You're going to see a lot of formulas in
Chemistry,
several of which you will be required to
memorize but instead of having to
memorize all of the different formulas of each
formula solved for each variable your
life, will be so much easier if you
understand how to rearrange one formula
into multiple formulas
all solved for different variables and
note a variable is a symbol or
letter that represents a value. To
understand how to rearrange a formula we
need to review these algebra rules.
When you are trying to move the variable
to the opposite side of the formula
you must do the opposite operation and
do this for both sides of the formula.
I know this may feel really basic but
please stay with me, don't skip this part
because we'll be going over more
complicated formulas that most students
get wrong because they didn't review these
rules.
Alright, so say we wanted to solve for
x for both of these questions. We look at
what isn't allowing x to be by itself which is the y and
since y is being added
we must do the opposite operation which
is subtraction. We must subtract y from both sides to
get x, same concept for this next question. Y is
now being subtracted
so we will do the opposite operation and
add both sides by y, this is what our x equals. We can see
this again for multiplication and
division. Let's solve for x for each
question. x and y are being multiplied so in order
to get x by itself we will do the
opposite operation and divide
by y to both sides this is what x now
equals.
Apply this concept again, x and y are
being divided.
In order for x to be by itself we
perform the
opposite operation and multiply both
sides by y
and this is our answer. This next trick
works for when you have two fractions
that are set equal to each other.
If you don't want to deal with the
fractions then you can multiply
diagonally.
So multiply the a and the d then set
this equal to b
times c. Note since this is being
multiplied the order does not matter.
We could have written this as da and cb.
Moving on to roots and powers, to get rid
of a power
simply raise both sides by the same root.
For example, to solve for x and remove
this power of 2,
we will take the square root of both
sides. The square root and power of 2 now
cancel out to get this
as our answer for x. If we wanted to get
rid of a root
we would raise it to the same power so
to get rid of a square root
we need to square both sides, the square
root is now gone
and this is our answer for x. We can see
this again
with other powers and roots that are not
two again, to get rid of a power simply
take the root of both sides
and the root would be the same number as
the power.
This is the opposite for when we want to
get rid of a root
simply raise both sides by the same
power of the root.
On to the examples, this is a formula
you'll see in thermochemistry.
We're asked to solve for q since we want
q to be by itself, we need to move the w to
the opposite side by subtracting w
from both sides, the w's now cancel out
and we can flip this around to show q
is equal to this. The most common
mistakes I've seen students make is with
the gas law formulas.
Here's the ideal gas law, let's solve for
n.
Start with asking what isn't allowing n
to be by itself.
The R and the T, and since everything is
being multiplied we need to perform the
opposite operation and divide
both the R and T together to both sides,
this now cancels and I'll flip this
around to get this as our answer.
Here's another gas law, let's solve for
V1.
V1 is here and what's not allowing it to
be by itself is its denominator of T1.
So we will perform the opposite
operation and multiply both sides by
T1, the T1s now cancel and looking at the
right side we can combine this.
Remember that there's actually a 1 here
as our denominator
and we can multiply straight across to
get this as our V1.
Using the same gas law, let's now solve
for T1. Since these are two fractions set
equal to each other we can use our trick
and multiply diagonally to get rid of
the fractions.
When we do this we get V1 times T2
and V2 times T1. Again order doesn't
matter we could have said this was
T2 times V1 and T1 times V2
and so on. Next we can divide both sides
by V2 to get T1
by itself,  I'll flip this around to get
this as our answer.
Rearranging the combined gas law tends
to confuse a lot of students and let's
practice this and solve for T2.
We again have two fractions set equal to
each other
so we can use our trick and multiply
diagonally to get rid of the fractions.
We'll multiply P1 V1 times T2
to get all these variables together on
one side,
set this equal to P2 V2 times T1
on the other side. Again order doesn't
matter here since we are multiplying.
We are solving for T2 so we need to get
rid of anything that is not allowing
T2 to be by itself we will divide P1 and
V1 at the same time to both sides
these cancel and this is our answer for
T2.
Ready for a challenge? Let's use the
formula from Bohr's model and solve for
n initial. Since n initial is in
parentheses
we must get rid of everything outside of
the parentheses
first, so since this number is being
multiplied
we will perform the opposite operation
of division and divide
this number to both sides and cancel
this out. Now that there is nothing left
outside of the parentheses we can drop
the parentheses.
This fraction that is being subtracted
isn't allowing
n initial to be by itself so we will
perform the opposite operation and add
both sides by this fraction.
Unfortunately we can't use our trick and
multiply diagonally since that trick
only works
when there is only one fraction on each
side of the equal sign.
Instead we will multiply both sides by n
initial.
There is no need to distribute since the
goal is to isolate
n initial, instead we can divide both
sides by
everything in parentheses since these
two are being multiplied.
Almost done, we need to get rid of this
squared by taking the square root of
both sides, this is our answer. Okay I'll admit that
one was just crazy!
It will be a lot easier when you are
given the values
of the variables and only asked to find
one variable but it still is really important to know
how to properly move values and variables around so
click the link in the description and
practice this by
completing all the practice problems
then move on to the next video in this
playlist.
