe, it seems easier. I have 1 on the left and 2 on the right. Great! I can do this….add a “2” on the left, in front of K4[Fe(SCN)6], so now I have:

2 K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 →  Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + K2SO4 + KNO3.

Fe is balanced, for now. 7 more atoms to go…

S looks tough since I see it in multiple terms on both sides. Save it for later. Move on to C. I have 12 on the left. There’s only 1 on the right. That means I’ll place a “12” in front of CO2.

2 K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 →  Fe2(SO4)3 + Cr2(SO4)312 CO2 + H2O + K2SO4 + KNO3

Awesome, 2 down, 6 more to go…

My next atom will be N. Piece of cake, kinda like C – 12 on the left and 1 on the right. So, add “12” in front of KNO3.

2 K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 →  Fe2(SO4)3 + Cr2(SO4)312 CO2 + H2O + K2SO4 + 12 KNO3

Gaining momentum and confidence… 3 down, 5 more to go.

H will be next. 2 on the left, 2 on the right. Well, look at that! It’s already balanced! Moving on to Cr. There’s 2 on the left and 2 on the right. Well, how about that?? Is it my lucky day or what?

So far I have balanced Fe, C, N, H and Cr. That only took 1 minute so far. What’s 3 more atoms (K, S and O), right? WRONG!!! Those 3 that are left are tough and that’s because they appear in multiple terms all over the place. I mean look at K, on the left, it appears in K4[Fe(SCN)6] and K2Cr2O7, and on the right, I see it in K2SO4 and KNO3. That’s considered the easier atom among the three. Look at O. On the left, it’s in K2Cr2O7 and H2SO4. On the right, it’s in Fe2(SO4)3, Cr2(SO4)3, CO2, H2O, K2SOand  KNO3. By the way, that’s EVERY single term on the right! I don’t know bout you, but I know I have better use of my time than to play trial and error with these 3 atoms.

It’s not going to be much better if I use Method 2 either. I mean, it will help in terms of keeping track on the number of atoms, but I’ll still need to do perform trial and error with the three atoms.

So, I moved on to Method 3. Took me 3 minutes to set up the algebraic equations and few more minutes to solve them all. So, what do you think is the final answer? Here it is:

 6 K4[Fe(SCN)6] + 97 K2Cr2O7 + 355 H2SO4 →  3 Fe2(SO4)3 + 97 Cr2(SO4)336 CO2 + 355 H2O + 91 K2SO4 + 36 KNO3

Here’s the video walking through the 4 steps in solving this complex equation:

11 thoughts on “Balancing Complex Chemical Equations”

  1. This (via ChatGPT)?

    We can balance it step by step:

    Balance the polyatomic ions first:
    K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 → Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + K2SO4 + KNO3

    Balance the transition metals:
    K4[Fe(SCN)6] + K2Cr2O7 + H2SO4 → 3Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + K2SO4 + KNO3

    Balance the sulfur (S) atoms:
    K4[Fe(SCN)6] + K2Cr2O7 + 3H2SO4 → 3Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + K2SO4 + KNO3

    Balance the potassium (K) atoms:
    4K4[Fe(SCN)6] + K2Cr2O7 + 3H2SO4 → 3Fe2(SO4)3 + Cr2(SO4)3 + CO2 + H2O + 4K2SO4 + KNO3

    Balance the oxygen (O) atoms:
    4K4[Fe(SCN)6] + K2Cr2O7 + 3H2SO4 → 3Fe2(SO4)3 + 2Cr2(SO4)3 + CO2 + 7H2O + 4K2SO4 + KNO3

    Now, the equation is balanced with the following coefficients:

    4K4[Fe(SCN)6] + K2Cr2O7 + 3H2SO4 → 3Fe2(SO4)3 + 2Cr2(SO4)3 + CO2 + 7H2O + 4K2SO4 + KNO3

  2. So I’m a stubborn motherfucker and refused to look at your method until I’d found the solution on my own…
    After 45 minutes I started throwing variables in because recalculating from real numbers over and over sucked. I did get the answer on my own eventually – by reinventing your method. It really is most efficient, especially for equations like this one that have 3 digit numbers and primes. Thanks for the challenging problem!

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