Stock Solution Calculator
Example 1
A laboratory technician needs 1 L of 0.1 M NaOH for a titration series. The stock reagent is 50% w/w NaOH solution with a density of 1.53 g/mL. The technician must calculate the volume of stock reagent needed.
Solution
The target is 1 L of 0.1 M NaOH. The moles of NaOH needed are M × V = 0.1 × 1.0 = 0.1 mol, which corresponds to 0.1 × 40.00 = 4.00 g of pure NaOH. Since the stock is only 50% w/w, the required mass of stock solution is 4.00 g / 0.50 = 8.00 g.
The formula relating stock volume to target concentration is:
Converting mass to volume using the stock density of 1.53 g/mL:
Answer
5.23 mL of 50% w/w NaOH stock
Carefully measure 5.23 mL of the stock solution and dilute to 1 L with distilled water. Add NaOH slowly to water while stirring, as the dissolution is highly exothermic.
Carefully measure 5.23 mL of the stock solution and dilute to 1 L with distilled water. Add NaOH slowly to water while stirring, as the dissolution is highly exothermic.
Source: Vogel's Textbook of Quantitative Chemical Analysis
Example 2
A researcher needs 500 mL of 0.5 M HCl for a series of analytical experiments. The stock bottle contains 12 M HCl. The researcher must determine the volume of concentrated acid required.
Solution
The researcher needs 500 mL of 0.5 M HCl from a 12 M stock. The dilution formula relates stock and target concentrations:
Rearranging to solve for the stock volume:
This is 20.8 mL of concentrated HCl needed.
Answer
20.8 mL of 12 M HCl
Measure 20.8 mL of concentrated HCl. Slowly add the acid to about 400 mL of distilled water while stirring, then dilute to 500 mL in a volumetric flask. Always add acid to water, never water to acid, due to the exothermic nature of the dilution.
Measure 20.8 mL of concentrated HCl. Slowly add the acid to about 400 mL of distilled water while stirring, then dilute to 500 mL in a volumetric flask. Always add acid to water, never water to acid, due to the exothermic nature of the dilution.
Source: NIST Standard Reference Database
Example 3
A biochemist needs 250 mL of 1.0 M NH₃ buffer. The stock reagent is 15 M NH₃ (concentrated ammonium hydroxide). The biochemist also needs to know the concentration of NH₃ in the stock to work safely in a fume hood.
Solution
The biochemist needs 250 mL of 1.0 M NH₃ from a 15 M stock. The dilution formula relates stock and target concentrations:
Solving for the stock volume:
Answer
16.7 mL of concentrated NH₃
Work in a fume hood and wear appropriate PPE. Add the concentrated ammonium hydroxide to approximately 200 mL of distilled water, then dilute to 250 mL.
Work in a fume hood and wear appropriate PPE. Add the concentrated ammonium hydroxide to approximately 200 mL of distilled water, then dilute to 250 mL.
Example 4
A biochemistry lab needs 1.0 L of 6.0 M acetic acid for a pH adjustment protocol. The stock reagent is glacial acetic acid (99.7% w/w, density 1.049 g/mL, molar mass 60.05 g/mol). Calculate the stock molarity and the volume needed to prepare the working solution.
Solution
First calculate the stock molarity using the formula that converts weight percent to molarity:
Substituting the values:
Now use the dilution formula to find the volume needed:
Answer
345 mL of glacial acetic acid
Dilute to 1.0 L with distilled water. Always add acid to water slowly with stirring. Acetic acid is corrosive and its vapour is irritating — work in a fume hood.
Dilute to 1.0 L with distilled water. Always add acid to water slowly with stirring. Acetic acid is corrosive and its vapour is irritating — work in a fume hood.
Published:
Updated:
References
- [1]Pearson, Vogel's Textbook of Quantitative Chemical Analysis, 2000.
- [2]IUPAC, IUPAC Gold Book - Molar Concentration. https://goldbook.iupac.org/terms/view/M03988
- [3]NIST, NIST Standard Reference Database. https://www.nist.gov/srd
Glossary
- Stock solution – A concentrated solution of precisely known concentration that is stored and used as a source for preparing more dilute working solutions. Stock solutions improve reproducibility by reducing the frequency of weighing and preparation steps.
- Dilution – The process of reducing the concentration of a solution by adding more solvent. The amount of solute remains constant during dilution, which is the basis for the relationship C₁V₁ = C₂V₂.
- C₁V₁ = C₂V₂ – The fundamental dilution equation in which C₁ and V₁ are the concentration and volume of the starting solution, and C₂ and V₂ are the concentration and volume of the final diluted solution. Any consistent concentration and volume units may be used.
- Working solution – A dilute solution prepared fresh from a stock solution for immediate use in an experiment, assay, or analytical procedure. Working solutions are typically prepared at concentrations suitable for direct application.
