Solutions and Molarity
Solutions, homogeneous mixtures of solute and solvent, are central to chemistry. Molarity, a key concentration measure, drives precise calculations in labs and industry. MathMultiverse’s guide covers molarity, molality, dilution, visualizations, and applications.
Molarity
Molarity (\( M \)) is moles of solute per liter of solution:
\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
Moles:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
Molality (\( m \)), temperature-independent, is:
\[ m = \frac{\text{moles of solute}}{\text{kg of solvent}} \]
Calculations
Molarity
234 g \( \ce{NaCl} \) (\( M_m = 58.44 \, \text{g/mol} \)) in 3 L:
\[ M \approx 1.33 \, \text{M} \]
Mass
0.75 L of 2.5 M \( \ce{H2SO4} \):
\[ \text{Mass} \approx 183.9 \, \text{g} \]
Volume
40 g \( \ce{KOH} \) for 0.2 M:
\[ V \approx 3.565 \, \text{L} \]
Molality
18 g \( \ce{C6H12O6} \) in 0.5 kg water:
\[ m = 0.2 \, \text{mol/kg} \]
Dilution
Moles conserved: \( M_1 V_1 = M_2 V_2 \).
Final Volume
0.25 L of 6 M \( \ce{HCl} \) to 1.5 M:
\[ V_2 = 1 \, \text{L} \]
Initial Concentration
0.1 L to 0.5 L becomes 0.2 M:
\[ M_1 = 1 \, \text{M} \]
Stock Volume
12 M \( \ce{HNO3} \) for 2 L of 0.5 M:
\[ V_1 \approx 83.3 \, \text{mL} \]
Visualizations
Molarity vs. Volume
Applications
- Titration: 0.025 L of 0.1 M \( \ce{NaOH} \) neutralizes 0.05 M \( \ce{HCl} \).
- Medicine: 0.9% saline is 0.154 M \( \ce{NaCl} \).
- Industry: 2 M \( \ce{NH4NO3} \) requires 160.08 g/L.
- Environment: 100 mL of 5 M \( \ce{NaOCl} \) for 0.5 M solution.