Please check your inputs. Time 2 must differ from Time 1.
Change in Value ($\Delta y$):
Change in Time ($\Delta t$):
Graph Slope:
Chemical Behavior:
Calculated Reaction Rate
How to Calculate Reaction Rate from a Graph
In chemical kinetics, determining the speed at which a reaction proceeds is fundamental. Often, data is collected experimentally and plotted on a graph with Time on the X-axis and a measurable quantity (such as Concentration, Volume of gas produced, or Mass) on the Y-axis. This calculator helps you determine the reaction rate by analyzing the slope of the line between two points on such a graph.
Understanding the Graph Axes
Before calculating, it is crucial to understand what your graph represents:
X-axis (Independent Variable): This is almost always Time ($t$). Units are typically seconds ($s$), minutes ($min$), or hours ($hr$).
Y-axis (Dependent Variable): This represents the amount of substance. It could be Molarity ($M$ or $mol/L$), Volume ($cm^3$ or $L$), or Mass ($g$).
The Formula: Calculating the Slope
The reaction rate represents the change in the dependent variable over the change in time. Mathematically, this is the slope of the line (or the secant line for an average rate) connecting two points on the graph.
$y_2$ and $y_1$ are the concentration/amount values at the final and initial points.
$t_2$ and $t_1$ are the final and initial times.
Reactants vs. Products
The sign of the slope tells you what is happening in the reaction:
Negative Slope: The value on the Y-axis is decreasing over time. This indicates a Reactant is being consumed. Since reaction rates are conventionally expressed as positive values, we take the absolute value (magnitude) of the slope.
Positive Slope: The value on the Y-axis is increasing over time. This indicates a Product is being formed.
Average Rate vs. Instantaneous Rate
This calculator determines the rate based on two specific coordinates. Depending on how you choose these points, you are calculating one of two things:
Average Rate: If you choose points separated by a significant time interval (e.g., $t=0$ and $t=60$), you calculate the average rate over that duration.
Instantaneous Rate: To find the rate at a specific moment, you must draw a tangent line touching the curve at that exact time. You then pick two points on that tangent line and input them into this calculator.
Example Calculation
Imagine a graph plotting the concentration of reactant [A] over time.
At $t_1 = 0$ s, the concentration $y_1 = 1.0$ M.
At $t_2 = 20$ s, the concentration $y_2 = 0.6$ M.
Step 1: Calculate $\Delta y$ (Change in Concentration)
$0.6 – 1.0 = -0.4$ M
Step 2: Calculate $\Delta t$ (Change in Time)
$20 – 0 = 20$ s
Step 3: Divide to find Slope
$-0.4 / 20 = -0.02$ M/s
Step 4: Determine Rate
Since the rate is the magnitude of the slope for reactants: Rate = 0.02 M/s.
function calculateReactionRate() {
// Get input values
var t1 = document.getElementById('rr_t1').value;
var y1 = document.getElementById('rr_y1').value;
var t2 = document.getElementById('rr_t2').value;
var y2 = document.getElementById('rr_y2').value;
var resultBox = document.getElementById('rr-result-box');
var errorBox = document.getElementById('rr-error');
// Validation
if (t1 === "" || y1 === "" || t2 === "" || y2 === "") {
errorBox.style.display = 'block';
errorBox.innerText = "Please fill in all four fields.";
resultBox.style.display = 'none';
return;
}
t1 = parseFloat(t1);
y1 = parseFloat(y1);
t2 = parseFloat(t2);
y2 = parseFloat(y2);
if (isNaN(t1) || isNaN(y1) || isNaN(t2) || isNaN(y2)) {
errorBox.style.display = 'block';
errorBox.innerText = "Please enter valid numbers.";
resultBox.style.display = 'none';
return;
}
if (t2 === t1) {
errorBox.style.display = 'block';
errorBox.innerText = "Time 2 cannot be the same as Time 1 (infinite slope).";
resultBox.style.display = 'none';
return;
}
// Hide error if previously shown
errorBox.style.display = 'none';
// Calculations
var dy = y2 – y1;
var dt = t2 – t1;
var slope = dy / dt;
var rate = Math.abs(slope);
// Logic for behavior
var behavior = "";
if (slope 0) {
behavior = "Product (Formed)";
} else {
behavior = "No Change (Equilibrium/Stopped)";
}
// Formatting Output (up to 4 decimal places, or less if integer)
function formatVal(num) {
return (Math.round(num * 10000) / 10000).toString();
}
// Display Results
document.getElementById('res-dy').innerHTML = formatVal(dy);
document.getElementById('res-dt').innerHTML = formatVal(dt);
document.getElementById('res-slope').innerHTML = formatVal(slope);
document.getElementById('res-behavior').innerHTML = behavior;
document.getElementById('res-rate').innerHTML = formatVal(rate) + " units/time";
resultBox.style.display = 'block';
}