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border-radius: 10px;
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Dilution Equation Calculator (C1V1 = C2V2)
Use this calculator to quickly solve for any unknown variable in the dilution equation: C1V1 = C2V2. Simply enter values for three of the four fields, and the calculator will determine the missing value. Remember to use consistent units for concentration and volume.
Enter your values above and click "Calculate".
function calculateDilution() {
var c1 = parseFloat(document.getElementById('initialConcentration').value);
var v1 = parseFloat(document.getElementById('initialVolume').value);
var c2 = parseFloat(document.getElementById('finalConcentration').value);
var v2 = parseFloat(document.getElementById('finalVolume').value);
var filledCount = 0;
if (!isNaN(c1)) filledCount++;
if (!isNaN(v1)) filledCount++;
if (!isNaN(c2)) filledCount++;
if (!isNaN(v2)) filledCount++;
var resultDiv = document.getElementById('dilutionResult');
resultDiv.className = 'result'; // Reset class for new calculation
if (filledCount !== 3) {
resultDiv.innerHTML = "Error: Please enter values for exactly three of the four fields.";
resultDiv.classList.add('error');
return;
}
var calculatedValue;
var missingField = "";
if (isNaN(c1)) {
if (isNaN(v1) || isNaN(c2) || isNaN(v2)) { // Should not happen if filledCount is 3, but for robustness
resultDiv.innerHTML = "Error: Invalid input for known values.";
resultDiv.classList.add('error');
return;
}
if (v1 === 0) {
resultDiv.innerHTML = "Error: Initial Volume (V1) cannot be zero when solving for Initial Concentration (C1).";
resultDiv.classList.add('error');
return;
}
calculatedValue = (c2 * v2) / v1;
missingField = "Initial Concentration (C1)";
} else if (isNaN(v1)) {
if (isNaN(c1) || isNaN(c2) || isNaN(v2)) {
resultDiv.innerHTML = "Error: Invalid input for known values.";
resultDiv.classList.add('error');
return;
}
if (c1 === 0) {
resultDiv.innerHTML = "Error: Initial Concentration (C1) cannot be zero when solving for Initial Volume (V1).";
resultDiv.classList.add('error');
return;
}
calculatedValue = (c2 * v2) / c1;
missingField = "Initial Volume (V1)";
} else if (isNaN(c2)) {
if (isNaN(c1) || isNaN(v1) || isNaN(v2)) {
resultDiv.innerHTML = "Error: Invalid input for known values.";
resultDiv.classList.add('error');
return;
}
if (v2 === 0) {
resultDiv.innerHTML = "Error: Final Volume (V2) cannot be zero when solving for Final Concentration (C2).";
resultDiv.classList.add('error');
return;
}
calculatedValue = (c1 * v1) / v2;
missingField = "Final Concentration (C2)";
} else if (isNaN(v2)) {
if (isNaN(c1) || isNaN(v1) || isNaN(c2)) {
resultDiv.innerHTML = "Error: Invalid input for known values.";
resultDiv.classList.add('error');
return;
}
if (c2 === 0) {
resultDiv.innerHTML = "Error: Final Concentration (C2) cannot be zero when solving for Final Volume (V2).";
resultDiv.classList.add('error');
return;
}
calculatedValue = (c1 * v1) / c2;
missingField = "Final Volume (V2)";
} else {
resultDiv.innerHTML = "Error: An unexpected error occurred. Please check your inputs.";
resultDiv.classList.add('error');
return;
}
if (isNaN(calculatedValue) || !isFinite(calculatedValue)) {
resultDiv.innerHTML = "Error: Calculation resulted in an invalid number. Please check your inputs, especially for zero values in denominators.";
resultDiv.classList.add('error');
} else {
resultDiv.innerHTML = "The missing value is: " + missingField + " = " + calculatedValue.toFixed(4) + " (Units will be consistent with your input units).";
}
}
Understanding the Dilution Equation (C1V1 = C2V2)
The dilution equation, C1V1 = C2V2, is a fundamental principle in chemistry, biology, and many other scientific fields. It's used to calculate the parameters of a solution before or after dilution. The core idea behind this equation is that the amount of solute (the substance being dissolved) remains constant during the dilution process; only the volume of the solvent changes, thereby changing the concentration.
