How many mL of 10 % NaOH do I need to make 100 mL of 1 %
NaOH?
V1 X C1 = V2 X C2
V1 X 10 % NaOH = (100 mL)(1 % NaOH)
V1 = (100 mL) (1%)/ (10%)
V1 = 10 mL
His answer is correct, but his equation is wrong because I followed his example below.
V1 = 100 x 2% x 10% = 0.2 ????????????
Or 100 x 2 x 10 = 2000
Placing numerics in brackets in linear proximity indicates multiplication should take place, placing a times sign means "of" Or when there is a
percentage one multiplies as a percntage. So His bracketed example above is incorrect and because of that I fail to understand the equation.
Therefore his explanation is infuriating. If you know what he means then it is obvious to you, but for people learning like myself it is so
infuriating that inadequate explanation is given.kavu - 18-7-2012 at 02:37
Go through some basic arithmetics.
c1 V1 = c2 V2 | : c1
V1 = (c2 V2)/c1
with rational expressions (ab)/c is also equal to a(b/c) and b(a/c) and if you will ab(1/c) too. This means that the above can be rearranged in the
following form:
V1 = V2*(c2/c1)
This form is used in your example. This c1V1 business is just a way of presenting inversely proportional quantities as an equation. If the final
volume is 2 times the initial volume, concentration will be 1/2. If it's 3 times, 1/3 and so forth.
[Edited on 18-7-2012 by kavu]CHRIS25 - 18-7-2012 at 03:17
Hi Kavu, what you kindly wrote: V1 = (c2 V2)/c1 is the correct way to write it. His is simply misleading. What you wrote I fully understand, I
spent 15 minutes on his stupid equation I spent 1.5 seconds on yours. Efficient Learning comes by efficient explanation and example. That is why it
infuriates me. Maths is not my profession, it is my weakest subject that I have not touched for 30 years. But I have taken up the challenge to
master some things instead of relying upon computers and other people.
Even your example here: with rational expressions (ab)/c is also equal to a(b/c) and b(a/c) and if you will ab(1/c) too. Just throws me into
despair, It is not something I can "see" or work out.
Having said all that your whole explanation actually helps me because you have treated it thoroughly, not in disconnected bites, I have not seen this
formula treated as you have just explained in any book, and believe me I have sat in the library on a number of occasions. Thankyou.kavu - 18-7-2012 at 03:51
I'll try to show the fractions presented.
(ab)/c
well multiplication ab is equal to a + a + ... + a b times, right? Let's substitute that in
(ab)/c = (a + a + ... + a)/c
Now we can divide each a in upstairs by denominator c to get
(ab)/c = a/c + a/c + ... + a/c (b times)
we know that a/c + a/c + ... + a/c added b times is the same as multiplication of a/c by b, so:
(ab)/c = a/c + a/c + ... + a/c = b(a/c)
Using similar reasoning we can also get to the result a(b/c). If we just start with b + b + ... + b a times
It's not very useful having to prove these relation every time they are used, so here's a visual way of memorizing this stuff:
If your upstairs is a multiplication, you can slide a member of that multiplication down in front of the ratio left behind:
Code:
AB B
---- = A ---
C C
Code:
AB A
---- = B ---
C C
You can slip both A and B in front of the expression as well! We just have to remember that any number times one equals itself. So AB = 1AB
Code:
AB 1*AB 1*B 1
---- = ------ = A ----- = AB ---
C C C C
So division by C is nothing but multiplication by 1/C
BUT, this does NOT apply to additions!
Code:
A+B B A B
----- IS NOT A + --- BUT IS --- + ---
C C C C
(Note for all those who are really into math: I have excluded some definitions from this example to make it more clear and understandable)
[Edited on 18-7-2012 by kavu]CHRIS25 - 18-7-2012 at 04:18
ok, it clicks now. Thankyou, guess I was working in brain overload for the last two days. But your codes really helped, thankyou.
