write an AP chemstry rundown on Dilution Calculations, include examples, and use the MathJax notation to depict chemical equations, do NOT use code blocks

Dilution Calculations

Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent like adding more water to a solution. It doesn’t change the amount of solute present, just the concentration.

Key Concept: The number of moles of solute remains constant during dilution.

Molarity Equation:

Molarity (M) is defined as moles of solute per liter of solution:

$ M = \frac{moles , of , solute}{liters , of , solution} $

Dilution Equation:

Because the moles of solute remain constant, we can derive the following equation for dilution calculations:

$ M_1V_1 = M_2V_2 $

Where:

• $ M_1 $ is the initial molarity * $ V_1 $ is the initial volume
• $ M_2 $ is the final molarity * $ V_2 $ is the final volume

Units:

While the units for volume can technically be any unit as long as they are consistent on both sides of the equation, it is generally easiest to work with liters (L) or milliliters (mL). Make sure your units are consistent!

Example 1:

What volume of a 12.0 M HCl solution is required to prepare 250.0 mL of a 0.500 M HCl solution?

1. Identify knowns and unknowns:

   $ M_1 $ = 12.0 M $ V_1 $ = ? $ M_2 $ = 0.500 M $ V_2 $ = 250.0 mL

2. Apply the dilution equation:

   $ (12.0 , M)(V_1) = (0.500 , M)(250.0 , mL) $

3. Solve for $ V_1 $ :

   $ V_1 = \frac{(0.500 , M)(250.0 , mL)}{12.0 , M} = 10.4 , mL $

Therefore, 10.4 mL of the 12.0 M HCl solution is needed.

Example 2:

You have 50.0 mL of a 2.50