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How to Calculate Rate of Disappearance from Rate of Appearance
In chemical kinetics, the rate at which reactants are consumed (disappear) is directly linked to the rate at which products are formed (appear). However, these rates are rarely identical unless the stoichiometric coefficients in the balanced chemical equation are equal.
This calculator helps you solve stoichiometry problems where you are given the rate of appearance of a product and need to find the corresponding rate of disappearance of a reactant.
The Stoichiometric Relationship
For a general balanced chemical equation:
aA + … → bB + …
Where:
- A is the Reactant (disappearing).
- B is the Product (appearing).
- a is the stoichiometric coefficient of A.
- b is the stoichiometric coefficient of B.
The fundamental relationship between the rates is defined by dividing the rate of change of concentration by the stoichiometric coefficient:
Rate = -(1/a) Δ[A]/Δt = (1/b) Δ[B]/Δt
Calculation Formula
To isolate the Rate of Disappearance of A (defined as the magnitude of Δ[A]/Δt), we rearrange the formula:
Rate of Disappearance (A) = (a / b) × Rate of Appearance (B)
Real-World Example
Consider the synthesis of ammonia: N2 + 3H2 → 2NH3.
If we know that Ammonia (NH3) is appearing at a rate of 0.6 M/s, and we want to know how fast Hydrogen (H2) is disappearing:
- Identify coefficients: H2 (reactant) = 3, NH3 (product) = 2.
- Apply formula: Rate H2 = (3 / 2) × 0.6 M/s.
- Calculate: 1.5 × 0.6 = 0.9 M/s.
This means Hydrogen is being consumed faster than Ammonia is being produced, due to the 3:2 ratio required for the reaction.
function calculateDisappearanceRate() {
// Get input elements by ID strictly matching HTML
var coeffReactantInput = document.getElementById('coeffReactant');
var coeffProductInput = document.getElementById('coeffProduct');
var rateAppearanceInput = document.getElementById('rateAppearance');
var resultBox = document.getElementById('resultBox');
var resultValue = document.getElementById('resultValue');
var resultExplanation = document.getElementById('resultExplanation');
// Parse values
var a = parseFloat(coeffReactantInput.value);
var b = parseFloat(coeffProductInput.value);
var rateB = parseFloat(rateAppearanceInput.value);
// Validation logic
if (isNaN(a) || isNaN(b) || isNaN(rateB)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (a <= 0 || b <= 0) {
alert("Stoichiometric coefficients must be positive numbers greater than zero.");
return;
}
if (rateB < 0) {
alert("Rate of appearance implies a positive formation rate. Please enter a positive number.");
return;
}
// Calculation Logic: Rate A = Rate B * (a / b)
var ratio = a / b;
var rateA = rateB * ratio;
// Display Results
resultBox.style.display = "block";
// Format to reasonable decimal places (up to 4)
var formattedRate = rateA % 1 === 0 ? rateA : rateA.toFixed(4);
resultValue.innerHTML = formattedRate + " M/s";
// Dynamic explanation string
resultExplanation.innerHTML = "Calculated using ratio (" + a + "/" + b + "). For every " + b + " moles of product formed, " + a + " moles of reactant are consumed.";
}