Dilution Knowledge-Based Study

Study notes

1. What Is Dilution?

   In chemistry, dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent without adding more solute.

   When additional solvent (such as water) is introduced into a solution:

   • The total volume of the solution increases.
   • The concentration (molarity or mass percentage) decreases.
   • The total amount (number of moles or mass) of the solute remains strictly constant.

   Because the solute particles become spread throughout a larger volume, the number of solute particles per unit volume decreases.

   Mathematical Principles

   The mathematical foundation of dilution relies on the principle of conservation of solute:

   $n_{\text{initial}} = n_{\text{final}}$

   Since molarity ($M$) is defined as the moles of solute ($n$) divided by the volume of solution in liters ($V$), we can express moles as $n = M \times V$. Therefore, for any dilution process involving molar concentration:

   $$M_1 V_1 = M_2 V_2$$

   • $M_1$: Initial molarity of the concentrated solution (stock solution)
   • $V_1$: Initial volume of the stock solution used
   • $M_2$: Final molarity of the diluted solution
   • $V_2$: Final total volume of the diluted solution

   Note: The same relationship applies to other concentration units, such as mass percent or volume percent, written as $C_1 V_1 = C_2 V_2$, provided that the units on both sides match.

   Sample Problem: Calculating Final Concentration

   Problem: A student takes 50.0 mL of a 2.00 M stock solution of $\text{NaCl}$ and adds enough distilled water to bring the total volume to 250.0 mL. What is the molarity of the diluted solution?

   Solution Steps:

   1. Identify the given variables:
      $M_1 = 2.00\text{ M}$
      $V_1 = 50.0\text{ mL}$
      $V_2 = 250.0\text{ mL}$
      $M_2 = ?$
   2. Rearrange the dilution formula:
      $$M_2 = \frac{M_1 V_1}{V_2}$$
   3. Substitute the values and calculate:
      $$M_2 = \frac{(2.00\text{ M})(50.0\text{ mL})}{250.0\text{ mL}} = 0.400\text{ M}$$

   The final concentration of the sodium chloride solution is 0.400 M.

   Total Volume vs. Volume of Water Added

   One of the most frequent misconceptions in dilution calculations is confusing the final total volume ($V_2$) with the volume of solvent added ($\Delta V$).

   Assuming additive volumes:

   $$V_2 = V_1 + V_{\text{added}}$$

   • If a question asks for the volume of water that must be added, you must first calculate $V_2$ using $M_1 V_1 = M_2 V_2$, and then subtract $V_1$:
     $V_{\text{added}} = V_2 - V_1$.
   • Always ensure volume units on both sides of the equation are identical (e.g., both in milliliters or both in liters) before performing calculations.

   Laboratory Safety Rule

   When diluting concentrated acids, always add the acid slowly to water ("Add Acid to Water"), never water to acid, to prevent dangerous exothermic splattering.