okay so let's go through a problem regarding balancing
equations, so here are four equations that we're
going to need to balance if you'll notice they are not currently balanced
and so this is pretty straightforward there's nothing much more to say if you
need any help with this concept and some strategies that you can use in order to
do this check out my tutorial on balancing equations otherwise when
you're ready go ahead and give these a try.
so let's start with this first one
we have CaCl2 plus Na3PO4 yields Ca3(PO4)2 plus NaCl so if you
have trouble with these and you want to be very very thorough in your approach
the best ways to make a table like this where we've listed every element that is
involved in the reaction and then we can tally the number of atoms of each
element on the left side and on the right side. so let's go ahead and do that
now, we have got one calcium atom on the left and three calcium atoms on the
right. for chlorine we have two on the left because we have Cl2 and on the
right we have just one in NaCl. for sodium we have 3 on the left and we have
one on the right. for phosphorus we have one on the left and then we have two on
the right, don't forget that with PO4 in parenthesis then we have the two outside
of the parenthesis that means there are two phosphate polyatomic ions so it's
PO4 twice that means we have PO4 and another PO4 so that's two phosphorus
atoms. and then four oxygens, same thing on the left we have four on the right we
actually have eight because we have O4
but PO4 is twice so we have O4 and another O4 that's 8, that's 8 oxygen
atoms so that's the number of atoms of each element that we have on
each side and now all of those need to be balanced. so where shall we start
let's just go ahead and start with calcium. so all we need is a coefficient
to the left of some substance to balance the number of atoms of that particular
element to get the same number on each side. so for calcium we have one on the
left and three on the right, so the easiest thing to do will be to put a
three right here. so now we have CaCl2 but that coefficient of three means we
have three of those so we have CaCl2, CaCl2 and another of CaCl2.
so that means we have one calcium for each of those so we have three calcium
atoms total. so let's change our tally for calcium on the left side to three so
calcium is now balanced, we have three on the left and three on the right so
that's done but what we must realize is that we also have made it so that there
are six chlorine atoms on the left, because we have Cl2 but we have three
of those so two chlorine atoms per formula unit times three of those means
there are six chlorine atoms on the left now. so what shall we do next? so we'll
come back to chlorine but what we want to understand is that there's a simpler
way to do this than to do phosphorus and oxygen separately because phosphorus and
oxygen are involved in the phosphate ion. it's a polyatomic ion and those are not
going to get split up they remain together so we can actually balance the
entire phosphate ion at the same time so we take a look at the left we have a PO4
and then on the right we have (PO4)2 so we can treat that as though it's an
individual thing we can just try to get the same number of phosphate ions on
both sides so as we said we have two phosphate ions on the right so if we put
a two here that means we are gonna have two phosphate ions on the left and now
look at what we've done we have made it so that there are two phosphorus atoms
on the left and eight oxygen atoms on the left because we have Na3PO4
we have two of those so all of those are multiplied by two and now
both phosphorus and oxygen are balanced. however we have also altered the number
of sodium atoms on the left side because we have Na3 and we have multiplied that
by 2 so we need to change the number of sodium atoms on the left side to 6 so
what should we do next well as it turns out we can go ahead and take care of
both chlorine and sodium at the same time because on the right we have NaCl
it looks like we need to put a 6 here because we have six sodiums on the left
and six chlorines on the left and only one of each on the right so if we put a
six there we are going to change the number of sodium and chlorine atoms on
the right both to six and so that is going to balance both of those elements
and that will actually completely balance the equation so those are the
coefficients in the balanced equation for this reaction. okay let's look at the
next one we have a combustion reaction we have C2H6O plus O2 yields CO2 plus
H2O, so let's make our table. it's a little bit smaller all we have is carbon
hydrogen and oxygen so let's make our initial tally for carbon. we have two
carbon atoms on the left and one carbon atom on the right. for hydrogen we have
six atoms on the left and we have two on the right. and for oxygen we have three
on the left because we have one oxygen atom in C2H6O and we have an O2 molecule
and then on the right we have also three because we have O2 in the CO2 and we
have one oxygen atom in water so that is our initial tally. so where should we
start, well here is one handy tip anytime you have some element that is by itself
in a particular species you want to do that one last because you have the most
freedom with that one you can get everything else balanced and
then you can just put whatever coefficient you want for that element to
make it work without affecting the numbers for any other element. so we are
gonna do oxygen last also because currently it is balanced so we're gonna
have to mess with the other two elements first but in general if you see O2 or N2 or
H2 you can feel free to do that one last. so why don't we start with carbon, we
have two on the left and one on the right so what we need to do is put a 2
next to CO2 so that we have two carbon atoms on the right so now carbon is
balanced. however we have also changed the number of oxygen atoms on the right
we have four from CO2 because we have two CO2
so there's a CO2 and another CO2 each of those has two oxygen atoms so that's
four oxygen atoms from CO2 plus the one from water and that gives us five oxygen
atoms on the right. now let's balance hydrogen we have six on the left and we
have two on the right so we need to put a three next to water because that is
going to give us three water molecules each of which has two hydrogen atoms
that gives us a total of six hydrogen atoms on the right and that will balance
hydrogen, however we have also again changed the number of oxygen atoms
because we now have four from CO2 plus three from water because we have three
waters for a total of seven oxygen atoms on the right so lastly we can balance
oxygen now we have seven on the right and on the left we have one from C2H6O
and we're probably not going to want to mess with that because that will alter
the number of carbons and hydrogens and so what we want to do is manipulate O2.
