Rate Law Expression Calculator

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Rate Law Expression Calculator

Calculated Reaction Rate:

function calculateRateLaw() { var k = parseFloat(document.getElementById('rate_k').value); var a = parseFloat(document.getElementById('conc_a').value); var m = parseFloat(document.getElementById('order_m').value); var b = parseFloat(document.getElementById('conc_b').value); var n = parseFloat(document.getElementById('order_n').value); if (isNaN(k) || isNaN(a) || isNaN(m)) { alert("Please enter at least the Rate Constant, Concentration [A], and Order (m)."); return; } var rate; var bTerm = 1; if (!isNaN(b) && !isNaN(n)) { bTerm = Math.pow(b, n); } rate = k * Math.pow(a, m) * bTerm; var resultDiv = document.getElementById('rate-result'); var rateOutput = document.getElementById('rate_output'); var eqOutput = document.getElementById('equation_output'); resultDiv.style.display = 'block'; rateOutput.innerHTML = rate.toExponential(4) + " M/s"; var eqText = "Rate = " + k + " × [" + a + "]^" + m; if (!isNaN(b) && !isNaN(n)) { eqText += " × [" + b + "]^" + n; } eqOutput.innerHTML = eqText; }

Understanding the Rate Law Expression

In chemical kinetics, the rate law expression is a mathematical equation that links the reaction rate with the concentrations of its reactants. It is fundamental for chemical engineers and researchers to predict how fast a reaction will proceed under specific conditions.

The Rate Law Formula

The general form for a reaction involving two reactants (A and B) is:

Rate = k [A]m [B]n
  • Rate: The speed of the reaction, usually measured in Molar per second (M/s).
  • k: The rate constant, which depends on temperature and the specific reaction.
  • [A] and [B]: The molar concentrations of the reactants.
  • m and n: The reaction orders (usually integers like 0, 1, or 2, though they can be fractions).

Example Calculation

Imagine a reaction where the rate constant k is 0.02, the concentration of [A] is 0.5 M, and the reaction is second-order (m = 2) with respect to A. If there is no reactant B:

  1. Identify values: k = 0.02, [A] = 0.5, m = 2.
  2. Plug into formula: Rate = 0.02 × (0.5)2.
  3. Calculate power: 0.5 × 0.5 = 0.25.
  4. Multiply by k: 0.02 × 0.25 = 0.005 M/s.

Why is the Rate Law Important?

Knowing the rate law allows scientists to determine the reaction mechanism. It reveals which steps in a multi-step reaction are the slowest (the rate-determining steps). It also helps in industrial settings to optimize the time required for chemical synthesis, ensuring efficiency and safety in large-scale production.

Note: The reaction orders (m and n) cannot be determined from the balanced chemical equation; they must be determined experimentally by observing how the rate changes when concentration varies.

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