All calculatorsPercentage Concentration → Molarity Calculator
Convert percentage concentration to molarity (M) for w/w, w/v, and v/v mixtures. Enter %, molar mass, and (when needed) density. See steps and visualize with a mini chart and a molarity gauge.
Background
For a 2-component solution, define percent as follows:
- w/w % = g solute per 100 g solution → needs solution density ρ (g·mL⁻¹)
- w/v % = g solute per 100 mL solution → no density needed
- v/v % = mL solute per 100 mL solution → needs solute density ρsolute (g·mL⁻¹)
Let percent be p (%), molar mass be Mm (g·mol⁻¹), and density be ρ (g·mL⁻¹). Then:
w/v: M = (p × 10) / Mm
w/w: M = (p × ρ × 10) / Mm
v/v: M = (p × ρsolute × 10) / Mm
Here 10 converts “per 100 mL” to “per liter”.
How to use this calculator
- Pick % type (w/w, w/v, v/v), enter % and molar mass. Provide density when prompted.
- We use: w/v → M = (p × 10) / Mm; w/w → M = (p × ρ × 10) / Mm; v/v → M = (p × ρsolute × 10) / Mm.
- Toggle sig-fig rounding; view steps and visuals.
Formula & Equation Used
w/v % → M: M = (p × 10) / Mm
w/w % → M: M = (p × ρ × 10) / Mm
v/v % → M: M = (p × ρsolute × 10) / Mm
Here 10 converts “per 100 mL” to “per liter”. Use ρ in g·mL−1.
Example Problems & Step-by-Step Solutions
Example 1 — 37% w/w HCl (ρ=1.19 g/mL)
M = (37 × 1.19 × 10) / 36.46 ≈ 12.1 M.
Example 2 — 5.0% w/v NaCl
M = (5.0 × 10) / 58.44 ≈ 0.855 M.
Example 3 — 70% v/v ethanol (ρ=0.789 g/mL)
M = (70 × 0.789 × 10) / 46.07 ≈ 12.0 M.
Frequently Asked Questions
Q: Why is density needed for w/w and v/v?
Because those definitions involve mass per mass or volume per volume; converting to moles per liter requires density to connect mass and volume.
Q: What units should density use?
g/mL. The equations above assume ρ in g·mL⁻¹.
Q: Does temperature matter?
Density is temperature-dependent; if precision matters, use a density at your working temperature.
