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function calculateK() {
// 1. Get Elements
var order = parseInt(document.getElementById('reactionOrder').value);
var initConc = parseFloat(document.getElementById('initialConc').value);
var finalConc = parseFloat(document.getElementById('finalConc').value);
var time = parseFloat(document.getElementById('timeElapsed').value);
var timeUnit = document.getElementById('timeUnit').value;
var resultContainer = document.getElementById('rccResult');
var errorContainer = document.getElementById('rccError');
var resultK = document.getElementById('resultK');
var resultHalfLife = document.getElementById('resultHalfLife');
var resultOrder = document.getElementById('resultOrder');
// 2. Reset Display
errorContainer.style.display = 'none';
resultContainer.style.display = 'none';
// 3. Validation
if (isNaN(initConc) || isNaN(finalConc) || isNaN(time)) {
errorContainer.innerHTML = "Please enter valid numbers for all fields.";
errorContainer.style.display = 'block';
return;
}
if (time <= 0) {
errorContainer.innerHTML = "Time must be greater than zero.";
errorContainer.style.display = 'block';
return;
}
if (initConc <= 0 || finalConc 0.";
errorContainer.style.display = 'block';
return;
}
// Logic constraint: For reaction to proceed forward, final conc usually initConc) {
// Usually valid for reactant decay calculator
errorContainer.innerHTML = "For reactant decomposition, Final Concentration should be less than Initial Concentration.";
errorContainer.style.display = 'block';
// We allow it to proceed but warn? No, let's block to prevent negative k for standard decay logic
return;
}
if (finalConc === initConc) {
errorContainer.innerHTML = "Concentration did not change. Rate constant cannot be calculated from zero change over time.";
errorContainer.style.display = 'block';
return;
}
// 4. Calculation Logic
var k = 0;
var halfLife = 0;
var unitLabel = "";
// Normalize unit label for display
var tUnitDisplay = "s";
if(timeUnit === "min") tUnitDisplay = "min";
if(timeUnit === "hr") tUnitDisplay = "hr";
if (order === 0) {
// Zero Order: k = ([A]0 – [A]t) / t
k = (initConc – finalConc) / time;
// Half Life: t1/2 = [A]0 / 2k
halfLife = initConc / (2 * k);
unitLabel = "M/" + tUnitDisplay;
} else if (order === 1) {
// First Order: k = ln([A]0 / [A]t) / t
if (finalConc <= 0) {
errorContainer.innerHTML = "Final concentration must be greater than 0 for First Order calculations (logarithm restriction).";
errorContainer.style.display = 'block';
return;
}
k = Math.log(initConc / finalConc) / time;
// Half Life: t1/2 = ln(2) / k
halfLife = 0.693147 / k;
unitLabel = "/" + tUnitDisplay; // e.g., s^-1
} else if (order === 2) {
// Second Order: k = (1/[A]t – 1/[A]0) / t
if (finalConc <= 0) {
errorContainer.innerHTML = "Final concentration must be greater than 0 for Second Order calculations.";
errorContainer.style.display = 'block';
return;
}
k = ((1 / finalConc) – (1 / initConc)) / time;
// Half Life: t1/2 = 1 / (k * [A]0)
halfLife = 1 / (k * initConc);
unitLabel = "1/(M·" + tUnitDisplay + ")";
}
// 5. Output Formatting
// Format numbers to appropriate sig figs (e.g., 5 decimal places or scientific notation if very small)
var displayK = k;
if (k 10000) {
displayK = k.toExponential(4);
} else {
displayK = k.toPrecision(5);
}
var displayHL = halfLife;
if (halfLife 10000) {
displayHL = halfLife.toExponential(4);
} else {
displayHL = halfLife.toPrecision(5);
}
// 6. Set Results
resultK.innerHTML = displayK + " " + unitLabel + "";
resultHalfLife.innerHTML = displayHL + " " + tUnitDisplay;
var orderText = "";
if(order === 0) orderText = "Zero Order";
if(order === 1) orderText = "First Order";
if(order === 2) orderText = "Second Order";
resultOrder.innerHTML = orderText;
// Show container
resultContainer.style.display = 'block';
}
Rate Constant Calculator (k)
Calculate the reaction rate constant based on reaction order and concentration changes.
Zero Order (Rate = k)
First Order (Rate = k[A])
Second Order (Rate = k[A]²)
Seconds (s)
Minutes (min)
Hours (hr)
Rate Constant (k):
–
Reaction Half-Life (t₁/₂):
–
Order of Reaction:
–
Understanding the Rate Constant Formula
In chemical kinetics, the rate constant (k) is a crucial proportionality factor in the rate law of a reaction. It relates the molar concentration of reactants to the rate of the reaction. The value of the rate constant depends heavily on temperature (described by the Arrhenius equation) but is independent of the reactant concentrations.
How to Calculate Rate Constant (k)
The formula to calculate the rate constant changes depending on the Order of Reaction. This calculator uses the integrated rate laws for Zero, First, and Second-order reactions:
1. Zero Order Reaction
For a zero-order reaction, the rate is independent of concentration. The formula is:
k = ([A]₀ – [A]ₜ) / t
- Units: M/s (Molarity per second)
- Half-life: [A]₀ / (2k)
2. First Order Reaction
For a first-order reaction, the rate depends linearly on one reactant. This is the most common scenario for radioactive decay and many decomposition reactions.
k = ln([A]₀ / [A]ₜ) / t
- Units: 1/s (per second)
- Half-life: ln(2) / k ≈ 0.693 / k
3. Second Order Reaction
For a second-order reaction, the rate is proportional to the square of the concentration of a single reactant (or the product of two reactants).
k = (1/[A]ₜ – 1/[A]₀) / t
- Units: 1/(M·s) (per Molar per second)
- Half-life: 1 / (k[A]₀)
Definition of Terms
- [A]₀: Initial concentration of the reactant (Molarity).
- [A]ₜ: Concentration of the reactant at time t.
- t: The time elapsed during the reaction.
- M: Molarity (moles per liter).