Prepare a 0.0200 mM dye solution at low pH by dilution 0.40 ml of the stock 0.100 mM chemical X into the appropriate volume of 2.5 M HCl.

What is the amount of HCL required for dilution, the final concentration of HCl in the solution, and the pH?

I know there's the MV = MV, but I'm not sure how to begin to solve this. The 2.5 M HCl throws me off since there's two concentrations now (2.5 and the .02)

The 2.5 M HCl is the diluting agent and has nothing to do with the calculation for the dye. (Another way of saying it is that the 2.5 M HCl is just water as far as the dye dilution is concerned.). My MV = MV gets 2 mL.

The HCl is 2.5 x (1.6/2.0) = ?? if we assume the volumes are additive.

How were you able to get the 1.6?

To solve this problem, we can use the concept of dilution. The equation you mentioned, MV = MV (Molarity x Volume = Molarity x Volume), is the principle behind dilution calculations. Here's how we can apply it to find the amount of HCl required for dilution, the final concentration of HCl, and the pH:

1. Firstly, let's determine the amount of HCl needed for the dilution. We are starting with 0.40 mL of a 0.100 mM solution and we want to prepare a 0.0200 mM solution. Since the concentration is being decreased, we can set up the dilution equation as follows:

(0.100 mM) x (0.40 mL) = (0.0200 mM) x (V mL)

Simplifying this equation will give you the volume of HCl solution required for dilution.

2. Next, let's calculate the final concentration of HCl in the solution. We initially have a 2.5 M HCl solution, and after dilution, we should obtain the final concentration. To determine the final concentration, we use the dilution equation again:

(Initial Concentration) x (Initial Volume) = (Final Concentration) x (Final Volume)

In this case, the initial concentration is 2.5 M HCl, and the initial volume is the volume of HCl solution we found in step 1. The final concentration will be the final amount of HCl divided by the final volume, which is the sum of the HCl solution volume and the volume of the dye solution you want to prepare.

3. Finally, let's calculate the pH of the resulting solution. Since we are adding HCl, which is a strong acid, to the dye solution, we can assume that the final pH will be determined by the HCl concentration. You can use the pH equation, pH = -log([H+]), to calculate the pH based on the concentration of HCl.

Substituting the final concentration of HCl into the pH equation will give you the pH of the solution.

By following these steps, you should be able to solve the problem and find the amount of HCl required for dilution, the final concentration of HCl in the solution, and the pH.