.calc-container {
max-width: 800px;
margin: 20px auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
background: #f9f9f9;
border: 1px solid #e0e0e0;
border-radius: 8px;
padding: 30px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-header {
text-align: center;
margin-bottom: 25px;
color: #2c3e50;
}
.calc-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: #444;
}
.input-group input, .input-group select {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.input-group .help-text {
font-size: 12px;
color: #777;
margin-top: 3px;
}
.calc-btn {
grid-column: span 2;
background-color: #27ae60;
color: white;
padding: 15px;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background 0.3s;
width: 100%;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #219150;
}
.results-area {
grid-column: span 2;
background: #fff;
border: 1px solid #ddd;
padding: 20px;
border-radius: 4px;
margin-top: 20px;
display: none;
}
.result-row {
display: flex;
justify-content: space-between;
padding: 10px 0;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
color: #555;
font-weight: 600;
}
.result-value {
color: #2c3e50;
font-weight: bold;
font-size: 1.1em;
}
.error-msg {
color: #c0392b;
text-align: center;
grid-column: span 2;
display: none;
margin-top: 10px;
}
/* Article Styles */
.content-area {
max-width: 800px;
margin: 40px auto;
font-family: 'Georgia', serif;
line-height: 1.6;
color: #333;
}
.content-area h2 {
color: #2c3e50;
border-bottom: 2px solid #27ae60;
padding-bottom: 10px;
margin-top: 30px;
}
.content-area p {
margin-bottom: 15px;
}
.content-area ul {
margin-bottom: 20px;
padding-left: 20px;
}
.content-area li {
margin-bottom: 8px;
}
.formula-box {
background: #edf7ed;
padding: 15px;
border-left: 4px solid #27ae60;
font-family: monospace;
margin: 20px 0;
}
@media (max-width: 600px) {
.calc-grid {
grid-template-columns: 1fr;
}
.calc-btn, .results-area, .error-msg {
grid-column: span 1;
}
}
function calculateDecomposition() {
var initial = document.getElementById('initialAmount').value;
var remaining = document.getElementById('remainingAmount').value;
var time = document.getElementById('timeElapsed').value;
var unit = document.getElementById('timeUnit').value;
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('resultsArea');
// Reset display
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
// Validation
if (initial === "" || remaining === "" || time === "") {
errorDiv.innerHTML = "Please fill in all fields.";
errorDiv.style.display = 'block';
return;
}
var N0 = parseFloat(initial);
var Nt = parseFloat(remaining);
var t = parseFloat(time);
if (isNaN(N0) || isNaN(Nt) || isNaN(t)) {
errorDiv.innerHTML = "Please enter valid numbers.";
errorDiv.style.display = 'block';
return;
}
if (t <= 0) {
errorDiv.innerHTML = "Time elapsed must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
if (Nt = N0) {
errorDiv.innerHTML = "Remaining quantity must be less than initial quantity (Decomposition implies loss).";
errorDiv.style.display = 'block';
return;
}
// Logic: First Order Kinetics
// Formula: k = -ln(Nt / N0) / t
var ratio = Nt / N0;
var logRatio = Math.log(ratio); // Natural log
var k = -1 * (logRatio / t);
// Half life formula: t(1/2) = ln(2) / k
var halfLife = Math.log(2) / k;
// Formatting results
// Rate constant unit is usually inverse time (e.g., s^-1, min^-1)
var unitSuffix = "";
if(unit === "seconds") unitSuffix = " s⁻¹";
else if(unit === "minutes") unitSuffix = " min⁻¹";
else if(unit === "hours") unitSuffix = " h⁻¹";
else if(unit === "days") unitSuffix = " d⁻¹";
else if(unit === "years") unitSuffix = " yr⁻¹";
document.getElementById('rateConstant').innerHTML = k.toPrecision(6) + unitSuffix;
document.getElementById('halfLife').innerHTML = halfLife.toFixed(2) + " " + unit;
resultsDiv.style.display = 'block';
}
How to Calculate Rate of Decomposition
Calculating the rate of decomposition is a fundamental concept in physical chemistry, pharmacology, and environmental science. It allows researchers to understand how quickly a substance breaks down into its constituent parts or simpler compounds over time. This process typically follows First-Order Kinetics, where the rate of the reaction depends linearly on the concentration of one reactant.
Whether you are determining the shelf-life of a drug, the radioactive decay of an isotope, or the breakdown of an organic pollutant, understanding the mathematical relationship between concentration and time is essential.
The First-Order Rate Equation
For most decomposition reactions, the rate at which the substance disappears is proportional to the amount of substance remaining at that instant. This relationship is described by the integrated rate law:
ln(Nₜ / N₀) = -kt
Where:
- Nₜ = The quantity of substance remaining at time t.
- N₀ = The initial quantity of the substance.
- k = The decomposition rate constant.
- t = The time elapsed.
To solve for the rate constant (k), which is the specific metric calculated by the tool above, we rearrange the formula:
k = -ln(Nₜ / N₀) / t
Understanding Half-Life
A derived metric commonly used alongside the rate of decomposition is the Half-Life (t½). This represents the time required for the quantity of the substance to reduce to exactly half of its initial value. It is inversely proportional to the rate constant:
t½ = ln(2) / k ≈ 0.693 / k
A higher rate constant (k) implies a faster decomposition and a shorter half-life. Conversely, a stable substance will have a very low k value and a long half-life.
Steps to Perform the Calculation
- Measure Initial Quantity (N₀): Determine the starting mass, molarity, or percentage (usually 100%) of the substance.
- Measure Remaining Quantity (Nₜ): After a specific period, measure how much of the substance remains undecomposed.
- Record Time (t): Note the exact duration between the two measurements. Ensure units (seconds, minutes, days) are consistent.
- Apply the Logarithm: Divide the remaining amount by the initial amount and take the natural logarithm (ln) of the result.
- Divide by Time: Divide the negative of the log result by the time elapsed to find k.
Applications of Decomposition Rates
Pharmacology: Pharmaceutical companies use these calculations to determine expiration dates. If a drug decomposes too quickly, it loses efficacy. The rate constant helps predict when the drug's concentration will fall below the therapeutic threshold.
Forensics: In forensic science, biological decomposition rates (often modified by temperature, known as Accumulated Degree Days) help estimate the Post-Mortem Interval (PMI). While biological systems are complex, the underlying concept of measuring decay over time remains central.
Environmental Science: Calculating how fast pollutants decompose in water or soil helps in assessing environmental impact and planning remediation strategies.