Understanding Rate Laws
The rate law for a chemical reaction expresses the relationship between the rate of the reaction and the concentrations of the reactants. For a general reaction:
aA + bB → products
The rate law is typically written as:
Rate = k[A]^m[B]^n
Where:
Rate is the speed of the reaction.k is the rate constant, which is specific to the reaction and temperature.[A] and [B] are the molar concentrations of reactants A and B, respectively.m and n are the orders of the reaction with respect to reactants A and B, respectively. These exponents are determined experimentally and do not necessarily equal the stoichiometric coefficients (a and b).
The overall order of the reaction is the sum of the individual orders (m + n).
How to Use This Calculator:
To use this calculator, you need to input data from experiments. Typically, you would have multiple experiments where the initial concentrations of reactants are varied, and the initial rate of the reaction is measured for each condition. You will need to have determined the experimental orders of reaction with respect to each reactant (m and n) beforehand, often through methods like the method of initial rates.
Once you have the initial concentration of a reactant, the initial rate of reaction, and the experimentally determined order of that reactant, you can use this calculator to find the rate constant (k).
Example Calculation:
Consider the reaction: 2NO(g) + O₂(g) → 2NO₂(g)
Let's say you have determined the rate law to be Rate = k[NO]²[O₂]¹.
From an experiment, you find the following data:
- Initial [NO] = 0.020 mol/L
- Initial [O₂] = 0.010 mol/L
- Initial Rate = 5.0 x 10⁻⁵ mol/(L·s)
- Order with respect to NO (m) = 2
- Order with respect to O₂ (n) = 1
Inputting these values into the calculator:
- Initial Concentration of Reactant A (NO): 0.020
- Initial Concentration of Reactant B (O₂): 0.010
- Initial Rate of Reaction: 0.00005
- Order of Reaction with respect to A (NO): 2
- Order of Reaction with respect to B (O₂): 1
The calculator will then determine the value of k.
function calculateRateLawConstant() {
var initialConcentrationA = parseFloat(document.getElementById("initialConcentrationA").value);
var initialConcentrationB = parseFloat(document.getElementById("initialConcentrationB").value);
var initialRate = parseFloat(document.getElementById("initialRate").value);
var exponentA = parseFloat(document.getElementById("exponentA").value);
var exponentB = parseFloat(document.getElementById("exponentB").value);
var resultElement = document.getElementById("rateLawResult");
resultElement.innerHTML = ""; // Clear previous results
if (isNaN(initialConcentrationA) || isNaN(initialConcentrationB) || isNaN(initialRate) || isNaN(exponentA) || isNaN(exponentB)) {
resultElement.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (initialConcentrationA <= 0 || initialConcentrationB <= 0 || initialRate < 0) {
resultElement.innerHTML = "Concentrations must be positive, and rate cannot be negative.";
return;
}
// Rate = k * [A]^m * [B]^n
// k = Rate / ([A]^m * [B]^n)
var denominator = Math.pow(initialConcentrationA, exponentA) * Math.pow(initialConcentrationB, exponentB);
if (denominator === 0) {
resultElement.innerHTML = "Cannot calculate: Denominator is zero (division by zero).";
return;
}
var rateConstant = initialRate / denominator;
// Determine units of k based on overall reaction order
var overallOrder = exponentA + exponentB;
var unitsOfK = "";
if (overallOrder === 0) {
unitsOfK = "s⁻¹"; // units of Rate (mol/L·s)
} else if (overallOrder === 1) {
unitsOfK = "L/(mol·s)"; // units of Rate (mol/L·s) / (mol/L)
} else if (overallOrder === 2) {
unitsOfK = "L²/(mol²·s)"; // units of Rate (mol/L·s) / ((mol/L)²)
} else if (overallOrder === 3) {
unitsOfK = "L³/(mol³·s)"; // units of Rate (mol/L·s) / ((mol/L)³)
} else {
// General case for other orders
unitsOfK = "L^" + overallOrder + "/(mol^" + overallOrder + "·s)";
}
resultElement.innerHTML = "The calculated rate constant (k) is:
" + rateConstant.toExponential() + " " + unitsOfK + "";
}
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