– Alright so concentrations
and volumes of two solutions. And so in this section what
they mean by two solutions is a solution before
dilution and a solution after dilution so you're taking the sum solution, like
100 mL of a let's say 10% sodium chloride solution. And you're going to dilute it. So let's talk about
what this means this 10% sodium chloride solution. Can I figure out how much of
that 100 mL is sodium chloride? Well 10%, how do we find 10% of 100? Well there's a few ways
that you can do it. You can just, if you know
what percent is you can just straight up use this idea of percent. 10 per, 10% equals 10
per 100 so to find 10% of 100 mL you would take
10% of means to multiply 100 mL * 10% = 100 mL
* 10/00 and we reduce that fraction right the 100s cancel and we end up with 10 mL. So all the 100 mL, just
10 mL of that solution is sodium chloride.
Okay so what happens if we dilute it? So say I do a one to two dilution on that. So you can go through the
calculations of this right, that means I have one part sodium chloride of my sodium chloride, 100 mL
of sodium chloride solution to two parts total volume. So that means I'm going
to add one part of my 10% sodium chloride solution. And let's say we're using
water, and one part water. Alright so if I have 100
mL of sodium chloride and I want to use all of it, of my 10% sodium chloride solution,
I would add another 100 mL of water, right? So one part to one part
means I add the same amount.
So I'm going to add
another 100 mL of water, and this is going somewhere I promise. So if I add another 100
mL of water I now have 10, did the amount of sodium chloride that I've got in there change? No it stays the same, I'm diluting it, I'm increasing the total volume. So now I've got 10 mL in two,
or 10 mL of sodium chloride in 200 mL of water which
means I now have a 5%, how did I figure that out? 10 divided by 200, I guess
I should write that down. So now I have a 5% concentration. And I have 200 mL of that
5% sodium chloride solution. So and if we check it
out, if we take the 5% and multiply by the 200 we
still get back to the 10. So what we're going to
exploit in this section is that the amount of the
substance that we're talking about, the pure substance
in there doesn't change. The percent changes, the volume changes. As the volume changes what
happens to the percent? Our substance gets diluted further and our percentage goes down.
Because remember the
percent is parts per 100. Percent represents part of a whole or what fraction of a whole. So this is the idea
that we're going to use in this section. So if I take, if I look at after diluting and I take the amount,
the volume which we're going to call V2, V for volume and 2 for the second amount, and
I take the percent, 5%, and I multiply them together,
I should get the same as if I took what I started with, the concentration 10% and
multiply by the original volume that I had, 100 mL.
So we're going to use
this formula where the V1 is the original volume
that I started with, the C for concentration,
the 1 for beginning right, the first concentration
that you had and we multiply those together that should equal, that gives us the amount right? That gives us the 10 mL that
gives us the amount we have. It's still the same
even though we dilute it we're not changing the pure amount of the substance we had,
it should be equal to if I take the volume after
I dilute and multiply by that smaller percentage
after I dilute it. So we're going to use this formula, you can memorize it or
you can just remember this idea that regardless
of whether I dilute it, no matter how much I dilute
the amount that 10 mL is going to stay the same. And we're going to use this
equality of this equation to solve a few different
problems in this section..
