The rate of effusion is a concept in chemistry that describes how quickly a gas escapes through a small opening (like a pinhole in a container). This phenomenon is governed by Graham's Law of Effusion.
Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass, provided that temperature and pressure are constant. Mathematically, it can be expressed as:
$$ \text{Rate}_1 $$ is the rate of effusion of Gas 1
$$ \text{Rate}_2 $$ 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 rates of effusion between two gases, given their molar masses. The gas with the lower molar mass will effuse faster than the gas with the higher molar mass. For instance, hydrogen (H₂), with a molar mass of approximately 2.016 g/mol, will effuse significantly faster than nitrogen (N₂), which has a molar mass of about 28.014 g/mol, under the same conditions.
To use the calculator, simply enter the molar masses of the two gases you wish to compare, and it will output the ratio of their effusion rates.
function calculateEffusionRate() {
var molarMassGas1 = parseFloat(document.getElementById("molarMassGas1").value);
var molarMassGas2 = parseFloat(document.getElementById("molarMassGas2").value);
var resultDiv = document.getElementById("result");
// Clear previous results
resultDiv.innerHTML = "";
if (isNaN(molarMassGas1) || isNaN(molarMassGas2) || molarMassGas1 <= 0 || molarMassGas2 <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for both molar masses.";
return;
}
// Calculate the ratio of effusion rates using Graham's Law
// Rate1 / Rate2 = sqrt(M2 / M1)
var rateRatio = Math.sqrt(molarMassGas2 / molarMassGas1);
resultDiv.innerHTML = "Ratio of Rate (Gas 1 / Gas 2): " + rateRatio.toFixed(4);
}