A stock solution containing Mn^2+ ions was prepared by dissolving 1.584 g pure manganese metal i

A stock solution containing Mn^2+ ions was prepared by...

A stock solution containing $\mathrm{Mn}^{2+}$ ions was prepared by dissolving 1.584 g pure manganese metal in nitric acid and diluting to a final volume of 1.000 L. The following solutions were then prepared by dilution: For solution A, 50.00 mL of stock solution was diluted to 1000.0 mL. For solution B, 10.00 mL of solution A was diluted to 250.0 mL. For solution C, 10.00 mL of solution B was diluted to 500.0 mL. Calculate the concentrations of the stock solution and solutions A, B, and C.

A stock solution containing $\mathrm{Mn}^{2+}$ ions was prepared by dissolving 1.584 g pure manganese metal in nitric acid and diluting to a final volume of 1.000 L. The following solutions were
then prepared by dilution:
For solution A, 50.00 mL of stock solution was diluted to 1000.0 mL.
For solution B, 10.00 mL of solution A was diluted to 250.0 mL.
For solution C, 10.00 mL of solution B was diluted to 500.0 mL.
Calculate the concentrations of the stock solution and solutions A, B, and C.

Key Concepts

Dilution Calculations

Dilution calculations are based on the principle that the number of moles of solute remains constant before and after the dilution process. The relationship C?V? = C?V?, where C refers to concentration and V to volume, allows one to calculate new concentrations when a solution is diluted by adding more solvent.

Serial Dilutions

Serial dilutions refer to a series of successive dilutions, where each step systematically reduces the concentration of the original solution. This method is commonly used to prepare solutions of very low concentration with improved accuracy and reproducibility by reducing cumulative errors in each dilution step.

Molarity

Molarity is a way of expressing the concentration of a solution, defined as the number of moles of solute per liter of solution. It provides a standardized measure to compare how much of a substance is present in different amounts of solution, facilitating stoichiometric calculations and reactions in aqueous media.

Stoichiometry

Stoichiometry involves the calculation of quantities of reactants and products in chemical reactions. In the context of preparing solutions, it is used to convert the mass of a solute into moles using its molar mass, which is essential for determining the initial concentration of a solution.

Transcript

00:01 So in this video, we're going to go over question 48 from chapter 4, which says a stock solution containing magnesium plus 2 ions was prepared by dissolving 1 .584 grams of pure manganese metal and nitric acid and diluting to a final volume of 1 liter.

00:15 The following solutions were then prepared by dilution.

00:19 For solution a, 50 milliliters of stock was diluted to 1 liter.

00:22 For b, 10 mil liters of stock was diluted to 250 mil liters.

00:26 And for c, 10 mil liters of stock was diluted to 500 milliliters.

00:30 Calculate the concentrations of the stock solution and solutions a, b, and c.

00:35 So first of all, to calculate the concentration of the stock solution, let's start out by calculating the number of moles that were in the 1 .584 grams of pure manganese metal that we dissolved in nitric acid.

00:48 So how many moles of manganese do we start with? so we have our mass and we divide by our molar mass, which is 54 .94 grams per mole, and that gives us 0 .0 .2 .2 .2 .2.

01:00 So we have our mass, and we divide by our molar mass, which is 54 .5 grams per mole.

01:00 To 883 moles of pure manganese metal.

01:03 But we're going to go ahead and assume that all of our manganese is converted to manganese plus two ions once we dissolve it in our nitric acid.

01:12 So since we started out with that number of moles of pure manganese metal, then we're going to have that many moles of manonese plus two ions in our solution.

01:22 So then we just take that number of moles and we divide by our total volume, which was one and that gives us 0 .02883 molar.

01:30 That's our concentration of manganese plus two ions in our stock solution.

01:36 So what about solution a? in solution a, we're diluting 50 milliliters of stock solution to 1 ,000 milliliters.

01:43 So the key equation when you're doing dilutions is c1 v1 equals c2 v2.

01:50 So in this case c1 is our stock solution...

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