Question

How would you prepare a 0.1M solution of HCl starting with a 1.0M solution? Assume you want to prepare 100 ml of solution.

Answer 1

When diluting solutions, the idea is to take a small amount of the concentratied solution, and add water until its volume is what you need, thereby decreasing the concentration. Mathematically, this looks like:
\[M_1*V_1 = M_2*V_2\] where M1 and V1 are the concentration and volume of the concentrated solution, and M2 and V2 are the concentration and volume of the finished, dilute solution.
In order to make 100mL of 0.1M solution from 1.0M HCl, you have to take the concentrated stuff and dilute it by a factor of 10 (make it 10x weaker). the quickest way to do that is to multiply its volume by 10. Since you have to end up with 100mL of solution, what is 1/10 of 100mL?

It's 10mL.

10mL of concentrated HCl, when diluted up to 100mL, will give you an HCl soolution with a concentration of 0.1M. Watch the math:
\[M_1*V_1 = M_2*V_2\]\[1.0M * V_1 = 0.1M* 0.100L\]\[V_1 = \frac{0.1M*0.100L}{1.0M} = 0.010L = 10mL\]