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function calculateRate() {
// Get elements
var initialConcInput = document.getElementById('initialConc');
var finalConcInput = document.getElementById('finalConc');
var initialTimeInput = document.getElementById('initialTime');
var finalTimeInput = document.getElementById('finalTime');
var resultBox = document.getElementById('resultBox');
var rateResult = document.getElementById('rateResult');
var calculationSteps = document.getElementById('calculationSteps');
var errorMsg = document.getElementById('errorMsg');
// Parse values
var c1 = parseFloat(initialConcInput.value);
var c2 = parseFloat(finalConcInput.value);
var t1 = parseFloat(initialTimeInput.value);
var t2 = parseFloat(finalTimeInput.value);
// Validation
errorMsg.style.display = 'none';
resultBox.style.display = 'none';
if (isNaN(c1) || isNaN(c2) || isNaN(t1) || isNaN(t2)) {
errorMsg.innerText = "Please enter valid numbers for all fields.";
errorMsg.style.display = 'block';
return;
}
if (t2 <= t1) {
errorMsg.innerText = "Final time must be greater than initial time.";
errorMsg.style.display = 'block';
return;
}
if (c1 < 0 || c2 < 0) {
errorMsg.innerText = "Concentration cannot be negative.";
errorMsg.style.display = 'block';
return;
}
// Calculation: Rate = – Δ[A] / Δt
// Rate = – (Final Conc – Initial Conc) / (Final Time – Initial Time)
var deltaConc = c2 – c1;
var deltaTime = t2 – t1;
// Rate of disappearance implies the value should be positive if the reactant is disappearing.
// The standard formula includes a negative sign to handle the negative slope.
var rate = -1 * (deltaConc / deltaTime);
// Formatting result
// Check if rate is negative (which technically means rate of appearance)
var rateText = "";
var labelNote = "";
if (rate 0.001 && Math.abs(rate) < 1000) {
formattedRate = rate.toFixed(5);
}
rateResult.innerText = formattedRate + " M/s";
// Show steps
// Formula: – ( [A]2 – [A]1 ) / ( t2 – t1 )
var stepHtml = "Rate = – (" + c2 + " M – " + c1 + " M) / (" + t2 + " s – " + t1 + " s)";
stepHtml += "Rate = – (" + deltaConc.toFixed(4) + ") / (" + deltaTime + ")";
stepHtml += "Result = " + formattedRate + " M/s" + labelNote;
calculationSteps.innerHTML = stepHtml;
resultBox.style.display = 'block';
}
How to Calculate Average Rate of Disappearance
In chemical kinetics, calculating the average rate of disappearance is essential for understanding how fast a reactant is consumed during a chemical reaction. Unlike the instantaneous rate, which looks at a specific moment in time, the average rate looks at the change in concentration over a defined time interval.
This calculator helps chemistry students and professionals quickly determine the rate at which a reactant concentration decreases, expressed typically in Molarity per second (M/s).
The Average Rate of Disappearance Formula
The rate of disappearance describes the decrease in the concentration of a reactant. Since the concentration of reactants decreases over time, the change in concentration ($\Delta[A]$) is negative. To express the rate as a positive value, we add a negative sign to the formula.
Formula:
Rate = – $\frac{\Delta [Reactant]}{\Delta t} = – \frac{[A]_{final} – [A]_{initial}}{t_{final} – t_{initial}}$
- $[A]_{final}$: The concentration of the reactant at the end of the interval (M).
- $[A]_{initial}$: The concentration of the reactant at the start of the interval (M).
- $t_{final}$: The time at the end of the interval (seconds).
- $t_{initial}$: The time at the start of the interval (seconds).
Step-by-Step Calculation Example
Let's look at a practical example involving the decomposition of Nitrogen Dioxide ($NO_2$).
Scenario: At the start of an experiment ($t = 0$ s), the concentration of $NO_2$ is 0.100 M. After 60 seconds, the concentration drops to 0.0066 M. What is the average rate of disappearance?
- Identify Values:
- Initial Conc ($[A]_1$) = 0.100 M
- Final Conc ($[A]_2$) = 0.0066 M
- Initial Time ($t_1$) = 0 s
- Final Time ($t_2$) = 60 s
- Calculate Change in Concentration ($\Delta[A]$):
$0.0066 – 0.100 = -0.0934 \text{ M}$
- Calculate Change in Time ($\Delta t$):
$60 – 0 = 60 \text{ seconds}$
- Apply Formula:
Rate $= – \frac{-0.0934}{60}$
Rate $= – (-0.001557)$
Rate $= 1.557 \times 10^{-3} \text{ M/s}$
Why is the Negative Sign Important?
In math and physics, rates are generally positive quantities. However, because reactants are being used up, their final concentration is always lower than their initial concentration, resulting in a negative number for $\Delta[A]$.
By placing a negative sign in front of the formula for reactants ($Rate = -\Delta[A]/\Delta t$), we convert that mathematical negative into a positive rate value, which makes physical sense (e.g., a car traveling at 60 mph, not -60 mph).
Common Units
While Molarity per second (M/s) is the standard SI unit for reaction rates in solution, you may also encounter:
- mol/L/s: Equivalent to M/s.
- M/min: Used for slower reactions.
- atm/s: Used for gaseous reactions involving partial pressures.