Calculate the Ratio of Effusion Rates of Cl2 to He

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Effusion Rate Ratio Calculator (Graham's Law)

g/mol
g/mol

Understanding Effusion and Graham's Law

Effusion is the process by which gas molecules escape from a container through a tiny hole. The rate at which a gas effuses is inversely proportional to the square root of its molar mass. This principle is famously described by Graham's Law of Effusion.

Graham's Law states that for two gases at the same temperature and pressure, the ratio of their rates of effusion is equal to the inverse ratio of the square roots of their molar masses. Mathematically, this can be expressed as:

$$ \frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}} $$

Where:

  • Rate₁ is the rate of effusion of gas 1
  • Rate₂ is the rate of effusion of gas 2
  • M₁ is the molar mass of gas 1
  • M₂ is the molar mass of gas 2

In this calculator, we are comparing the effusion rate of Chlorine (Cl₂) to Helium (He). Chlorine (Cl₂) has a molar mass of approximately 70.906 g/mol, and Helium (He) has a molar mass of approximately 4.0026 g/mol. Using these values, we can determine how much faster or slower one gas effuses compared to the other.

Example Calculation:

Let's use the standard molar masses:

  • Molar Mass of Cl₂ (M₁) = 70.906 g/mol
  • Molar Mass of He (M₂) = 4.0026 g/mol

Using Graham's Law:

$$ \frac{\text{Rate}_{\text{Cl}_2}}{\text{Rate}_{\text{He}}} = \sqrt{\frac{M_{\text{He}}}{M_{\text{Cl}_2}}} $$

$$ \frac{\text{Rate}_{\text{Cl}_2}}{\text{Rate}_{\text{He}}} = \sqrt{\frac{4.0026 \text{ g/mol}}{70.906 \text{ g/mol}}} $$

$$ \frac{\text{Rate}_{\text{Cl}_2}}{\text{Rate}_{\text{He}}} \approx \sqrt{0.05645} $$

$$ \frac{\text{Rate}_{\text{Cl}_2}}{\text{Rate}_{\text{He}}} \approx 0.2376 $$

This means that for every unit of Helium that effuses, approximately 0.2376 units of Chlorine effuse. In other words, Helium effuses significantly faster than Chlorine.

function calculateEffusionRatio() { var molarMassCl2 = parseFloat(document.getElementById("molarMassCl2").value); var molarMassHe = parseFloat(document.getElementById("molarMassHe").value); var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(molarMassCl2) || isNaN(molarMassHe) || molarMassCl2 <= 0 || molarMassHe <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for molar masses."; return; } var ratio = Math.sqrt(molarMassHe / molarMassCl2); resultDiv.innerHTML = "The ratio of the effusion rate of Cl₂ to He is approximately: " + ratio.toFixed(4) + ""; resultDiv.innerHTML += "This means that for every unit of Helium that effuses, approximately " + ratio.toFixed(4) + " units of Chlorine effuse under the same conditions."; }

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