- Serial dilution – A stepwise dilution technique in which each successive dilution is prepared from the previous dilution rather than directly from the stock. Serial dilutions are widely used in microbiology, biochemistry, and pharmaceutical testing to achieve very low concentrations with minimal stock consumption.
- Concentrated solution – A solution containing a relatively high amount of solute per unit volume. In laboratory practice, concentrated reagents such as 12 M HCl, 18 M H₂SO₄, and 15 M NH₃ are common stock solutions that must be handled with appropriate safety precautions.
- Purity – The mass fraction of the desired compound in a commercial chemical reagent, expressed as a percentage. Reagent-grade chemicals typically have purity ≥ 98% and must be factored into calculations when precise concentrations are required.
- Hydrate – A crystalline compound that contains water molecules within its crystal lattice as an integral part of its structure. For example, CuSO₄ · 5H₂O is copper(II) sulfate pentahydrate. The water of hydration contributes to the molar mass and must be included in calculations.
- Anhydrous – A compound that does not contain water of hydration, either because it naturally lacks water molecules in its crystal lattice or because the water has been removed by heating. Anhydrous compounds have a lower molar mass than their hydrated forms.
- Temperature correction – An adjustment applied to volume measurements to account for thermal expansion or contraction of liquids. At 25 °C, water expands by approximately 0.025% per °C. Precise volumetric work requires temperature-controlled conditions or correction factors from standard tables.
How to Use?
- 1
Select Calculation Mode
Choose "Stock Molarity" to convert purity and density to molarity, or "Volume Needed" for dilution calculations.
- 2
Input Solution Data
Enter purity (%), density (g/mL), and molar mass (g/mol). Use Quick Fill to instantly load values for common concentrated acids and bases.
- 3
Use Quick Fill for Fast Chemical Lookup
Search for common acids and bases by name. Purity, density, and molar mass fill automatically from PubChem data, saving you manual lookups.
- 4
Perform Calculation
Click Calculate to get instant results. Enable Advanced Mode for normality and temperature-corrected density.
- 5
Verify Your Results
Cross-check the calculated volume by computing the dilution factor DF = C₁ / C₂. A reasonable DF confirms your inputs are correct. For example, preparing 0.1 M HCl from 12.08 M stock gives DF = 120.8.
Frequently Asked Questions
A stock solution is a concentrated solution of precisely known concentration that is prepared in advance and stored for later use. It is important because it saves preparation time: a single accurate preparation can be diluted repeatedly to produce working solutions of various concentrations. Stock solutions also minimize weighing errors, improve batch-to-batch consistency, and often have better chemical stability than highly dilute solutions. They are essential in analytical chemistry, biochemistry, and pharmaceutical laboratories where reproducibility and accuracy are critical.
Always wear appropriate personal protective equipment (PPE) including chemical-resistant gloves, safety goggles, and a lab coat when handling concentrated stock solutions.
Work in a fume hood when handling volatile acids like concentrated HCl or HNO₃.
When diluting concentrated acids, always add acid to water slowly while stirring, never water to acid, to prevent violent splashing.
Use a volumetric pipette or graduated cylinder for accurate volume measurement.
Neutralize any spills immediately and follow institutional chemical hygiene protocols.
Work in a fume hood when handling volatile acids like concentrated HCl or HNO₃.
When diluting concentrated acids, always add acid to water slowly while stirring, never water to acid, to prevent violent splashing.
Use a volumetric pipette or graduated cylinder for accurate volume measurement.
Neutralize any spills immediately and follow institutional chemical hygiene protocols.
Storage life depends on the chemical nature and concentration of the stock solution.
Concentrated acids like HCl (12 M) and H₂SO₄ (18 M) are stable for years when stored in sealed containers.
Dilute solutions degrade faster: 0.1 M NaOH absorbs CO₂ from air within weeks, forming carbonate.
Light-sensitive solutions should be stored in amber bottles.
Always label with preparation date and recommended expiry.
For critical analytical work, prepare fresh stock solutions monthly and verify concentration by standardization before use.
Concentrated acids like HCl (12 M) and H₂SO₄ (18 M) are stable for years when stored in sealed containers.
Dilute solutions degrade faster: 0.1 M NaOH absorbs CO₂ from air within weeks, forming carbonate.
Light-sensitive solutions should be stored in amber bottles.
Always label with preparation date and recommended expiry.
For critical analytical work, prepare fresh stock solutions monthly and verify concentration by standardization before use.
No. The maximum concentration of any stock solution is limited by the solute's solubility at the given temperature. Attempting to exceed the solubility limit will result in undissolved solid or precipitation. Always check the solute's solubility curve before selecting a stock concentration. For example, NaCl has a solubility of ~359 g/L at 25°C, giving a maximum ~6.14 M stock. If a higher concentration is needed, consider using a more soluble salt or heating the solution (if the solute is more soluble at higher temperatures).
