function updateLabels() {
var sUnit = document.getElementById('substanceUnit').value;
var tUnit = document.getElementById('timeUnit').value;
var resultUnitDisplay = sUnit + "/" + tUnit;
document.getElementById('resultUnit').innerHTML = resultUnitDisplay;
var qtySpans = document.getElementsByClassName('qtyUnitDisplay');
for(var i = 0; i < qtySpans.length; i++) {
qtySpans[i].innerText = sUnit;
}
var timeSpans = document.getElementsByClassName('timeUnitDisplay');
for(var i = 0; i < timeSpans.length; i++) {
timeSpans[i].innerText = tUnit;
}
}
function calculateRate() {
// Get inputs
var initVal = document.getElementById('initVal').value;
var finalVal = document.getElementById('finalVal').value;
var startTime = document.getElementById('startTime').value;
var endTime = document.getElementById('endTime').value;
var errorDiv = document.getElementById('errorDisplay');
var resultBox = document.getElementById('resultBox');
// Reset UI
errorDiv.style.display = 'none';
resultBox.style.display = 'none';
// Validation
if (initVal === "" || finalVal === "" || startTime === "" || endTime === "") {
errorDiv.innerText = "Please fill in all fields.";
errorDiv.style.display = 'block';
return;
}
var a1 = parseFloat(initVal);
var a2 = parseFloat(finalVal);
var t1 = parseFloat(startTime);
var t2 = parseFloat(endTime);
if (isNaN(a1) || isNaN(a2) || isNaN(t1) || isNaN(t2)) {
errorDiv.innerText = "Please enter valid numbers.";
errorDiv.style.display = 'block';
return;
}
if (t2 A1, rate is negative.
// Display Results
document.getElementById('calcResult').innerText = rate.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 6});
document.getElementById('deltaQty').innerText = deltaA.toFixed(4);
document.getElementById('deltaTime').innerText = deltaT.toFixed(4);
updateLabels(); // Ensure units are synced
resultBox.style.display = 'block';
}
// Initialize labels on load
updateLabels();
How to Calculate Average Rate of Decomposition
In chemical kinetics, the rate of decomposition refers to the speed at which a reactant is used up in a chemical reaction. Unlike reaction rates for product formation, decomposition rates focus on the disappearance of a substance over a specific period.
Because the concentration of a reactant decreases over time, the change in concentration ($\Delta[A]$) is mathematically negative. To express the rate as a positive value (which is standard convention in chemistry), a negative sign is applied to the formula.
Formula:
Average Rate = – (Δ[Reactant] / Δt)
Average Rate = – ([A]₂ – [A]₁) / (t₂ – t₁)
Variables Explained
[A]₁: The initial concentration, mass, or quantity of the reactant at the start time.
[A]₂: The final concentration, mass, or quantity of the reactant at the end time.
t₁: The initial time (often 0 seconds).
t₂: The final time at which the measurement is taken.
Step-by-Step Calculation Example
Let's assume we are monitoring the decomposition of Hydrogen Peroxide ($H_2O_2$). We start with a concentration of 1.00 M. After 120 seconds, the concentration drops to 0.65 M.
Given:
[A]₁ = 1.00 M
[A]₂ = 0.65 M
t₁ = 0 s
t₂ = 120 s
The units for the average rate of decomposition depend on the input values used:
Quantity Type
Time Unit
Rate Unit
Molarity (M)
Seconds (s)
M/s (Molar per second)
Moles (mol)
Minutes (min)
mol/min
Mass (g)
Hours (h)
g/h
Instantaneous vs. Average Rate
This calculator determines the average rate over a specific time interval. In reality, the rate of decomposition usually slows down as the concentration of the reactant decreases (according to the rate law of the reaction). To find the instantaneous rate at a specific moment, one would typically calculate the slope of the tangent line to the concentration-time curve at that specific point, typically using calculus derivatives.
Why is the Rate Positive?
Mathematically, the slope of a decomposition graph is negative because the value on the Y-axis (concentration) is dropping. However, chemists express "rate" as a scalar, positive magnitude representing speed. Therefore, we multiply the negative slope by -1 to get a positive rate value.