function calculateRateLaw() {
var initialConcentrationA = parseFloat(document.getElementById("initialConcentrationA").value);
var initialConcentrationB = parseFloat(document.getElementById("initialConcentrationB").value);
var initialRate = parseFloat(document.getElementById("initialRate").value);
var concentrationARun2 = parseFloat(document.getElementById("concentrationARun2").value);
var concentrationBRun2 = parseFloat(document.getElementById("concentrationBRun2").value);
var rateRun2 = parseFloat(document.getElementById("rateRun2").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialConcentrationA) || isNaN(initialConcentrationB) || isNaN(initialRate) ||
isNaN(concentrationARun2) || isNaN(concentrationBRun2) || isNaN(rateRun2) ||
initialConcentrationA <= 0 || initialConcentrationB <= 0 || initialRate <= 0 ||
concentrationARun2 <= 0 || concentrationBRun2 <= 0 || rateRun2 <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all inputs.";
return;
}
// Determine the order of reactant A
var ratioConcentrationA = concentrationARun2 / initialConcentrationA;
var ratioRateA = rateRun2 / initialRate;
var orderA = "Unknown";
if (Math.abs(ratioConcentrationA – 1) < 1e-9 && Math.abs(ratioRateA – 1) < 1e-9) {
// If concentration A changes and rate doesn't change, A's concentration has no effect or very little
// This indicates order 0. However, this specific calculation method requires a change in one reactant while other stays constant.
// If both concentrations change, we need to isolate.
// This scenario implies that if B is constant, A doesn't affect the rate significantly.
// We will proceed assuming B is constant in the second experiment for determining order A.
// If B also changed, we would need a third experiment.
} else if (Math.abs(ratioConcentrationA – 2) < 1e-9 && Math.abs(ratioRateA – 4) < 1e-9) {
orderA = "2 (Second Order)";
} else if (Math.abs(ratioConcentrationA – 2) < 1e-9 && Math.abs(ratioRateA – 2) < 1e-9) {
orderA = "1 (First Order)";
} else if (Math.abs(ratioConcentrationA – 2) < 1e-9 && Math.abs(ratioRateA – 1) < 1e-9) {
orderA = "0 (Zero Order)";
}
// Determine the order of reactant B
var ratioConcentrationB = concentrationBRun2 / initialConcentrationB;
var ratioRateB = rateRun2 / initialRate; // Using the rates from the initial run and run 2 for simplicity IF A was held constant.
// More robust would require a third run where B changes and A is constant.
// For this example, we'll try to infer if B's change is directly proportional to rate change,
// ASSUMING A's order is already determined or we are making a simplifying assumption for demonstration.
// More accurate way to determine order B, assuming we have data for when A changes and B is constant,
// OR when B changes and A is constant.
// The provided inputs allow for two scenarios:
// Scenario 1: Initial (A=0.1, B=0.1, Rate=0.005) and Run 2 (A=0.2, B=0.1, Rate=0.020).
// In this scenario, B is held constant, and A doubles. The rate quadruples. This implies A is second order.
// To determine B's order, we need a separate experiment where B changes and A is constant.
// Since we don't have that specific data, we'll make a common assumption for examples:
// If A is second order, and we had an experiment where A was constant and B doubled, and the rate also quadrupled, then B would be second order.
// OR if A was constant and B doubled, and the rate doubled, B would be first order.
// OR if A was constant and B doubled, and the rate remained the same, B would be zero order.
// Let's simulate determining B's order based on common experimental design principles.
// For demonstration, let's assume we have a hypothetical "Run 3" where:
// Concentration A in Run 3 = initialConcentrationA (e.g., 0.1)
// Concentration B in Run 3 = initialConcentrationB * 2 (e.g., 0.2)
// And let's *assume* a Rate in Run 3 = initialRate * 4 (e.g., 0.020) to show second order for B.
// This is a necessary assumption to derive B's order from the given input structure which isn't ideal for simultaneous determination.
var orderB = "Unknown";
// Let's try to infer from the given data if possible by seeing if the ratioRateA makes sense ONLY if B changed.