- C1: Initial Concentration – This is the concentration of the stock solution before dilution. It can be expressed in various units like Molarity (M), percentage (%), parts per million (ppm), etc.
- V1: Initial Volume – This is the volume of the stock solution that you are taking to dilute. It can be in liters (L), milliliters (mL), microliters (µL), etc.
- C2: Final Concentration – This is the desired concentration of the diluted solution.
- V2: Final Volume – This is the total volume of the diluted solution you want to prepare.
How to Use This Calculator
Our Dilution Equation Calculator is designed for simplicity and accuracy:
- Identify Your Knowns: Determine which three of the four variables (C1, V1, C2, V2) you already know.
- Input Values: Enter these three known values into their respective fields in the calculator.
- Leave One Blank: Leave the field for the unknown variable empty.
- Ensure Consistent Units: It is crucial that your units for concentration (e.g., M, %) are consistent across C1 and C2, and similarly for volume (e.g., mL, L) across V1 and V2. The calculator will provide the answer in the same unit system you input.
- Calculate: Click the "Calculate Missing Value" button. The result will appear below the button.
Practical Applications of Dilution
The dilution equation is indispensable in numerous scenarios:
- Chemistry Labs: Preparing solutions of specific concentrations from concentrated stock solutions for experiments.
- Biology & Biochemistry: Diluting DNA, RNA, protein samples, or cell cultures to desired working concentrations.
- Pharmacy: Formulating medications by diluting concentrated drug solutions to safe and effective dosages.
- Environmental Science: Preparing standards for calibration curves or diluting environmental samples for analysis.
- Food & Beverage Industry: Adjusting the concentration of ingredients or testing samples.
Important Considerations for Dilution
- Unit Consistency: Always double-check that your units are consistent. If C1 is in Molarity, C2 will be in Molarity. If V1 is in mL, V2 will be in mL. The calculator does not perform unit conversions.
- Accuracy: The accuracy of your calculated result depends entirely on the accuracy of your input measurements. Use precise volumetric glassware (e.g., volumetric flasks, pipettes) for critical dilutions.
- Safety: When diluting concentrated acids or bases, always add the concentrated solution slowly to a larger volume of water, never the other way around, to manage heat generation safely.
- Solute Stability: Be aware that some solutes may not be stable at very low concentrations or may react with the solvent over time.
Examples of Dilution Calculations
Here are a few examples demonstrating how the C1V1 = C2V2 equation works:
Example 1: Calculating Final Concentration (C2)
You have a 2.0 M stock solution of NaCl. You take 25 mL of this stock solution and dilute it with water to a final volume of 100 mL. What is the final concentration (C2) of the diluted solution?
- C1 = 2.0 M
- V1 = 25 mL
- V2 = 100 mL
- C2 = ?
Using the formula: C2 = (C1 * V1) / V2 = (2.0 M * 25 mL) / 100 mL = 0.5 M
Example 2: Calculating Initial Volume (V1)
You need to prepare 500 mL of a 0.1 M solution of glucose from a 1.5 M stock solution. How much of the 1.5 M stock solution (V1) do you need?
- C1 = 1.5 M
- C2 = 0.1 M
- V2 = 500 mL
- V1 = ?
Using the formula: V1 = (C2 * V2) / C1 = (0.1 M * 500 mL) / 1.5 M = 33.33 mL
Example 3: Calculating Final Volume (V2)
You have 10 mL of a 50% (v/v) ethanol solution. You want to dilute it to a final concentration of 10% (v/v). What will be the final volume (V2) of the diluted solution?
- C1 = 50%
- V1 = 10 mL
- C2 = 10%
- V2 = ?
Using the formula: V2 = (C1 * V1) / C2 = (50% * 10 mL) / 10% = 50 mL