Mixing Ratio Calculator

Ethanol mixing: mL stock per 1000 mL final volume

Mixing Ratio Calculator: Complete Guide

When two solutions of different concentrations are blended, conservation of solute gives: C1 x V1 + C2 x V2 = Ct x (V1+V2). The alligation method solves for the mixing ratio directly: V1:V2 = (Ct-C2):(C1-Ct). This works for any concentration unit -- %, ppm, mol/L, g/L -- as long as the same unit is used consistently for all three values.

Alligation derivation and worked examples

From C1*V1 + C2*V2 = Ct*(V1+V2): rearrange to V1*(C1-Ct) = V2*(Ct-C2); so V1/V2 = (Ct-C2)/(C1-Ct). Example 1: prepare 70% v/v ethanol from 100% + water (0%). Ratio = (70-0):(100-70) = 70:30 = 7:3. For 1 litre: 700 mL ethanol + 300 mL water. Example 2: prepare 1.0 mol/L NaOH from 2.0 mol/L stock A and 0.5 mol/L stock B. Ratio = (1.0-0.5):(2.0-1.0) = 0.5:1.0 = 1:2. For 300 mL: 100 mL of 2.0 M + 200 mL of 0.5 M. Verify: (100 x 2.0 + 200 x 0.5)/300 = 300/300 = 1.0 mol/L. Note for ethanol-water: volume contraction occurs on mixing -- measure the final volume in a volumetric flask rather than adding volumes.

Mixing with a non-zero diluent

When both solutions have non-zero concentration, C1V1=C2V2 no longer applies directly -- it assumes the diluent is pure solvent. Alligation is the correct method in all cases where C2 is greater than zero. Applications in analytical chemistry: HPLC mobile phase preparation blending aqueous (A) and organic (B) solvents to a target percent organic content; preparing intermediate-strength stock solutions from two master stocks; blending polymer solutions of different concentration for coating applications. The only requirement is that the target lies strictly between C1 and C2 -- if C2 = 0, alligation gives the same answer as C1V1 = C2V2.

Alligation in pharmacy

Pharmacists use alligation regularly to prepare intermediate-strength formulations. Example: 100 g of 2.5% hydrocortisone cream from 5% and 1% stocks. Ratio = (2.5-1):(5-2.5) = 1.5:2.5 = 3:5 (total 8 parts). Mass of 5% stock = 3/8 x 100 = 37.5 g; mass of 1% stock = 62.5 g. Verify: (37.5 x 5 + 62.5 x 1)/100 = 250/100 = 2.5%. This is a pharmacopoeia-recognised method tested in every pharmacy licensing examination. It applies to ointments, creams, solutions, alcohol preparations and any two-component blending where an intermediate potency is required.

Using this calculator in lab and coursework

All calculations run in your browser -- no data leaves your device. Results copy with one click and the formula is shown for verification and citation. This tool is part of the LazyTools mixtures and solutions suite, covering pH, concentration, dilution, molarity, buffer and solution preparation for A-level, IB, AP Chemistry and undergraduate analytical chemistry courses.

Key solution chemistry relationships

The equations connecting all solution chemistry: c = n/V (molarity); w% = m_solute/m_solution x 100; C1V1 = C2V2 (dilution and titration); pH = -log[H+]; pH = pKa + log([A-]/[HA]) (Henderson-Hasselbalch); pi = iMRT (osmotic pressure). Mastering these and their interconversions covers the quantitative requirements of solution chemistry from A-level through graduate-level analytical and pharmaceutical chemistry.

Worked step-by-step example

A student needs 500 mL of 0.100 mol/L NaOH from 2.00 mol/L stock. Step 1: moles needed = 0.100 x 0.500 = 0.0500 mol. Step 2: volume of stock = 0.0500 / 2.00 = 25.0 mL. Step 3: pipette 25.0 mL of stock into a 500 mL volumetric flask. Step 4: add approximately 400 mL distilled water and swirl to dissolve. Step 5: cool to room temperature, then make up to the 500 mL graduation mark. Step 6: stopper and invert ten times to homogenise. This systematic approach -- moles first, then volume or mass -- avoids unit errors and produces traceable calculations for laboratory records and quality control documentation.

