Calculate the Ratio of Effusion Rates of O2 and H2

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Graham's Law Effusion Ratio Calculator

Result Analysis

function calculateEffusionRatio() { var g1Name = document.getElementById("gas1Name").value; var g1Mass = parseFloat(document.getElementById("molarMass1").value); var g2Name = document.getElementById("gas2Name").value; var g2Mass = parseFloat(document.getElementById("molarMass2").value); var resultDiv = document.getElementById("effusionResult"); var ratioText = document.getElementById("ratioText"); var comparisonText = document.getElementById("comparisonText"); if (isNaN(g1Mass) || isNaN(g2Mass) || g1Mass <= 0 || g2Mass <= 0) { alert("Please enter valid molar masses greater than zero."); return; } // Graham's Law: Rate1 / Rate2 = sqrt(M2 / M1) var ratio = Math.sqrt(g2Mass / g1Mass); var inverseRatio = 1 / ratio; resultDiv.style.display = "block"; ratioText.innerHTML = "Ratio (Rate " + g1Name + " / Rate " + g2Name + "): " + ratio.toFixed(4); if (ratio 1) { comparisonText.innerHTML = g1Name + " effuses " + ratio.toFixed(2) + " times faster than " + g2Name + " because it has a lower molar mass."; } else { comparisonText.innerHTML = "Both gases effuse at the same rate because their molar masses are identical."; } }

Understanding Graham's Law: Effusion Rates of Oxygen and Hydrogen

In physical chemistry, the behavior of gases is governed by several fundamental principles. When calculating the ratio of effusion rates between two gases, such as Oxygen (O₂) and Hydrogen (H₂), we use Graham's Law of Effusion. This law provides a quantitative relationship between the molar mass of a gas and the speed at which it escapes through a tiny orifice into a vacuum.

The Formula for Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The mathematical formula is expressed as:

Rate₁ / Rate₂ = √(Molar Mass₂ / Molar Mass₁)

Step-by-Step Calculation: O₂ vs. H₂

To calculate the ratio of the effusion rates of Oxygen to Hydrogen, we follow these steps:

  1. Identify Molar Masses:
    • The molar mass of Oxygen (O₂) is approximately 32.00 g/mol (16.00 x 2).
    • The molar mass of Hydrogen (H₂) is approximately 2.016 g/mol (1.008 x 2).
  2. Apply the Formula: Let Gas 1 be Oxygen and Gas 2 be Hydrogen.
    • Rate(O₂) / Rate(H₂) = √(2.016 / 32.00)
    • Rate(O₂) / Rate(H₂) = √0.063
    • Rate(O₂) / Rate(H₂) ≈ 0.251

This result tells us that Oxygen effuses at only about 25% of the speed of Hydrogen. Alternatively, if we flip the ratio (Rate H₂ / Rate O₂), we find that Hydrogen effuses approximately 3.98 times faster than Oxygen.

Why Does This Happen?

Effusion is a kinetic process. According to the Kinetic Molecular Theory, at a given temperature, all gas molecules have the same average kinetic energy. Since Kinetic Energy = ½mv², a molecule with a smaller mass (m) must have a higher velocity (v) to maintain the same energy level as a heavier molecule. Because Hydrogen molecules are much lighter than Oxygen molecules, they move significantly faster and strike the effusion hole more frequently.

Real-World Applications

  • Isotope Separation: Graham's Law was historically used to separate Uranium isotopes for nuclear applications.
  • Safety: Understanding how quickly gases like natural gas or hydrogen leak in confined spaces.
  • Gas Analysis: Determining the molar mass of an unknown gas by comparing its effusion rate to a known standard.

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