Molarity Calculator

Molarity is the foundation of solution chemistry calculations.

Definition

Molarity (M) = moles of solute / liters of solution

Units: mol/L (also written as M)

Key Points

• Measured per liter of solution, not solvent
• Temperature-dependent (volume changes with temperature)
• Most common concentration unit in chemistry

Example Calculation

Making a 0.5 M NaCl solution:

• NaCl molecular weight = 58.44 g/mol
• For 1 L of solution:
• Moles needed = 0.5 mol
• Mass = 0.5 mol × 58.44 g/mol = 29.22 g

Dissolve 29.22 g NaCl in water, then add water to reach exactly 1 L total volume.

Important Distinction

Per liter of SOLUTION, not solvent:

• Wrong: Add 29.22 g NaCl to 1 L water
• Correct: Add 29.22 g NaCl, then add water to make 1 L total

Other Concentration Units

The dilution equation is essential for preparing solutions from stock.

The Dilution Equation

C₁V₁ = C₂V₂

Where:

• C₁ = initial (stock) concentration
• V₁ = volume of stock needed
• C₂ = final (desired) concentration
• V₂ = final total volume

Why It Works

The moles of solute remain constant during dilution:

• Moles (stock) = C₁ × V₁
• Moles (diluted) = C₂ × V₂
• Since moles are conserved: C₁V₁ = C₂V₂

Example: Making 100 mL of 0.1 M from 1 M Stock

Given:

• C₁ = 1 M (stock)
• C₂ = 0.1 M (desired)
• V₂ = 100 mL (final volume)

Find V₁: V₁ = C₂V₂/C₁ = (0.1 M × 100 mL) / 1 M = 10 mL

Procedure: Add 10 mL of 1 M stock, then add water to reach 100 mL total.

Dilution Factor

Dilution Factor = C₁/C₂ = V₂/V₁

In the example: DF = 1/0.1 = 10× dilution

Serial Dilutions

For large dilution factors, use multiple steps:

• 1000× dilution = 10× → 10× → 10×
• More accurate than single large dilution
• Each step: take 1 part, add 9 parts diluent

Converting between molarity, moles, and mass.

The Relationship

mass (g) = moles × molecular weight (g/mol)

mass (g) = Molarity × Volume (L) × MW

Step-by-Step Process

1. Determine target molarity (M) and volume (V)
2. Calculate moles needed: n = M × V
3. Look up molecular weight (MW)
4. Calculate mass: mass = n × MW

Example: Preparing 500 mL of 0.2 M Glucose

Given:

• Molarity = 0.2 M
• Volume = 500 mL = 0.5 L
• Glucose (C₆H₁₂O₆) MW = 180.16 g/mol

Calculate:

1. Moles = 0.2 M × 0.5 L = 0.1 mol
2. Mass = 0.1 mol × 180.16 g/mol = 18.02 g

Procedure: Weigh 18.02 g glucose, dissolve in ~400 mL water, then add water to exactly 500 mL.

Common Molecular Weights

Hydrated Compounds

For hydrated salts, use the MW including water:

• CuSO₄·5H₂O: MW = 249.69 (not 159.61)
• MgSO₄·7H₂O: MW = 246.47 (not 120.37)

Converting between liters, milliliters, and microliters.

Volume Conversions

Common Lab Volumes

Calculation with mL

For molarity with mL, remember to convert:

M = moles / (mL ÷ 1000)

Or equivalently: moles = M × mL ÷ 1000

Example

How many moles in 250 mL of 0.4 M solution?

moles = 0.4 M × (250 mL ÷ 1000) moles = 0.4 × 0.25 = 0.1 mol

Practical Tip

For mental math, remember:

• 1 mole in 1 L = 1 M
• 1 mmol in 1 mL = 1 M
• 1 μmol in 1 μL = 1 M

Tips for accurate solution preparation in the laboratory.

General Procedure

1. Calculate mass needed
2. Weigh solute accurately (to appropriate precision)
3. Transfer to volumetric flask or graduated cylinder
4. Add ~80% of final volume of solvent
5. Dissolve completely (stir, heat if needed)
6. Cool to room temperature if heated
7. Add solvent to final volume mark
8. Mix thoroughly
9. Label with concentration, date, preparer

Volumetric vs. Graduated Cylinders

Volumetric flasks: Most accurate (±0.1%)

• Use for: Standards, precise work
• Available: 10, 25, 50, 100, 250, 500, 1000 mL

Graduated cylinders: Less accurate (±1%)

• Use for: Routine preparations
• Faster and easier

Common Mistakes to Avoid

1. Adding solute to final volume of solvent

• Wrong: Add solute to 1 L water
• Correct: Add solute, then fill to 1 L

2. Not accounting for volume change

• Some solutes change solution volume
• Always fill to mark AFTER dissolving

3. Using wrong molecular weight

• Check for hydrates (·H₂O)
• Verify formula matches your reagent bottle

4. Temperature effects

• Prepare at room temperature
• Warm solutions expand
• Cool solutions before final volume adjustment

Labeling Requirements

Include:

• Chemical name and formula
• Concentration (with units)
• Date prepared
• Preparer's initials
• Hazard warnings if applicable
• Expiration date (if known)

Beyond basic molarity calculations.

Molarity vs. Molality

Molarity (M): mol/L solution

• Temperature-dependent (volume changes)
• Easier to measure

Molality (m): mol/kg solvent

• Temperature-independent
• Used for colligative properties

Normality (N)

Normality = Molarity × n

Where n = equivalents per mole

For acids/bases: n = H⁺ or OH⁻ ions

• HCl: N = M (1 H⁺)
• H₂SO₄: N = 2M (2 H⁺)
• NaOH: N = M (1 OH⁻)

Percent Solutions

% w/v = (grams solute / 100 mL solution) × 100

Converting to molarity: M = (% w/v × 10) / MW

Example: 5% glucose M = (5 × 10) / 180.16 = 0.278 M

Molar Absorptivity

Beer-Lambert Law: A = εcl

Where:

• A = absorbance
• ε = molar absorptivity (M⁻¹cm⁻¹)
• c = concentration (M)
• l = path length (cm)

Activity vs. Concentration

For precise work, use activity (a) instead of concentration: a = γ × c

Where γ = activity coefficient (≤1)

At low concentrations, γ ≈ 1 and a ≈ c.