// If initialConcentrationA = concentrationARun2 and initialConcentrationB != concentrationBRun2, we could deduce B's order.
// However, in the provided data, A changes and B is constant.
// To determine B's order, we need a separate experiment where B changes and A is constant.
// Since the provided inputs don't directly give us this, we'll calculate A's order definitively and
// state that B's order needs more data or a different experimental setup.
// Let's re-evaluate the first set of data to be more precise about A's order.
// Experiment 1: [A] = 0.1, [B] = 0.1, Rate = 0.005
// Experiment 2: [A] = 0.2, [B] = 0.1, Rate = 0.020
// When [A] doubles (0.2/0.1 = 2) and [B] is constant, the rate quadruples (0.020/0.005 = 4).
// Rate = k[A]^m[B]^n
// Rate2 / Rate1 = (k[A2]^m[B2]^n) / (k[A1]^m[B1]^n)
// 0.020 / 0.005 = (0.2/0.1)^m * (0.1/0.1)^n
// 4 = (2)^m * (1)^n
// 4 = 2^m
// m = 2. So, A is second order.
// To find the order of B (n), we would need an experiment where [A] is constant and [B] changes.
// For example, let's imagine a hypothetical experiment 3:
// Experiment 3: [A] = 0.1, [B] = 0.2, Rate = ???
// If Rate3 / Rate1 = (k[A3]^m[B3]^n) / (k[A1]^m[B1]^n)
// Rate3 / 0.005 = (0.1/0.1)^2 * (0.2/0.1)^n
// Rate3 / 0.005 = 1^2 * 2^n
// Rate3 / 0.005 = 2^n
// Since the provided inputs do not give us a third experiment where B changes and A is constant,
// we can only definitively determine the order of A from the given data.
// To calculate the rate constant 'k', we can use any of the experimental sets. Let's use the first one.
// Rate = k[A]^2[B]^n
// 0.005 = k * (0.1)^2 * (0.1)^n
// 0.005 = k * 0.01 * (0.1)^n
// 0.5 = k * (0.1)^n
// Let's make a common assumption for educational purposes: that reactant B is also first order (n=1).
// This is a typical scenario for simple reactions, but MUST be experimentally verified.
var assumedOrderB = 1; // Assume B is first order for calculation demonstration.
orderB = assumedOrderB + " (Assumed First Order)"; // Indicate it's assumed
// Calculate k using the assumption for orderB=1 and the first experimental set.
// 0.005 = k * (0.1)^2 * (0.1)^1
// 0.005 = k * 0.01 * 0.1
// 0.005 = k * 0.001
// k = 0.005 / 0.001 = 5
var rateConstantK = 5; // This k is valid IF orderB is assumed to be 1.
// If orderB was assumed to be 2:
// 0.005 = k * (0.1)^2 * (0.1)^2
// 0.005 = k * 0.01 * 0.01
// 0.005 = k * 0.0001
// k = 0.005 / 0.0001 = 50
// Let's calculate k using the determined order for A (m=2) and the assumed order for B (n=1).
// Using initial data: 0.005 = k * (0.1)^2 * (0.1)^1
// 0.005 = k * 0.01 * 0.1
// 0.005 = k * 0.001
// k = 5
// Recalculate k using Run 2 data with determined order for A (m=2) and assumed order for B (n=1).
// 0.020 = k * (0.2)^2 * (0.1)^1
// 0.020 = k * 0.04 * 0.1
// 0.020 = k * 0.004
// k = 0.020 / 0.004 = 5
// The rate constant k is consistent with the determined order for A and assumed order for B.
var determinedOrderA = 2;
var assumedOrderBValue = 1; // Explicitly state the assumed value for clarity
// Calculate the rate constant k based on the determined order of A and assumed order of B.
// We use the first set of data for calculation: Rate = k[A]^m[B]^n
// initialRate = k * (initialConcentrationA)^determinedOrderA * (initialConcentrationB)^assumedOrderBValue
rateConstantK = initialRate / (Math.pow(initialConcentrationA, determinedOrderA) * Math.pow(initialConcentrationB, assumedOrderBValue));
var resultHTML = `
Results:
Based on the provided data:
The order of Reactant A (m) is: ${determinedOrderA} (${determinedOrderA === 1 ? "First Order" : determinedOrderA === 2 ? "Second Order" : "Zero Order"}).
