Calculate Effusion Rate

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Graham's Law of Effusion Calculator

Understanding Graham's Law of Effusion

Graham's Law of Effusion is a fundamental principle in chemistry that describes the rate at which gases escape through a small opening (effusion) or mix with each other (diffusion). The law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass. In simpler terms, lighter gases move faster and therefore effuse or diffuse more quickly than heavier gases under the same conditions of temperature and pressure.

The mathematical expression for Graham's Law is:

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

Where:

  • $Rate_1$ is the rate of effusion of Gas 1
  • $Rate_2$ is the rate of effusion of Gas 2
  • $M_1$ is the molar mass of Gas 1
  • $M_2$ is the molar mass of Gas 2

This calculator helps you determine the ratio of the effusion rates of two gases based on their molar masses. This is particularly useful for understanding separation techniques like gas chromatography or predicting how quickly different gases will escape a container.

How to Use the Calculator:

  1. Enter the molar mass of the first gas in grams per mole (g/mol) into the "Molar Mass of Gas 1" field.
  2. Enter the molar mass of the second gas in grams per mole (g/mol) into the "Molar Mass of Gas 2" field.
  3. Click the "Calculate Rate Ratio" button.
  4. The result will show the ratio of the effusion rate of Gas 1 to the effusion rate of Gas 2. A ratio greater than 1 indicates that Gas 1 effuses faster than Gas 2.

Example:

Let's compare the effusion rate of Helium (He) with Nitrogen ($N_2$).

  • Molar Mass of Helium ($M_1$): Approximately 4.00 g/mol
  • Molar Mass of Nitrogen ($M_2$): Approximately 28.01 g/mol

Using our calculator, you would input 4.00 for Gas 1 and 28.01 for Gas 2. The result will tell you how much faster Helium effuses compared to Nitrogen.

function calculateEffusionRate() { var molarMass1 = parseFloat(document.getElementById("molarMass1").value); var molarMass2 = parseFloat(document.getElementById("molarMass2").value); var resultDiv = document.getElementById("result"); if (isNaN(molarMass1) || isNaN(molarMass2) || molarMass1 <= 0 || molarMass2 <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for molar masses."; return; } var rateRatio = Math.sqrt(molarMass2 / molarMass1); resultDiv.innerHTML = "The ratio of the effusion rate of Gas 1 to Gas 2 is: " + rateRatio.toFixed(4) + " (This means Gas 1 effuses " + rateRatio.toFixed(4) + " times faster than Gas 2 if Gas 1 is lighter, or slower if Gas 1 is heavier)."; }

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