Gas Rate Comparator (Graham's Law)
Compare the effusion/diffusion rates of two gases based on their molar masses.
Calculation Results
"; outputHtml += "According to Graham's Law of Effusion:"; if (ratioAB > 1) { outputHtml += "Gas A travels " + ratioAB.toFixed(3) + " times faster than Gas B."; outputHtml += "Because Gas A is lighter (" + massA + " g/mol) than Gas B (" + massB + " g/mol), it effuses at a higher rate."; } else if (ratioAB < 1) { outputHtml += "Gas B travels " + (1/ratioAB).toFixed(3) + " times faster than Gas A."; outputHtml += "Because Gas B is lighter (" + massB + " g/mol) than Gas A (" + massA + " g/mol), it effuses at a higher rate."; } else { outputHtml += "Both gases have the same molar mass and will effuse at the same rate."; } outputHtml += "Theoretical ratio (Rate A : Rate B) is " + ratioAB.toFixed(4) + " : 1"; resultDiv.style.display = "block"; resultDiv.innerHTML = outputHtml; }Free Gas Rate Calculator: Understanding Graham's Law
In chemistry and physics, understanding how fast gases move is crucial for processes ranging from industrial separation to respiration. Gases do not stay still; their particles are in constant, random motion. This calculator helps determine the relative speed at which different gases travel using a principle known as Graham's Law.
What are Effusion and Diffusion?
Before calculating rates, it is important to understand the physical processes being measured:
- Diffusion: The process whereby gaseous atoms or molecules transfer from a region of higher concentration to a region of lower concentration. Think of perfume spreading across a room.
- Effusion: The process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules. Think of air leaking out of a tiny pinhole in a tire.
While distinct, both processes depend heavily on the speed of the gas particles.
Graham's Law of Effusion
The "Free Gas Rate Calculator" above utilizes Graham's Law. Formulated by Scottish chemist Thomas Graham in 1848, this law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Put simply: Lighter gases move faster than heavier gases (at the same temperature and pressure).
The formula used for comparing two gases (Gas A and Gas B) is:
Rate A / Rate B = √(Molar Mass B / Molar Mass A)
How to Use This Calculator
This tool is designed to compare the relative rates of two different gases. To use it, you need the molar mass of each gas, usually expressed in grams per mole (g/mol). You can find these values on a standard periodic table by adding the atomic masses of the constituent elements.
Example Calculation
Let's compare how fast Hydrogen gas (H₂) effuses compared to Oxygen gas (O₂).
- Find Molar Mass A (H₂): Hydrogen has an atomic mass of approximately 1.01. Since H₂ is diatomic, its molar mass is 1.01 * 2 = 2.02 g/mol. Enter 2.02 into the "Gas A" field.
- Find Molar Mass B (O₂): Oxygen has an atomic mass of approximately 16.00. Its molar mass is 16.00 * 2 = 32.00 g/mol. Enter 32.00 into the "Gas B" field.
- Calculate: Click the button. The calculator applies Graham's Law: √(32.00 / 2.02) = √15.84 ≈ 3.98.
The result will show that Hydrogen gas (Gas A) travels approximately 3.98 times faster than Oxygen gas (Gas B) because it is significantly lighter.