How many milliliters of concentrated HCl 12.1 M should be diluted to prepare 200.0 ml of an acid solution with a pH of 1.50?

Question

 This was an example for a exam review, not sure how to solve. A list of steps would be greatly appreciated, so I actually know how to solve it myself and can apply it to other examples like this.

Answer 1

In this problem, they give you a solution expressed in molarity, i.e. 12.1 M and ask you to prepare a new solution, but this is expressed in pH, i.e. 1.50.  When you see something like this, you want to change the pH of 1.50 to molarity.  We know that pH = -log [H⁺] and since HCl is a strong acid, this is the same as the [HCl].  For pH = 1.50, [H⁺] = [HC] = 1x10^-1.50.

Expressed in a more familiar manner, [HC] = 3.16x10^-2 M.  The problem now reads, "how many mls of 12.1 M HCl should be diluted to prepare 200 mls of HCl with a concentration of 3.16x10-2 M (0.0316 M)?  Now, you can simply use V1M1 = V2M2 as follows:

(x ml)(12.1 M) = (200 mls)(0.0316 M)

x = 0.522 mls