Common calculation errors and how to avoid them

Frequent mistakes in solution chemistry: (1) Confusing mass of solution with mass of solvent -- always: m_solution = m_solute + m_solvent. (2) Using the wrong molar mass -- check for water of crystallisation in hydrated salts such as CuSO4.5H2O versus anhydrous CuSO4. (3) Unit mismatch -- all concentrations in a calculation must use identical units. (4) Forgetting stoichiometric ratios -- H2SO4 requires 2 mol NaOH per mol acid; H3PO4 requires 3. (5) Assuming density equals 1 g/mL for concentrated solutions -- this is only valid for dilute aqueous solutions; concentrated HCl has density 1.19 g/mL, concentrated H2SO4 1.84 g/mL. Always check supplier certificates of analysis for the exact density and percent composition of concentrated reagents before calculating dilutions or neutralisations.

Step-by-step worked numerical example

A student needs 500 mL of 0.100 mol/L NaOH from 2.00 mol/L stock. Step 1: moles needed = 0.100 x 0.500 = 0.0500 mol. Step 2: volume of stock required = 0.0500 / 2.00 = 0.0250 L = 25.0 mL. Step 3: using a pipette, transfer exactly 25.0 mL of 2.00 mol/L NaOH stock into a 500 mL volumetric flask. Step 4: add approximately 400 mL of distilled water and swirl gently until fully dissolved. Step 5: allow the solution to cool to room temperature (dilution of NaOH is slightly exothermic). Step 6: top up carefully to the 500 mL graduation mark with distilled water, using a dropper for the final millilitres. Step 7: stopper the flask and invert ten times to homogenise. Label the flask immediately with: solute, concentration, volume, date prepared, and preparer initials. This systematic approach -- moles first, then volume or mass -- avoids unit errors and produces fully traceable calculations for laboratory records, quality management systems and regulatory submissions.

Common errors in solution chemistry calculations

Five frequently made mistakes: (1) Confusing mass of solution with mass of solvent. The mass of the solution is the total mass including the solute: m_solution = m_solute + m_solvent. This error inflates the denominator in % w/w calculations and underestimates the true percent. (2) Wrong molar mass from hydrated salts. CuSO4.5H2O (M_r 249.69) is not the same as anhydrous CuSO4 (M_r 159.61). Always use the formula as written on the reagent bottle, including all water of crystallisation. (3) Mixing units within a calculation. Concentrations in mmol/L and mol/L cannot be combined directly in C1V1=C2V2; convert to the same unit first. (4) Forgetting stoichiometric ratios. H2SO4 provides two H+ per molecule; H3PO4 provides three; NaOH provides one OH per molecule; Ca(OH)2 provides two. Ignoring this in neutralisation calculations leads to errors by factors of 2 or 3. (5) Assuming density equals 1 g/mL for concentrated solutions. This is only valid for dilute aqueous solutions. Concentrated HCl has density 1.19 g/mL; concentrated H2SO4 1.84 g/mL. Always check the supplier certificate of analysis for exact density and percent composition before calculating dilutions or neutralisations.

Connecting this calculation to the broader solution chemistry toolkit

Every solution chemistry calculation connects to others. Molarity (c = n/V) underpins dilution (C1V1=C2V2), which underpins titration (Ca*Va*na = Cb*Vb*nb at the equivalence point). Mass percent connects to molarity via M = (% w/w x density x 10) / molar mass. Buffer pH uses the Henderson-Hasselbalch equation, itself derived from the Ka expression. Buffer capacity (beta = dn/dpH) is the derivative of the H-H equation with respect to pH. Each calculator in the LazyTools mixtures and solutions suite handles one node in this interconnected network -- use the related tools section at the bottom of this page to move between calculations in multi-step problems, and use the copy button to carry results between tools without transcription errors.

Accuracy, precision and significant figures

All results are displayed to four significant figures (four decimal places for percent values, four significant figures for volumes and masses). In practice, laboratory balances typically read to 0.001 g and Grade A volumetric glassware has tolerances of 0.03 to 0.06 mL at 20 degrees C. The limiting factor in real solution preparation is usually the balance precision, not the calculation. For routine analytical work, three significant figures in the final result are generally sufficient and match the precision of the glassware used. For primary standard solutions prepared for calibration work, four significant figures should be used throughout and the exact concentration should be verified by back-titration or independent analytical measurement before use.

Frequently asked questions