Dilution Calculations help.?

Question

Can someone tell me where I am going wrong with these problems? I need it step by step please. Also, I asked this somewhere else, but both the answers that I got were wrong, so if your not sure, please don't answer. Thank you!

A concentrated HCl solution is 12.0 M. You have to make 300 ml of 0.600 M solution. How would you prepare it?

I worked it this way, which is the way the book tells us, but obviously get the wrong answer every time.
12.0 M x V1= 0.600 M x .300 L/ 12.0 M=

A concentrated solution of 15% w/v KOH solution is available. How would you prepare 20.0 ml of a 0.10% w/v KOH solution.

I worked this one (%1)V1=(%2)V2, by saying
(15%)V1=(.10%)(.200L)/ 15%
again the answer I get is wrong.
Can someone explain to me what I am doing wrong with these problems? Thanks so much!

Answer 1

I think you are leaving out the first step.

Remember that 12.0 M means 12 moles of HCL per liter of aqueous solution.

To understand the equations so that you can use them correctly, first think that you will have to add some amount of water to some amount of the concentrated solution to make it the dilute solution.

so, 12 mol/liter , assuming you had a liter of the solution, you keep the same number of moles and add water

how much water do you add to get to the weak, .6 mol/liter concentration

12 mol/ (1+x) liters = .6 mol/liter

12/(1+x)=.6
12=.6(1+x)=.6+.6x
11.4=.6x
19 = x

so if you had a liter of the solution at 12 M, you would have to add 19 liters of water and then you would have 20 liters of solution at the diluted .6 M

but you don't need that much of the final solution, so you use the same ratio of water addition, but only start with enough concentrated to end with 300 ml

the ratio is 19 to 1

so 1/20 * 300 = 15 you need 15 ml of the conc. solution
19/20 * 300 = 285 you add 285 ml of water

the total is 300 ml of the .6 M solution

now look back at the equations and you will see where they came from and how to apply them properly

Answer 2

m1*v1=m2*v2
is practically all you need to know in chemistry. I'm kidding. But it's is very helpful.
You are doing m1*v1=m2*v2/m1. See the difference? You're dividing by m1 too many times.
Try it without the second m1. I got the same answer the guy above me got, so I think you'll find it works much better. It should work for both equations-although in the second one you also have 20 ml as .2 L when it is actually .02L. That's gonna make a difference. (I got 1.3x10^-4L or .1333 ml, which seems reasonable. It's a big dilution.)
That's what you're doing wrong! Simple enough to fix, really.
Write me if you have problems.

Answer 3

C1V1=C2V2

other than that i'd go with the first answer.