Labelling prevents accidental misuse of expired or incorrectly identified solutions, which is a leading cause of experimental errors and safety incidents in laboratories. The preparation date allows users to assess whether the solution is still within its stable shelf life. Recording the exact concentration (including the units and temperature at which it was measured) ensures that subsequent dilutions yield accurate working solutions. Always include chemical name, concentration, preparation date, initials of the preparer, and any hazard warnings on the label.
Because molarity is volume-based and liquids expand or contract with temperature, the actual concentration of a stock solution varies with temperature. For high-precision work, prepare and use stock solutions at a controlled room temperature (typically 25°C). Alternatively, enable the Advanced Mode in this calculator, which applies a thermal expansion correction factor (β ≈ 0.00021/°C) to density. For routine dilutions where temperature is within 5°C of the standard, the volume error is usually under 0.1% and can be ignored.
Serial dilution is a stepwise dilution technique where a stock solution is diluted repeatedly by a constant factor to produce a series of progressively lower concentrations. It is commonly used in microbiology for plate counting, in biochemistry for ELISA and standard curve preparation, and in pharmaceutical analysis for generating calibration standards. Each step involves mixing a precise volume of the previous solution with a precise volume of diluent. The total dilution factor is the product of all individual dilution factors.
For a multi-step (serial) dilution, multiply the individual dilution factors of each step. If you perform a 10-fold dilution followed by another 10-fold dilution, the total dilution factor is 10 × 10 = 100 (100-fold). For each step, the dilution factor is V_final / V_stock. The overall concentration after n steps is C_final = C_initial / DF_total. Record each step carefully because a single pipetting error propagates through all subsequent dilutions.
Common mistakes include: using the wrong molar mass or n-factor, forgetting to account for solute purity when weighing, not calibrating the balance, filling the volumetric flask to the mark before the solution has reached room temperature, misreading the meniscus, using contaminated glassware, failing to mix thoroughly after dilution, and neglecting to label the container. Another frequent error is assuming that the volume of solvent added plus the volume of solute equals the final volume: always dissolve the solute in less solvent and then make up to the final volume in a volumetric flask.
First, calculate the stock molarity: (37 × 1.18 × 1000) / 36.46 = 12.08 M. Then use the C₁V₁ = C₂V₂ formula. For 500 mL of 0.1 M HCl: V₁ = (0.1 M × 500 mL) / 12.08 M = 4.14 mL. In the lab, fill a 500 mL volumetric flask halfway with distilled water. Slowly add 4.14 mL of 37% HCl (always add acid to water). Allow to cool, then make up to the 500 mL mark and mix thoroughly. Label with concentration and date.
Titrate the stock solution against a certified primary standard. For HCl, titrate against standardized NaOH using phenolphthalein indicator. For NaOH, titrate against potassium hydrogen phthalate (KHP). If the experimental molarity differs from the calculated value by more than 2%, check the label wt% and density values. Temperature differences, evaporation, or degradation can cause discrepancies. Re-standardize periodically for critical analytical work.
Weight/weight percent (w/w%) is grams of solute per 100 g of solution, which is what this calculator uses for stock molarity conversion. Weight/volume percent (w/v%) is grams of solute per 100 mL of solution. Volume/volume percent (v/v%) is milliliters of solute per 100 mL of solution. Concentrated acids are almost always labeled in w/w%, which is why density is required to convert to molarity.
Calculate the mass of solid needed using the formula: mass = M × V × molar mass. For 500 mL of 1 M NaCl: mass = 1 M × 0.5 L × 58.44 g/mol = 29.22 g. Weigh this on an analytical balance, dissolve in about 400 mL of distilled water in a beaker, then transfer to a 500 mL volumetric flask. Rinse the beaker and add rinsings. Make up to the mark and mix thoroughly. For solid stocks, the calculator's basic M = n/V formula applies rather than the wt% conversion.
Solutions degrade through multiple mechanisms:
NaOH absorbs CO₂ from air, forming Na₂CO₃ and reducing effective concentration.
HCl evaporates, especially if the container is frequently opened.
Light-sensitive compounds decompose under fluorescent or sunlight exposure.
Microorganisms can contaminate and metabolize organic solutes.
For critical applications, re-standardize monthly by titration against a certified reference material. For routine work, check quarterly.
NaOH absorbs CO₂ from air, forming Na₂CO₃ and reducing effective concentration.
HCl evaporates, especially if the container is frequently opened.
Light-sensitive compounds decompose under fluorescent or sunlight exposure.
Microorganisms can contaminate and metabolize organic solutes.
For critical applications, re-standardize monthly by titration against a certified reference material. For routine work, check quarterly.
Yes. For a serial dilution, treat each dilution step as an independent C₁V₁ = C₂V₂ calculation. For example, to prepare 10 mL of 0.01 M HCl from 12.08 M stock: first step dilution to 1 M, then second step to 0.1 M, then third step to 0.01 M. Use the Volume Needed mode for each step, entering the previous step concentration as C₁ and the desired concentration as C₂. The calculator handles the units automatically.
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