Question

Can someone walk through a few simple algebraic solution-making problems? I know how to use formulas, such as C1V1 = C2V2, however I'm having issues with the conceptual part, mostly for when using two solutes.

Problem #1:

Make 200 mL of a saline that has 5 mMol NaCl and 15 mMol KCl. Stocks are 0.1 M NaCl & 0.2 M KCl.

(and if it's simply the C1V1=C2V2 of one, and then the second, added together in a 200 mL flask with water added to make the difference, then PLEASE explain how adding that water doesn't change the new concentration of the solutes you just pulled from stock).

More practice, #2:

Make a saline that includes 5 mMol NaCl and 15 mMol KCl. No stocks, however powders are available--MWs are Na 23.0   K = 39.1   Cl = 35.5

#3, simple right?

Make 175 mL of a 0.75% NaCl solution.

Thanks

Answer 1

You're doing great by wanting to understand the concept behind the formula C1V1 = C2V2 when making dilutions; in this case, with more than one solute.

The concept is actually pretty simple:

1.- The molar concentration (C) of any solution is equal to the moles of the solute, divided by the volume of the solution:

(1) Where n_solute are the moles of the solute; and V_solvent is the volume of your solution (in L)

2.- When you do a dilution (prepare a solution with a smaller concentration from a stock, for example), what you are actually doing is just adding water. The moles remain the same throughout the whole process. This is true wether you have one or more stock solutions of different solutes: you are not adding any more moles of the given solute, because it's a different one; and so, calculations are made independently.

Mathematically, this can be expressed as follows:

and   (2) Where subindices ₍₁₎ and ₍₂₎ correspond to initial and final moles, respectively.

3.- Finally, combining equations (1) and (2), we obtain the formula your using:

and and since      

So, you are correct in the first problem, you just need to do one calculation, and then another one:

---> (NaCl stock)

---> (KCl stock)

So, to prepare the desired solution, you just need to add 10 mL of NaCl stock and 15 mL of KCl stock to a 200 mL volumetric flask and complete with water. I repeat: Calculations are made independently because moles of each different solute remain the same through the whole process. If we were preparing a solution with two different stocks of the same solute, calculations would be different, because moles would not remain constant.

Problem #2 is easier to understand, because the only liquid involved is pure water.

However, we need more: we need to know the volume of the solution you want to prepare.

With the volume you calculate the moles you need (using equation (1) of this answer)

Then, with these moles you can calculate the amount of mass you of each solute, using their respective MWs.

After this, you just weigh each solute sepparately, add them to a volumetric flask (of your desired volume), then complete with water.

Problem #3 is also lacking data. 0.75% what? mass/mass? mass/water? And also, with what are you preparing this solution from? From powders? From a stock with a given concentration?

I hope the explanation was detailed enough, and always keep that spirit of looking to fully understand the problems you are solving.