Using the concentration of the stock Cu solution and the volumes delivered, calculate the concentration of your standard Cu solutions in ppm.

Question

The concentration of the stock Cu solution is 53.9 ppm (40 mL solution)

The volumes delivered for:

1st standard Cu Solution: 1.00 mL

2nd standard Cu Solution: 2.00 mL

3rd standard Cu Solution: 3.00 mL

4th standard Cu Solution: 4.00 mL

Answer 1

I know this question was asked a long time ago, but hopefully the answer might prove useful to someone else with the same question. To determine the concentration of a solute after dilution to a new volume, we can use the relationship:

C₁V₁ = C₂V₂

where C₁ and V₁ are the concentration and volume of the first solution, and C₂ and V₂ are the concentration and volume of the second solution. In this situation we are taking aliquots of a Cu solution with a known concentration (solution #1) and adding those aliquots to several 40 mL volumes of some solution in order to make up some standards with known concentrations (solution #2). We will essentially just be using the above equation to calculate the new concentration after dilution four different times.

I like to write out all of my variables at this point so that I know what I have, and what I'm looking for. It's a little unclear from the question, but I'm going to assume that each of these aliquots is being added to 40 mL of solvent.

V₁ = 1, 2, 3, and 4 mL These are four aliquots being used to make up four standards

C₁ = 53.9 mL This is the concentration of my standard (solution #1)

V₂ = 40 mL + V₁ Each aliquot is added to 40 mL. Giving V₂'s of 41, 42, 43, and 44 mL

C₂ = ? This is what we're determining for each of the four solutions.

Knowing now that we need to solve for C₂ we can do a little algebra in order to isolate that variable in our equation. Diving by V₂ on both sides we get:

(C₁ V₁) / V₂ = C₂

Now we can just plug in our known values in order to solve for the concentrations of each of the standards. Here is a table explaining the process a bit.

C₁ (ppm) | V₁ (mL) | V₂ (mL) | C₂ (ppm)

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53.9 | 1 | 41 | 1.31

53.9 | 2 | 42 | 2.57

53.9 | 3 | 43 | 3.76

53.9 | 4 | 44 | 4.90

Given the prompt, those four values should be your answer. A more common process of making up standards is to dilute aliquots of the standard up to a fixed total volume rather than a changing total volume as we've just discussed. The process would be the same except V₂ would stay the same for each aliquot. This would be accomplished by using less solvent as larger aliquots are used, e.g., 36 mL of water and 4 mL of the stock solution make 40 mL of 5.39 ppm Cu standard using the above values.