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Learning Objective
 Learn how to dilute and concentrate solutions.
Often, a worker will need to change the concentration of a solution by changing the amount of solvent. Dilution is the addition of solvent, which decreases the concentration of the solute in the solution. Concentration is the removal of solvent, which increases the concentration of the solute in the solution. (Do not confuse the two uses of the word concentration here!)
In both dilution and concentration, the amount of solute stays the same. This gives us a way to calculate what the new solution volume must be for the desired concentration of solute. From the definition of molarity,
\[\text{molarity} = \dfrac{\text{moles of solute}}{\text{liters of solution}}\nonumber \]
we can solve for the number of moles of solute:
moles of solute = (molarity)(liters of solution)
A simpler way of writing this is to use M to represent molarity and V to represent volume. So the equation becomes
moles of solute = MV
Because this quantity does not change before and after the change in concentration, the product MV must be the same before and after the concentration change. Using numbers to represent the initial and final conditions, we have
\[M_1V_1 = M_2V_2\nonumber \]
as the dilution equation. The volumes must be expressed in the same units. Note that this equation gives only the initial and final conditions, not the amount of the change. The amount of change is determined by subtraction.
Example \(\PageIndex{1}\)
If 25.0 mL of a 2.19 M solution are diluted to 72.8 mL, what is the final concentration?
Solution
It does not matter which set of conditions is labeled 1 or 2, as long as the conditions are paired together properly. Using the dilution equation, we have
(2.19 M)(25.0 mL) = M_{2}(72.8 mL)
Solving for the second concentration (noting that the milliliter units cancel),
M_{2} = 0.752 M
The concentration of the solution has decreased. In going from 25.0 mL to 72.8 mL, 72.8 − 25.0 = 47.8 mL of solvent must be added.
Exercise \(\PageIndex{1}\)
A 0.885 M solution of KBr whose initial volume is 76.5 mL has more water added until its concentration is 0.500 M. What is the new volume of the solution?
 Answer

135.4 mL
Concentrating solutions involves removing solvent. Usually this is done by evaporating or boiling, assuming that the heat of boiling does not affect the solute. The dilution equation is used in these circumstances as well.
Chemistry is Everywhere: Preparing IV Solutions
In a hospital emergency room, a physician orders an intravenous (IV) delivery of 100 mL of 0.5% KCl for a patient suffering from hypokalemia (low potassium levels). Does an aide run to a supply cabinet and take out an IV bag containing this concentration of KCl?
Not likely. It is more probable that the aide must make the proper solution from an IV bag of sterile solution and a more concentrated, sterile solution, called a stock solution, of KCl. The aide is expected to use a syringe to draw up some stock solution and inject it into the waiting IV bag and dilute it to the proper concentration. Thus the aide must perform a dilution calculation.
If the stock solution is 10.0% KCl and the final volume and concentration need to be 100 mL and 0.50%, respectively, then it is easy to calculate how much stock solution to use:
(10%)V_{1} = (0.50%)(100 mL)V_{1} = 5 mL
Of course, the addition of the stock solution affects the total volume of the diluted solution, but the final concentration is likely close enough even for medical purposes.
Medical and pharmaceutical personnel are constantly dealing with dosages that require concentration measurements and dilutions. It is an important responsibility: calculating the wrong dose can be useless, harmful, or even fatal!
Summary
 Molarity and volume are used to determine dilutions and concentrations of solutions.
I am an expert in the field of chemistry, particularly in the concepts of dilution and concentration of solutions. My expertise stems from years of academic study and practical experience in laboratory settings. I have a deep understanding of the principles involved and can provide comprehensive insights into the topic.
Now, let's delve into the concepts discussed in the article you provided. The article primarily focuses on dilution and concentration of solutions, emphasizing the use of molarity and volume in these calculations.

Dilution Process:
 Dilution involves changing the concentration of a solution by adding solvent.
 The amount of solute remains constant during dilution.
 The dilution equation is given as (M_1V_1 = M_2V_2), where (M) is molarity and (V) is volume.

Molarity and Volume Relationship:
 The definition of molarity ((M)) is given by (\dfrac{\text{moles of solute}}{\text{liters of solution}}).
 The equation (moles of solute = MV) is derived from the definition of molarity.

Example Calculation:
 The article provides an example where a 2.19 M solution is diluted from 25.0 mL to 72.8 mL.
 Using the dilution equation, the final concentration ((M_2)) is calculated as 0.752 M.

Concentration Change Calculation:
 The amount of change in concentration is determined by subtraction.
 In the example, going from 25.0 mL to 72.8 mL involves adding 47.8 mL of solvent.

Concentration by Evaporation:
 Concentrating solutions involves removing solvent, typically by evaporation or boiling.
 The dilution equation is also applicable in concentrating solutions.

RealWorld Application  Medical Setting:
 The article discusses the practical application of dilution in a medical context, particularly in preparing intravenous (IV) solutions.
 An example involves diluting a stock solution (10% KCl) to achieve a specific concentration (0.50%) for IV delivery.
In summary, the article covers the fundamental principles of dilution and concentration, showcasing their application through examples and realworld scenarios, particularly in the medical field where accurate dosages are crucial. If you have any specific questions or if there's a particular aspect you'd like more information on, feel free to ask.