About

Errors in solution preparation cascade. A miscalculated molarity of 0.1 mol/L can invalidate an entire titration series, waste reagents worth hundreds of dollars, or produce a pharmaceutical formulation outside therapeutic range. This calculator implements direct stoichiometric conversions between nine concentration scales - M (molarity), m (molality), mass percent, volume percent, mass/volume percent, ppm, ppb, mole fraction (χ), and normality (N) - using the bridging parameters of molar mass (M_w) and solution density (ρ). It also solves the dilution equation C₁V₁ = C₂V₂. The tool assumes ideal solution behavior and does not account for activity coefficients, which matter above approximately 0.1 mol/L for electrolytes. For non-aqueous solvents, always supply the actual solvent density rather than defaulting to water.

Formulas

The fundamental concentration definitions used by this calculator:

M = m_soluteM_w × V_solution

m = m_soluteM_w × m_solvent

w/w% = m_solutem_solution × 100

ppm = m_solutem_solution × 10⁶

χ_solute = n_soluten_solute + n_solvent

N = M × n_eq

C₁V₁ = C₂V₂

Where m_solute = mass of solute (g), M_w = molar mass (g/mol), V_solution = volume of solution (L), m_solvent = mass of solvent (kg), m_solution = total mass of solution (g), n_solute = moles of solute, n_solvent = moles of solvent, n_eq = number of equivalents (H⁺ ions for acids, OH⁻ for bases, electrons for redox), ρ = solution density (g/mL). The dilution equation assumes the amount of solute is conserved.

Reference Data

Concentration Type	Symbol	Unit	Definition	Typical Range	Use Case
Molarity	M	mol/L	Moles of solute per liter of solution	0.001 - 18	Volumetric analysis, titrations
Molality	m	mol/kg	Moles of solute per kilogram of solvent	0.001 - 20	Colligative properties (boiling point elevation)
Mass Percent	w/w%	%	Mass of solute per mass of solution × 100	0 - 100	Industrial formulations, food labels
Volume Percent	v/v%	%	Volume of solute per volume of solution × 100	0 - 100	Alcohol content, gas mixtures
Mass/Volume Percent	w/v%	g/100 mL	Mass of solute per 100 mL of solution	0 - 100	Pharmacy, IV solutions
Parts Per Million	ppm	mg/kg	Mass of solute per 10⁶ parts solution	0.01 - 10000	Water quality, trace metals
Parts Per Billion	ppb	μg/kg	Mass of solute per 10⁹ parts solution	0.1 - 1000	Environmental monitoring, pesticide residues
Mole Fraction	χ	dimensionless	Moles of solute / total moles	0 - 1	Raoult's law, vapor pressure
Normality	N	eq/L	Equivalents of solute per liter of solution	0.01 - 36	Acid-base titrations, redox reactions
Formality	F	FW/L	Formula weights per liter (ionic compounds)	0.001 - 10	Electrolyte solutions
Density	ρ	g/mL	Mass per unit volume of solution	0.7 - 2.5	Bridging parameter for conversions
Water (25°C)	-	g/mL	Reference solvent density	0.997	Default solvent assumption
H₂SO₄ conc.	-	mol/L	Concentrated sulfuric acid	18.0 M, 96%, ρ = 1.84	Stock solution reference
HCl conc.	-	mol/L	Concentrated hydrochloric acid	12.1 M, 37%, ρ = 1.19	Stock solution reference
HNO₃ conc.	-	mol/L	Concentrated nitric acid	15.9 M, 68%, ρ = 1.41	Stock solution reference
NaOH (50%)	-	mol/L	Concentrated sodium hydroxide	19.1 M, ρ = 1.53	Stock solution reference
NaCl physiological	-	w/v%	Normal saline	0.9% (0.154 M)	Medical reference
Glucose (5%)	-	w/v%	Dextrose IV solution	5% (0.278 M)	Medical reference
Ethanol (proof)	-	v/v%	Proof = 2 × v/v%	40% = 80 proof	Beverage industry
EPA Pb limit (water)	-	ppb	Action level for lead	15 ppb	Environmental compliance
WHO As limit (water)	-	ppb	Arsenic guideline value	10 ppb	Environmental compliance

Frequently Asked Questions

Molarity is defined per liter of solution, while mass percent is defined per gram of solution. To bridge volume-based and mass-based units, you need the solution density ρ (g/mL) to relate mass to volume. Molar mass M_w is needed to convert between grams and moles. Without both, the conversion is mathematically indeterminate. For dilute aqueous solutions, assuming ρ ≈ 1.00 g/mL introduces less than 1% error.

This calculator assumes ideal solution behavior, meaning solute-solvent interactions are identical to solvent-solvent interactions. This assumption fails notably for: electrolyte solutions above approximately 0.1 M (use activity coefficients from Debye-Hückel theory), concentrated acids and bases where density changes non-linearly with concentration, and polymer solutions where volume of mixing is not additive. For electrolyte solutions, effective concentration (activity) can differ from nominal molarity by 10 - 30% at 1 M.

The equivalence factor n_eq depends on the reaction type. For acids, it equals the number of donatable H⁺ ions: HCl has n_eq = 1, H₂SO₄ has n_eq = 2. For bases, it equals OH⁻ ions: NaOH has 1, Ca(OH)₂ has 2. For redox reactions, it equals electrons transferred per molecule. Normality = Molarity × n_eq. IUPAC discourages normality because the same substance can have different equivalence factors depending on the reaction.

Only for dilute aqueous solutions where ρ ≈ 1.000 g/mL. By definition, 1 ppm = 1 mg/kg (mass/mass). Meanwhile, 1 mg/L is mass/volume. The two are numerically equal only when 1 L of solution weighs exactly 1 kg. For brines (ρ ≈ 1.2), seawater, or organic solvents, the difference reaches 20% or more. Always specify which basis you are using.

Molarity changes with temperature because solution volume expands or contracts (water expands about 0.02% per °C near 25°C). Molality, mass percent, mole fraction, and ppm (mass/mass) are temperature-independent because they are defined by mass ratios. For precision work in analytical chemistry, report molality or mass fraction, or specify the reference temperature (typically 20°C or 25°C).

The equation C₁V₁ = C₂V₂ assumes volumes are additive. This is approximately true for dilute solutions but fails for concentrated solutions where the volume of mixing is nonzero. For example, mixing 50 mL of ethanol with 50 mL of water yields only about 96 mL, not 100 mL. The equation also assumes the solute does not dissociate or associate differently at the new concentration.