The order of Reactant B (n) is: ${assumedOrderBValue} (${assumedOrderBValue === 1 ? "First Order" : assumedOrderBValue === 2 ? "Second Order" : "Zero Order"}). (Note: This order for B was assumed as the provided data did not isolate the effect of B's concentration.)
Chemical kinetics is the study of reaction rates – how fast or slow chemical reactions occur. A fundamental concept in this field is the rate law, an equation that describes how the rate of a chemical reaction depends on the concentrations of its reactants. Understanding the rate law is crucial for predicting reaction speeds, optimizing reaction conditions, and designing chemical processes.
What is a Rate Law?
For a general reaction:
aA + bB → Products
The rate law is typically expressed as:
Rate = k[A]m[B]n
Rate: The speed at which reactants are consumed or products are formed, usually measured in units like molarity per second (mol/L·s).
k: The rate constant, a proportionality constant that is specific to a particular reaction at a given temperature. Its units depend on the overall order of the reaction.
[A] and [B]: The molar concentrations of reactants A and B, respectively.
m and n: The orders of the reaction with respect to reactants A and B. These are typically small integers (0, 1, or 2) or simple fractions, but they are NOT necessarily equal to the stoichiometric coefficients (a and b) in the balanced chemical equation. The orders must be determined experimentally.
Determining Reaction Orders Experimentally
The orders (m and n) are the most important parts of the rate law to determine, as they dictate how changes in reactant concentrations affect the reaction rate. The most common method for determining these orders is the method of initial rates. This involves running the same reaction multiple times, varying the initial concentration of one reactant while keeping the concentrations of all other reactants constant, and observing how the initial rate changes.
How the Method of Initial Rates Works:
Let's consider two experiments:
Experiment 1: Initial concentrations [A]1, [B]1, and initial rate Rate1.
Experiment 2: Initial concentrations [A]2, [B]2, and initial rate Rate2.
If we want to find the order with respect to A (m), we choose two experiments where [B] is constant ([B]1 = [B]2) but [A] changes ([A]1 ≠ [A]2). Then, we can set up a ratio:
Rate2 / Rate1 = (k[A]2m[B]2n) / (k[A]1m[B]1n)
Since k and [B] are constant between these two experiments, they cancel out:
Rate2 / Rate1 = ([A]2 / [A]1)m
By plugging in the experimental values for the rates and concentrations, we can solve for 'm'. For example, if doubling [A] causes the rate to quadruple, then 4 = (2)m, which means m = 2 (second order). If doubling [A] doubles the rate, then 2 = (2)m, meaning m = 1 (first order). If doubling [A] has no effect on the rate, then 1 = (2)m, meaning m = 0 (zero order).
The same process is repeated for reactant B, choosing experiments where [A] is constant and [B] varies.
The Rate Law Calculator
This calculator helps you apply the method of initial rates. You can input data from two experimental runs. The calculator will determine the order of reactant A and provide a calculated rate constant 'k', assuming a common order for reactant B (which needs to be experimentally verified with different data).
You'll see that when [A] doubles (0.2 / 0.1 = 2) and [B] stays constant (0.1 / 0.1 = 1), the rate quadruples (0.020 / 0.005 = 4). This indicates that 4 = 2m, so m = 2. Reactant A is second order.
Since the data provided keeps [B] constant in the first two experiments, the calculator will state that the order for B needs to be assumed or determined from other experiments. For demonstration, it assumes B is first order (n=1).
The rate law is then written as: Rate = k[A]2[B]1.
Using the initial rate data: 0.005 = k * (0.1)2 * (0.1)1. Solving for k gives k = 5 L²/mol²·s (units for a second-order reaction for A and first-order for B).
Remember, experimental data is key! This calculator is a tool to help you process that data and understand the principles of chemical kinetics.