.calc-box {
background: #f8f9fa;
padding: 30px;
border-radius: 12px;
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
border: 1px solid #e9ecef;
margin-bottom: 40px;
}
.calc-title {
text-align: center;
color: #2c3e50;
margin-bottom: 25px;
font-size: 24px;
font-weight: 700;
}
.input-group {
margin-bottom: 20px;
}
.input-label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: #495057;
}
.calc-input {
width: 100%;
padding: 12px;
border: 1px solid #ced4da;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.2s;
box-sizing: border-box;
}
.calc-input:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 0 3px rgba(0,123,255,0.25);
}
.calc-btn {
width: 100%;
padding: 14px;
background: #007bff;
color: white;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: 600;
cursor: pointer;
transition: background 0.2s;
margin-top: 10px;
}
.calc-btn:hover {
background: #0056b3;
}
.result-box {
margin-top: 25px;
padding: 20px;
background: #ffffff;
border-radius: 8px;
border-left: 5px solid #007bff;
display: none;
}
.result-label {
font-size: 14px;
color: #6c757d;
text-transform: uppercase;
letter-spacing: 1px;
}
.result-value {
font-size: 32px;
font-weight: 700;
color: #2c3e50;
margin: 10px 0;
}
.result-explanation {
font-size: 14px;
color: #495057;
line-height: 1.5;
padding-top: 10px;
border-top: 1px solid #dee2e6;
}
.error-msg {
color: #dc3545;
font-size: 14px;
margin-top: 5px;
display: none;
}
.row {
display: flex;
gap: 20px;
}
.col {
flex: 1;
}
@media (max-width: 600px) {
.row { flex-direction: column; gap: 0; }
}
.article-content h2 {
color: #2c3e50;
border-bottom: 2px solid #007bff;
padding-bottom: 10px;
margin-top: 40px;
}
.article-content h3 {
color: #495057;
margin-top: 25px;
}
.article-content p {
line-height: 1.7;
margin-bottom: 15px;
}
.article-content ul {
margin-bottom: 20px;
padding-left: 20px;
}
.article-content li {
margin-bottom: 8px;
line-height: 1.6;
}
.formula-box {
background: #eef2f5;
padding: 15px;
border-radius: 6px;
font-family: monospace;
text-align: center;
font-size: 18px;
margin: 20px 0;
}
Understanding the Average Rate of Disappearance
In chemical kinetics, the Average Rate of Disappearance measures how quickly the concentration of a specific reactant decreases over a given time interval. As a reaction proceeds, reactants are consumed to form products, causing their concentration to drop. This calculator helps students, chemists, and researchers quantify that change efficiently.
The Formula
Because the concentration of reactants decreases over time, the change in concentration ($\Delta[A]$) is mathematically negative. To express the rate as a positive value (which is standard convention), we multiply the change by negative one. The formula is:
Rate = – ( [A]₂ – [A]₁ ) / ( t₂ – t₁ )
Where:
- [A]₁ = Initial concentration of the reactant (Molarity).
- [A]₂ = Final concentration of the reactant (Molarity).
- t₁ = Initial time (usually seconds or minutes).
- t₂ = Final time.
How to Calculate Rate of Disappearance
To perform the calculation manually or using the tool above, follow these steps:
- Identify the Initial Concentration at the start of your observation period.
- Measure the Final Concentration after a specific duration.
- Determine the total Time Elapsed ($t_2 – t_1$).
- Subtract the final concentration from the initial concentration to find the total amount lost.
- Divide that amount by the time elapsed.
Example Calculation
Consider the decomposition of Dinitrogen Pentoxide ($N_2O_5$). Suppose we have the following data:
- Initial Concentration ($t = 0$ s): 1.00 M
- Final Concentration ($t = 200$ s): 0.88 M
Calculation:
- $\Delta[A] = 0.88 M – 1.00 M = -0.12 M$
- $\Delta t = 200 s – 0 s = 200 s$
- Rate = -(-0.12) / 200 = 0.0006 M/s
Why is the Rate Positive?
Rates of reaction are defined as positive quantities. Since reactants are "disappearing," their final concentration is lower than their initial concentration, resulting in a negative change ($\Delta$). By adding a negative sign to the formula for reactants, we ensure the calculated rate represents a positive speed of reaction.
Instantaneous vs. Average Rate
It is important to note that this tool calculates the average rate over a specific time interval. The instantaneous rate is the rate at a specific moment in time (the slope of the tangent line on a concentration vs. time graph). As the time interval ($\Delta t$) becomes smaller, the average rate approaches the instantaneous rate.
function calculateDisappearanceRate() {
// Get DOM elements
var conc1Input = document.getElementById('conc1');
var conc2Input = document.getElementById('conc2');
var time1Input = document.getElementById('time1');
var time2Input = document.getElementById('time2');
var resultBox = document.getElementById('result-container');
var finalRateDisplay = document.getElementById('final-rate');
var stepsDisplay = document.getElementById('calculation-steps');
var errorMsg = document.getElementById('error-message');
// Parse values
var c1 = parseFloat(conc1Input.value);
var c2 = parseFloat(conc2Input.value);
var t1 = parseFloat(time1Input.value);
var t2 = parseFloat(time2Input.value);
// Validation
if (isNaN(c1) || isNaN(c2) || isNaN(t1) || isNaN(t2)) {
errorMsg.style.display = "block";
resultBox.style.display = "none";
errorMsg.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (t2 === t1) {
errorMsg.style.display = "block";
resultBox.style.display = "none";
errorMsg.innerHTML = "Final time cannot equal initial time (division by zero).";
return;
}
errorMsg.style.display = "none";
// Calculation: Rate = -(C2 – C1) / (t2 – t1)
var deltaConc = c2 – c1;
var deltaTime = t2 – t1;
// The formula typically includes a negative sign because reactants decrease
var rate = -(deltaConc) / deltaTime;
// Formatting results
// Determine units (generic assumption M/s based on placeholders, but dynamic in text)
var unit = "M/s"; // Molarity per second
// Handle edge case where user enters product data (concentration increases)
var note = "";
if (rate < 0) {
note = "
The negative result suggests the concentration increased. This calculates the 'Rate of Appearance' rather than disappearance.";
}
// Display results
resultBox.style.display = "block";
finalRateDisplay.innerHTML = rate.toExponential(4) + "
";
stepHtml += "Δ[A] = " + c2 + " – " + c1 + " = " + deltaConc.toFixed(4) + " M";
stepHtml += "Δt = " + t2 + " – " + t1 + " = " + deltaTime.toFixed(2) + " s";
stepHtml += "Rate = -(" + deltaConc.toFixed(4) + ") / " + deltaTime.toFixed(2);
stepHtml += note;
stepsDisplay.innerHTML = stepHtml;
}