function calculateRate() {
// Get input values
var t1Str = document.getElementById("time1").value;
var c1Str = document.getElementById("conc1").value;
var t2Str = document.getElementById("time2").value;
var c2Str = document.getElementById("conc2").value;
var errorDisplay = document.getElementById("errorDisplay");
var resultBox = document.getElementById("resultBox");
var rateResult = document.getElementById("rateResult");
var slopeExplanation = document.getElementById("slopeExplanation");
// Reset previous results
errorDisplay.style.display = "none";
resultBox.style.display = "none";
// Validate inputs
if (t1Str === "" || c1Str === "" || t2Str === "" || c2Str === "") {
errorDisplay.innerText = "Please enter values for all fields (Time and Concentration coordinates).";
errorDisplay.style.display = "block";
return;
}
var t1 = parseFloat(t1Str);
var c1 = parseFloat(c1Str);
var t2 = parseFloat(t2Str);
var c2 = parseFloat(c2Str);
if (isNaN(t1) || isNaN(c1) || isNaN(t2) || isNaN(c2)) {
errorDisplay.innerText = "Inputs must be valid numbers.";
errorDisplay.style.display = "block";
return;
}
if (t1 === t2) {
errorDisplay.innerText = "Time values (x1 and x2) cannot be the same (division by zero).";
errorDisplay.style.display = "block";
return;
}
// Calculation: Slope = (y2 – y1) / (x2 – x1)
var deltaY = c2 – c1;
var deltaX = t2 – t1;
var slope = deltaY / deltaX;
// Rate is typically expressed as a positive value magnitude
var rate = Math.abs(slope);
// Determine units placeholder
var unitY = "M"; // Default assumption Molarity
var unitX = "s"; // Default assumption Seconds
// Display Logic
resultBox.style.display = "block";
rateResult.innerText = rate.toFixed(5) + " units/time";
var direction = slope < 0 ? "decreasing (Reactant usage)" : "increasing (Product formation)";
slopeExplanation.innerHTML = "Calculation Details:" +
"Change in Y (Δy): " + deltaY.toFixed(4) + "" +
"Change in X (Δx): " + deltaX.toFixed(4) + "" +
"Slope (Gradient): " + slope.toFixed(5) + "" +
"Graph Trend: Concentration is " + direction + ".";
}
How to Calculate Rate of Reaction from a Graph
Calculating the rate of reaction from a graph is a fundamental skill in kinetics chemistry. Whether you are analyzing the disappearance of a reactant or the appearance of a product, the graphical method provides a visual representation of how fast a chemical change is occurring over time.
Understanding the Graph Axes
Before performing calculations, it is crucial to identify what is plotted:
X-axis (Horizontal): Represents Time. Common units include seconds (s), minutes (min), or hours (hr).
Y-axis (Vertical): Represents the Amount or Concentration of the substance. Common units include Molarity (M or mol/dm³), volume of gas (cm³), or mass (g).
The Mathematical Concept: Slope
The rate of reaction at any given interval is mathematically equivalent to the gradient (slope) of the line on the graph. This relationship is defined by the change in the y-axis divided by the change in the x-axis.
Rate = | Slope | = | (y₂ – y₁) / (x₂ – x₁) |
Note: Reaction rates are conventionally reported as positive values. If you are calculating the slope for a reactant (which decreases over time), the mathematical slope will be negative. We take the absolute value to determine the rate.
Method 1: Average Rate of Reaction
To find the average rate over a specific time period (a secant line):
Pick two points on the curve corresponding to the start ($t_1$) and end ($t_2$) of the time interval.
Read the corresponding concentrations ($y_1$ and $y_2$) from the y-axis.
Subtract the initial values from the final values to find $\Delta y$ and $\Delta x$.
Divide $\Delta y$ by $\Delta x$.
Example: If concentration drops from 0.50 M at 0s to 0.20 M at 60s:
$\Delta y = 0.20 – 0.50 = -0.30$
$\Delta x = 60 – 0$
Rate = $|-0.30 / 60| = 0.005 \text{ M/s}$
Method 2: Instantaneous Rate of Reaction
To find the rate at a specific moment in time (e.g., exactly at 30 seconds):
Locate the specific time on the x-axis and mark the point on the curve.
Draw a tangent line that just touches the curve at that exact point using a ruler.
Select two convenient points on this straight tangent line (they do not have to be on the curve itself, just on the line you drew).
Calculate the slope using the coordinate inputs in the calculator above.
Why Does the Rate Change?
On a typical concentration-time graph, the curve is steepest at the beginning ($t=0$). This indicates the reaction is fastest at the start because the concentration of reactants is highest. As the reaction proceeds, the reactants are used up, the frequency of effective collisions decreases, the curve flattens out, and the rate of reaction approaches zero.