Molar Calculator
Dilution

A molar calculator dilution tool combines molarity calculation (converting grams to moles using molecular weight) with dilution calculation (C₁V₁ = C₂V₂). This covers the complete workflow: weigh a solid reagent, dissolve to make a stock solution at a known molarity, then dilute to a working concentration. Two calculations in one tool.

This molar calculator bridges the gap between mass measurements and molar concentrations. When you weigh 5.84 g of NaCl (MW 58.44) and dissolve in 1 L, the molarity is 5.84/58.44 = 0.1 M. From there, C₁V₁ = C₂V₂ handles dilution to any target molarity. Chemical suppliers like Sigma-Aldrich, Fisher Scientific, and Alfa Aesar list molecular weights on product labels and certificates of analysis.

The molar calculation has two parts. First, Molarity (M) = moles ÷ volume (L) = [mass (g) ÷ MW (g/mol)] ÷ volume (L). This converts a weighed mass into a molar concentration. Second, C₁V₁ = C₂V₂ dilutes that stock to the desired working molarity.

Rearrange the equation to solve for any unknown:

For example, to prepare 100 mL of 10 mM NaCl from solid: mass = 0.01 M × 0.1 L × 58.44 g/mol = 0.05844 g. Weigh 58.44 mg on an analytical balance, dissolve in water, and bring to 100 mL in a volumetric flask. To then dilute this to 1 mM in 50 mL: V₁ = (1 × 50)/10 = 5 mL of the 10 mM stock + 45 mL water.

The dilution factor in molar terms equals the ratio of stock molarity to final molarity. Diluting 1 M to 1 mM is a 1000-fold dilution. Diluting 10 mM to 200 µM is a 50-fold dilution.

When converting between mass-volume (mg/mL) and molar (mM) concentrations, the molecular weight bridges the two: mM = (mg/mL ÷ MW) × 1000. A 1 mg/mL solution of glucose (MW 180.16) is 5.55 mM. A 1 mg/mL solution of BSA (MW ~66,500) is 0.015 mM. The molecular weight makes a dramatic difference — this molar calculator handles the conversion automatically.

Follow these steps to calculate your dilution:

Serial molar dilutions create a logarithmic concentration range for dose-response experiments. Starting from a 10 mM stock, a three-fold serial dilution generates: 10 mM, 3.33 mM, 1.11 mM, 370 µM, 123 µM, etc.

High-throughput screening facilities at pharmaceutical companies use automated dispensers to create serial molar dilution plates. Starting from 10 mM DMSO stocks stored in compound management systems (at companies like Pfizer, Merck, and AstraZeneca), robotic liquid handlers generate 10-point, half-log (3.16-fold) dilution series for IC₅₀ determination. This molar calculator dilution tool generates the concentration at each step for manual verification.

Problem: A student needs to prepare 250 mL of 25 mM citric acid from solid citric acid monohydrate (MW 210.14 g/mol), then dilute to 2.5 mM for a taste threshold experiment.