Dilution Calculator (C1V1 = C2V2)
Use this calculator to determine the volume of a stock solution needed to prepare a desired diluted solution, or to find the final concentration or volume after dilution. The fundamental principle is C1V1 = C2V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume.
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function convertToBaseConcentration(value, unit) {
// For simplicity, we'll treat all units as "base" and rely on user consistency.
// A more complex calculator would convert all to Molar or g/L.
// Here, we just return the value, assuming the user keeps units consistent for C1 and C2.
return value;
}
function convertToBaseVolume(value, unit) {
// Similar to concentration, we'll rely on user consistency for V1 and V2 units.
return value;
}
function calculateDilution() {
var initialConcentrationInput = document.getElementById('initialConcentration').value;
var initialVolumeInput = document.getElementById('initialVolume').value;
var finalConcentrationInput = document.getElementById('finalConcentration').value;
var finalVolumeInput = document.getElementById('finalVolume').value;
var concentrationUnitC1 = document.getElementById('concentrationUnitC1').value;
var volumeUnitV1 = document.getElementById('volumeUnitV1').value;
var concentrationUnitC2 = document.getElementById('concentrationUnitC2').value;
var volumeUnitV2 = document.getElementById('volumeUnitV2').value;
var resultDiv = document.getElementById('dilutionResult');
resultDiv.className = 'calculator-result'; // Reset class
var c1, v1, c2, v2;
var missingCount = 0;
var missingVariable = ";
if (initialConcentrationInput !== ") {
c1 = parseFloat(initialConcentrationInput);
if (isNaN(c1) || c1 < 0) {
resultDiv.innerHTML = 'Please enter a valid non-negative number for Initial Concentration (C1).';
resultDiv.classList.add('error');
return;
}
} else {
missingCount++;
missingVariable = 'C1';
}
if (initialVolumeInput !== '') {
v1 = parseFloat(initialVolumeInput);
if (isNaN(v1) || v1 < 0) {
resultDiv.innerHTML = 'Please enter a valid non-negative number for Initial Volume (V1).';
resultDiv.classList.add('error');
return;
}
} else {
missingCount++;
missingVariable = 'V1';
}
if (finalConcentrationInput !== '') {
c2 = parseFloat(finalConcentrationInput);
if (isNaN(c2) || c2 < 0) {
resultDiv.innerHTML = 'Please enter a valid non-negative number for Final Concentration (C2).';
resultDiv.classList.add('error');
return;
}
} else {
missingCount++;
missingVariable = 'C2';
}
if (finalVolumeInput !== '') {
v2 = parseFloat(finalVolumeInput);
if (isNaN(v2) || v2 1) {
resultDiv.innerHTML = 'Please leave only one field blank to calculate.';
resultDiv.classList.add('error');
return;
}
var calculatedValue;
var resultUnit;
var resultLabel;
// Perform calculation based on the missing variable
if (missingVariable === 'C1') {
if (v1 === 0) {
resultDiv.innerHTML = 'Initial Volume (V1) cannot be zero when calculating Initial Concentration (C1).';
resultDiv.classList.add('error');
return;
}
calculatedValue = (c2 * v2) / v1;
resultUnit = concentrationUnitC1;
resultLabel = 'Initial Concentration (C1)';
} else if (missingVariable === 'V1') {
if (c1 === 0) {
resultDiv.innerHTML = 'Initial Concentration (C1) cannot be zero when calculating Initial Volume (V1).';
resultDiv.classList.add('error');
return;
}
calculatedValue = (c2 * v2) / c1;
resultUnit = volumeUnitV1;
resultLabel = 'Initial Volume (V1)';
} else if (missingVariable === 'C2') {
if (v2 === 0) {
resultDiv.innerHTML = 'Final Volume (V2) cannot be zero when calculating Final Concentration (C2).';
resultDiv.classList.add('error');
return;
}
calculatedValue = (c1 * v1) / v2;
resultUnit = concentrationUnitC2;
resultLabel = 'Final Concentration (C2)';
} else if (missingVariable === 'V2') {
if (c2 === 0) {
resultDiv.innerHTML = 'Final Concentration (C2) cannot be zero when calculating Final Volume (V2).';
resultDiv.classList.add('error');
return;
}
calculatedValue = (c1 * v1) / c2;
resultUnit = volumeUnitV2;
resultLabel = 'Final Volume (V2)';
}
if (isNaN(calculatedValue)) {
resultDiv.innerHTML = 'An error occurred during calculation. Please check your inputs.';
resultDiv.classList.add('error');
} else {
resultDiv.innerHTML = 'The calculated ' + resultLabel + ' is:
' + calculatedValue.toFixed(4) + ' ' + resultUnit + '';
}
}
Understanding Dilution and the C1V1 = C2V2 Formula
Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. This is a fundamental technique in chemistry, biology, pharmacology, and many other fields. Whether you're preparing reagents in a lab, mixing cleaning solutions at home, or formulating a fertilizer for your garden, understanding dilution is crucial.
