Molarity Calculators

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Molarity (M) is the most commonly used concentration unit in chemistry and biology, defined as the number of moles of solute per liter of solution. The formula is M = n/V (moles per liter). Molarity is essential for stoichiometric calculations, solution preparation, titration, drug dosing, and biological assay design. Converting between molarity and mass concentration requires the solute's molar mass. Dilutions use the conservation-of-moles relationship: C₁V₁ = C₂V₂. Understanding molarity is fundamental to all quantitative work in the chemical and biological sciences.

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Molarity Formula

M = n / V

n = moles of solute; V = volume of solution in liters. Rearranged: n = M × V; V = n/M.

Mass to molarity: M = (mass in grams / molar mass) / V(L).

Example: dissolve 5.84 g NaCl (MW = 58.4 g/mol) in water to make 200 mL: n = 5.84/58.4 = 0.100 mol; M = 0.100/0.200 = 0.500 M.

Dilution: C₁V₁ = C₂V₂

Moles of solute are conserved: C₁V₁ = C₂V₂. Solve for any unknown. Example: prepare 500 mL of 0.1 M HCl from 12 M stock: V₁ = (0.1 × 500)/12 = 4.17 mL. Take 4.17 mL of 12 M HCl and dilute to 500 mL total volume.

Preparing Molar Solutions

Step-by-step: (1) Calculate mass: mass = M × V × MW. (2) Weigh accurately. (3) Dissolve in ~80% of final volume. (4) Adjust pH if needed. (5) Transfer quantitatively to a calibrated volumetric flask. (6) Add water to the exact mark (never fill beyond). (7) Invert and mix thoroughly.

Common Concentration Units and Conversions

  • μM = 10⁻⁶ M; nM = 10⁻⁹ M; pM = 10⁻¹² M
  • mg/mL to M: divide by molar mass (kDa × 1000 in g/mol if MW given in kDa)
  • % w/v to M: (% × 10 g/L) / MW. Example: 5% glucose (MW=180): M = 50/180 = 0.278 M

Glossary

Molarity (M)
Moles of solute per liter of solution: M = n/V; the standard concentration unit in chemistry; temperature-dependent; used for stoichiometry, dilutions, and solution preparation.
C₁V₁ = C₂V₂
The dilution equation expressing mole conservation: initial concentration × initial volume = final concentration × final volume; used to calculate how to dilute stock solutions.
Molar Mass
The mass of one mole of a substance in g/mol; equals atomic or molecular weight from the periodic table; used to convert between mass (grams) and amount (moles).

Frequently Asked Questions

Molarity (M) = moles of solute / liters of solution. To find moles from mass: n = mass (g) / molar mass (g/mol). Example: 7.30 g of HCl (MW = 36.5 g/mol) dissolved in enough water to make 200 mL: n = 7.30/36.5 = 0.200 mol; M = 0.200/0.200 L = 1.00 M. To prepare a solution of desired molarity: mass (g) = M × V(L) × MW. Example: prepare 250 mL of 0.15 M KCl (MW = 74.55): mass = 0.15 × 0.250 × 74.55 = 2.80 g.

C₁V₁ = C₂V₂ states that moles of solute are conserved: initial concentration × initial volume = final concentration × final volume. Solve for the unknown. Example: dilute 2 M NaOH to 0.05 M in 100 mL: V₁ = (0.05 × 100)/2 = 2.5 mL. Take 2.5 mL of 2 M NaOH and bring the total volume to 100 mL with water. The formula works for any consistent concentration units (M, mM, μg/mL) as long as both C values use the same units.

mg/mL to M: divide mg/mL by molar mass (g/mol) × 0.001 (converts mg to g), or: M = (mg/mL) / MW. Example: 10 mg/mL BSA (MW = 66,430 g/mol): M = 10/66430 = 1.51 × 10⁻⁴ M = 0.151 mM. M to mg/mL: mg/mL = M × MW. Example: 1 μM antibody (MW = 150,000 g/mol): mg/mL = 10⁻⁶ × 150,000 = 0.15 mg/mL = 150 μg/mL. These conversions are essential when working with protein concentrations reported in different units.

Molarity (M) = moles/liter of solution; temperature-dependent because solution volume changes with temperature. Molality (m) = moles/kilogram of solvent; temperature-independent. For dilute aqueous solutions at 25°C: M ≈ m (density ≈ 1 g/mL ≈ 1 kg/L). For colligative property calculations (boiling point elevation, freezing point depression), use molality because the formulas (ΔT = K × m) were derived using mass-based concentration. For reaction stoichiometry and solution preparation, use molarity.