Enter coordinates from your concentration-time graph or the tangent line drawn on the curve.
mol/dm³ (Molarity)
cm³ (Volume)
g (Mass)
mol (Moles)
seconds (s)
minutes (min)
hours (h)
For a curve, draw a tangent at the specific time and pick two points on that straight line.
Calculated Rate of Reaction:
Calculation Steps:
function calculateReactionRate() {
// Get inputs
var x1 = document.getElementById('x1').value;
var y1 = document.getElementById('y1').value;
var x2 = document.getElementById('x2').value;
var y2 = document.getElementById('y2').value;
var yUnit = document.getElementById('yUnit').value;
var xUnit = document.getElementById('xUnit').value;
// Validation
if (x1 === "" || y1 === "" || x2 === "" || y2 === "") {
alert("Please enter values for both Point 1 and Point 2.");
return;
}
var t1 = parseFloat(x1);
var c1 = parseFloat(y1);
var t2 = parseFloat(x2);
var c2 = parseFloat(y2);
if (isNaN(t1) || isNaN(c1) || isNaN(t2) || isNaN(c2)) {
alert("Please enter valid numbers.");
return;
}
if (t1 === t2) {
alert("Time coordinates (x1 and x2) cannot be the same. Division by zero error.");
return;
}
// Calculation: Gradient = (y2 – y1) / (x2 – x1)
var deltaY = c2 – c1;
var deltaX = t2 – t1;
var gradient = deltaY / deltaX;
// Reaction rate is conventionally positive even if reactants are decreasing (negative slope)
// However, we will show the slope and then the rate magnitude.
var absoluteRate = Math.abs(gradient);
// Formatting output
var resultArea = document.getElementById('result-area');
var finalRateDisplay = document.getElementById('finalRate');
var stepsDisplay = document.getElementById('calcSteps');
var interpDisplay = document.getElementById('interpretation');
resultArea.style.display = "block";
// Format to 4 decimal places for precision in chemistry
var formattedRate = absoluteRate.toPrecision(4);
var unitString = yUnit + " " + xUnit + "⁻¹"; // e.g. mol/dm³ s⁻¹
finalRateDisplay.innerHTML = formattedRate + " " + unitString;
// Generate Steps text
var stepsHTML = "";
stepsHTML += "Formula: Rate = Δy / Δx = (y₂ – y₁) / (x₂ – x₁)";
stepsHTML += "Δy (Change in Amount) = " + c2 + " – " + c1 + " = " + deltaY.toPrecision(4) + "";
stepsHTML += "Δx (Change in Time) = " + t2 + " – " + t1 + " = " + deltaX.toPrecision(4) + "";
stepsHTML += "Gradient = " + deltaY.toPrecision(4) + " / " + deltaX.toPrecision(4) + " = " + gradient.toPrecision(4) + "";
stepsHTML += "Rate Magnitude = |" + gradient.toPrecision(4) + "| = " + formattedRate + "";
stepsDisplay.innerHTML = stepsHTML;
// Interpretation
if (gradient 0) {
interpDisplay.innerHTML = "Note: The positive slope indicates the formation of a product (amount is increasing over time).";
} else {
interpDisplay.innerHTML = "Note: The slope is zero, indicating the reaction has stopped or reached equilibrium.";
}
}
How to Calculate Rate of Reaction from a Graph
Calculating the rate of reaction from a graph is a fundamental skill in kinetics, allowing chemists to determine how fast reactants are turned into products. Whether you are analyzing a curve representing the disappearance of a reactant or the appearance of a product, the mathematical principle remains finding the slope (gradient) of the line.
Types of Reaction Rates
Before using the calculator, it is important to identify which type of rate you are trying to calculate from your graph:
Average Rate: The rate calculated over a specific time interval. This is found by drawing a straight line (secant) between two points on the curve and calculating its slope.
Instantaneous Rate: The rate at a specific moment in time. This is found by drawing a tangent line touching the curve at that exact time $t$, and calculating the slope of that tangent.
Initial Rate: The instantaneous rate at $t=0$. This is found by drawing a tangent at the very start of the reaction curve.
The Calculation Formula
The rate of reaction is essentially the change in concentration (or volume/mass) divided by the change in time. If you have a graph where the y-axis is Concentration ($C$) and the x-axis is Time ($t$), the formula corresponds to the gradient formula in mathematics:
Rate = Change in Y / Change in X
Rate = (y₂ – y₁) / (x₂ – x₁)
Rate = Δ[Concentration] / ΔTime
Steps to Calculate from a Linear Graph
If your reaction is zero-order, the graph of concentration vs. time will be a straight line.
Pick two convenient points on the line. Let's call them $(x_1, y_1)$ and $(x_2, y_2)$.
Subtract the y-values: $y_2 – y_1$.
Subtract the x-values: $x_2 – x_1$.
Divide the difference in Y by the difference in X.
Steps to Calculate from a Curved Graph
Most reactions produce a curve where the rate slows down over time. To find the rate at a specific time (e.g., at 30 seconds):
Locate 30 seconds on the x-axis and mark the corresponding point on the curve.
Place a ruler against the curve at that point and draw a straight tangent line. The line should just touch the curve without cutting through it.
Extend the tangent line so it is long enough to read coordinates easily.
Pick two distinct points on this straight tangent line (not the curve itself). These are your coordinates $(x_1, y_1)$ and $(x_2, y_2)$.
Input these coordinates into the calculator above to find the slope.
Example Calculation
Imagine a reaction where we measure the volume of hydrogen gas produced over time. We want to find the rate at 20 seconds. We draw a tangent at $t=20$.
If you plot the concentration of a reactant against time, the curve goes down, resulting in a negative slope (e.g., -0.05 mol/dm³/s). However, reaction rate is typically defined as a positive quantity. Therefore, we take the absolute magnitude of the slope.
If you plot the concentration of a product, the curve goes up, and the slope is naturally positive.