The Dilution Formula: C1V1 = C2V2
The most common and straightforward formula for calculating dilutions is C1V1 = C2V2, where:
- C1 = Initial Concentration (the concentration of your stock solution)
- V1 = Initial Volume (the volume of the stock solution you will use)
- C2 = Final Concentration (the desired concentration of your diluted solution)
- V2 = Final Volume (the desired total volume of your diluted solution)
This formula works because the total amount of solute remains constant during dilution. You're simply spreading the same amount of solute over a larger volume of solvent.
How to Use This Calculator
This calculator is designed to solve for any one of the four variables (C1, V1, C2, or V2) when the other three are known. Simply enter the values you have into the corresponding fields and leave the field you wish to calculate blank. Select the appropriate units for each input. It's critical that the units for initial and final concentrations are consistent (e.g., both Molar or both percent), and similarly for initial and final volumes (e.g., both mL or both L).
Practical Examples of Dilution
-
Preparing a Reagent in a Lab:
You have a 10 M stock solution of Tris-HCl and you need to prepare 250 mL of a 0.5 M Tris-HCl solution for an experiment.
- C1 (Initial Concentration): 10 M
- V1 (Initial Volume): ? (This is what you want to find)
- C2 (Final Concentration): 0.5 M
- V2 (Final Volume): 250 mL
Using the calculator: V1 = (0.5 M * 250 mL) / 10 M = 12.5 mL. You would take 12.5 mL of the 10 M stock and add enough solvent (e.g., distilled water) to bring the total volume to 250 mL.
-
Diluting a Cleaning Concentrate:
A concentrated cleaning solution is 20% active ingredient. You need to make 5 liters of a 2% solution for general cleaning.
- C1 (Initial Concentration): 20 %
- V1 (Initial Volume): ?
- C2 (Final Concentration): 2 %
- V2 (Final Volume): 5 L
Using the calculator: V1 = (2 % * 5 L) / 20 % = 0.5 L. You would use 0.5 liters of the concentrate and add 4.5 liters of water to make 5 liters of the 2% solution.
-
Determining Final Concentration:
You take 50 mL of a 1 M solution and add 150 mL of water to it. What is the final concentration?
- C1 (Initial Concentration): 1 M
- V1 (Initial Volume): 50 mL
- C2 (Final Concentration): ?
- V2 (Final Volume): 50 mL (initial) + 150 mL (added water) = 200 mL
Using the calculator: C2 = (1 M * 50 mL) / 200 mL = 0.25 M. The final concentration will be 0.25 M.
Important Considerations
- Unit Consistency: Always ensure that your concentration units (C1 and C2) are the same, and your volume units (V1 and V2) are the same. The calculator will assume this consistency.
- Adding Solvent: When diluting, you typically add the calculated volume of the concentrated solution to a portion of the solvent, then bring the total volume up to the desired final volume with more solvent. This ensures accurate final volume and concentration.
- Safety: Always follow safety guidelines when handling concentrated chemicals, including wearing appropriate personal protective equipment (PPE) and working in a well-ventilated area.