Solution Concentration Formulas

Overview

This lecture focuses on the formulas for calculating concentration in solutions, their applications, and step-by-step examples, including situations where solutions are diluted or mass is given.

Concentration Formula & Units

• The main formula: ( C = \frac{n}{V} ) where ( C ) is concentration, ( n ) is moles, and ( V ) is volume.
• Volume (( V )) is measured in decimeters cubed (dm³).
• Concentration (( C )) is measured in moles per decimeter cubed (mol·dm⁻³).
• Only use this formula for solutions (not gases).

Alternative Forms of the Formula

• When given mass, use ( n = \frac{m}{M} ) where ( m ) is mass and ( M ) is molar mass.
• The combined formula: ( C = \frac{m}{MV} ), allowing direct calculation of concentration from mass.

Formula Triangle & Rearrangement

• The formula triangle places ( n ) at the top, ( C ) and ( V ) at the bottom.
• To find ( n ): ( n = CV ).
• To find ( V ): ( V = \frac{n}{C} ).
• To find ( C ): ( C = \frac{n}{V} ).

Dilution & Conservation of Moles

• When diluting (adding water), the amount of solute (moles) stays the same, but concentration decreases.
• The formula ( C_1V_1 = C_2V_2 ) is used when the number of moles before and after dilution is the same.
• Always use total final volume after adding water.

Worked Examples

• Example: 6 moles in 2 dm³ yields ( 3,\text{mol·dm}^{-3} ).
• Example: 60 g NaOH in 2 dm³; find moles using molar mass, then concentration.
• Example: Adding water to 20 dm³ of 5 mol·dm⁻³ solution; final concentration uses ( C_1V_1 = C_2V_2 ) with total new volume.
• Example: Given moles and changing volume, use ( C = \frac{n}{V} ).
• Example: Mass to concentration problems use ( C = \frac{m}{MV} ).
• Example: Finding mass from concentration and volume requires calculating moles, then multiplying by molar mass.

Key Terms & Definitions

• Concentration (( C )) — amount of solute per unit volume of solution, measured in mol·dm⁻³.
• Mole (( n )) — amount of substance.
• Volume (( V )) — amount of space solution occupies, measured in dm³.
• Molar Mass (( M )) — mass of one mole of a substance, from the periodic table.

Action Items / Next Steps

• Practice problems applying the formulas for different solution scenarios.
• Review the use of ( C_1V_1 = C_2V_2 ) for dilution questions.
• Use periodic table to find molar masses as needed for calculations.