Concentration Calculations (Molarity) - Chemistry

1. Fundamental Concepts

Molarity Definition: Molarity () is a unit of solution concentration, defined as the moles of solute dissolved in 1 liter of solution.

Core Formula:

$$M=\frac{n}{V}$$

= moles of solute (mol)
= volume of solution (L, not volume of solvent)

Key Premise: The solution volume includes both solute and solvent; molarity is temperature-dependent (volume changes with temperature).

2. Key Concepts

Solute vs. Solvent: Solute is the substance being dissolved; solvent is the dissolving medium (usually water for aqueous solutions).

Unit Conversion Rules:

Mass of solute → moles: $n=\frac{\text{mass}}{\text{molar mass}}$

Volume conversion: mL → L (divide by 1000)

Dilution Principle: When diluting a solution, moles of solute remain constant. Formula:

$$M_1V_1=M_2V_2$$

$M_1/V_1$ = initial molarity/volume; $M_2/V_2$ = final molarity/volume

Common Units: Molarity is expressed in mol/L or M (e.g., 0.5 M NaCl = 0.5 mol NaCl per 1 L solution).

3. Examples

Easy

Calculate the molarity of a solution containing 5.85 g NaCl (molar mass = 58.5 g/mol) dissolved in 0.1 L of solution.

Step 1: Calculate moles of NaCl → $n=\frac{5.85\ \text{g}}{58.5\ \text{g/mol}}=0.1\ \text{mol}$

Step 2: Calculate molarity → $M=\frac{0.1\ \text{mol}}{0.1\ \text{L}}=1.0\ \text{M}$

Medium

What volume of 2.0 M HCl solution is required to obtain 0.5 mol of HCl?

Rearrange formula: $V=\frac{n}{M}$

Calculation: $V=\frac{0.5\ \text{mol}}{2.0\ \text{mol/L}}=0.25\ \text{L}=250\ \text{mL}$

Hard

A 100 mL sample of 6.0 M H₂SO₄ is diluted to a final volume of 500 mL. What is the molarity of the diluted solution? Then, calculate the mass of H₂SO₄ (molar mass = 98 g/mol) in the diluted solution.

Step 1: Dilution calculation → $M_1V_1=M_2V_2$

$6.0\ \text{M} \times 0.1\ \text{L}=M_2 \times 0.5\ \text{L}$ → $M_2=1.2\ \text{M}$

Step 2: Moles of H₂SO₄ (constant before/after dilution) → $n=6.0\ \text{M} \times 0.1\ \text{L}=0.6\ \text{mol}$

Step 3: Mass calculation → $\text{mass}=0.6\ \text{mol} \times 98\ \text{g/mol}=58.8\ \text{g}$

4. Problem-Solving Techniques

Identify Known/Unknown Quantities: Label given values (mass, volume, molar mass) and the target variable ($M$, $n$, or $V$) first.

Check Unit Consistency: Convert volume to liters and mass to moles before calculation; avoid confusing solvent volume with solution volume.

Apply Dilution Formula for Dilution Problems: Confirm that moles of solute are unchanged; use $M_1V_1=M_2V_2$ directly without calculating moles separately.

Verify Calculation Logic: After solving, check if the result is reasonable (e.g., molarity decreases after dilution; higher solute mass leads to higher molarity for the same volume).

Round to Correct Significant Figures: Follow significant figure rules based on given data (e.g., 2 significant figures for 5.8 g, 3 for 5.85 g).