so if we need to get seven on the left and one of them is in C2H6O that leaves
a total of six that we need from O2. now luckily that's going to be very
easy to do because all we have to do is put a 3 here and now we have 3O2
molecules so an O2 + O2 and another O2 and that adds up to six oxygen atoms so
the six oxygens from oO plus the other one gives us 7 on the left and now
oxygen is balanced and the equation is balanced in general. let's move on to our
third example we have CO + H2 yields C8H18 + H2O. so let's make our table
again once again we just have C, H and O so let's make our tally. carbon we've got
one carbon atom on the left and we have eight carbon atoms on the right from C8.
for hydrogen we have just 2 on the left and on the right we have 20 because we
have H18 and we have each 2 from water so 18 plus 2 is 20. and then for oxygen
we have just the one from CO and the one from H2O. so once again remember that
last trick that we learned if we have one element that's by itself we want to
do that one last and in this case that's hydrogen so we want to save hydrogen for
last. now oxygen happens to be balanced at the
moment so let's start with carbon. for carbon we've got eight carbon atoms on
the right and we have just one on the left so we're gonna need to put an eight
here so that we have eight CO molecules and therefore eight carbon atoms on the
left. and now carbon is balanced, however we have also altered the number of
oxygen atoms on the left side. we now have eight of those so now let's go
ahead and balance oxygen. since we have disrupted that balance we have eight on
the left and we have one on the right so let's put an eight here and now we have
eight oxygen atoms on both sides and oxygen is balanced now let's do hydrogen
on the right side we have 18 from C8H18 and we have 16 from water because we
have two hydrogen atoms in each water molecule times eight water molecules and
18 plus 16 is 34 so we have 34 on the right side but this is the easy part
because on the left we have H2 by itself so all we have to do is put a
coefficient next to H2 that will make this balanced and it won't affect any
other element. so 34 divided by 2 is 17, that means we need 17 H2 molecules. that
will give us 34 hydrogen atoms on the left and hydrogen is now balanced and
the equation is balanced okay one more NH4NO3 yields N2 + O2 + H2O. once
again we make our table this time it has N H and O, for nitrogen we have 2 on the
left and two on the right, for hydrogen we have 4 on the left and two on the
right, and for oxygen we have 3 on the left and 3 on the right. so it seems that
everything is balanced except hydrogen so let's go ahead and work with that
first. we have 4 on the left and two on the right so we need to put a 2 next to
water because two water molecules will yield 4 hydrogen atoms so now we have 4
on the right and hydrogen is balanced however we have changed the number of
oxygen atoms on the right, we have 2 from O2 and now we have 2 from water, one per
water molecule and 2 water molecules so now we have 4 oxygen atoms on the right
so let's go ahead and balance oxygen now here's where it gets a little bit
trickier because we have 4 on the right and we have 3 on the left so there's
nothing we can immediately do to balance it but we know that we have more oxygen
on the right than we do on the left and we only have one thing on the left that
we can work with so let's just go ahead and put a 2 here because we need more
on the left but this is the best we can do so let's just put a two here and that
will give us six oxygen atoms on the left so now we have something to work
with on the right, we can we can do some things to balance oxygen a little bit
later but we needed to do that to get more oxygen on the left. however we have
now changed some other things we now have eight hydrogen atoms on the left
so unfortunately hydrogen is no longer balanced. we also have four nitrogen
atoms on the left now because each of those has two nitrogen atoms and now we
have two of them so we have four nitrogen atoms on the left so now let's
start balancing again. let's go to oxygen one more time we have six on the left
and we have four on the right so what is one way that we could get two more
oxygen atoms? well we have oxygen in water so to get two more oxygens we
could just have two more waters so let's change this to four waters and that
gives us six oxygen atoms on the right so oxygen is balanced. it also gives us
eight hydrogen atoms on the right which means that hydrogen is also balanced so
that was a good step. lastly we just need to do nitrogen, luckily nitrogen is by
itself on the right side so to get four nitrogen atoms on the right side we just
put a two here so that we have 2N2 that gives us four nitrogens on the right so
now nitrogen is balanced and the equation is balanced.