Gas Effusion Rate Calculator (Graham's Law)

Calculate and compare the effusion rates of two gases using Graham's Law.

Input the molar masses and effusion rates of two gases. Leave one field blank to solve for it. Supports step-by-step solutions and real-world examples.

Examples

See how to use the calculator with real-world scenarios.

Calculate rate ratio for Helium and Oxygen

Rate

Find the effusion rate ratio of Helium (M₁=4.00 g/mol) and Oxygen (M₂=32.00 g/mol).

Gas 1 Molar Mass (M₁): 4 g/mol

Gas 2 Molar Mass (M₂): 32 g/mol

Gas 1 Effusion Rate (r₁):

Gas 2 Effusion Rate (r₂):

Volume (V):

Time (t):

Unit: mL/s

Find the effusion rate ratio of Helium (M₁=4.00 g/mol) and Oxygen (M₂=32.00 g/mol).

Find unknown rate for Nitrogen

Rate

Given Nitrogen (M₁=28.0 g/mol) effuses at 1.5 mL/s, what is the rate for Oxygen (M₂=32.0 g/mol)?

Gas 1 Molar Mass (M₁): 28 g/mol

Gas 2 Molar Mass (M₂): 32 g/mol

Gas 1 Effusion Rate (r₁): 1.5 mL/s

Gas 2 Effusion Rate (r₂):

Volume (V):

Time (t):

Unit: mL/s

Given Nitrogen (M₁=28.0 g/mol) effuses at 1.5 mL/s, what is the rate for Oxygen (M₂=32.0 g/mol)?

Find unknown molar mass

Rate

A gas effuses at 0.5 times the rate of Hydrogen (M₁=2.0 g/mol). What is its molar mass?

Gas 1 Molar Mass (M₁): 2 g/mol

Gas 2 Molar Mass (M₂): g/mol

Gas 1 Effusion Rate (r₁): 2 mL/s

Gas 2 Effusion Rate (r₂): 1 mL/s

Volume (V):

Time (t):

Unit: mL/s

A gas effuses at 0.5 times the rate of Hydrogen (M₁=2.0 g/mol). What is its molar mass?

Absolute rate from volume and time

Absolute

If 100 mL of gas effuses in 50 seconds, what is the effusion rate?

Gas 1 Molar Mass (M₁): g/mol

Gas 2 Molar Mass (M₂): g/mol

Gas 1 Effusion Rate (r₁):

Gas 2 Effusion Rate (r₂):

Volume (V): 100 mL

Time (t): 50 s

Unit: mL/s

If 100 mL of gas effuses in 50 seconds, what is the effusion rate?

Other Titles
Understanding Gas Effusion Rate Calculator: A Comprehensive Guide
Master Graham's Law and gas effusion with this step-by-step tool.

What is Gas Effusion and Graham's Law?

  • Definition of Effusion
  • Graham's Law Explained
  • Why Effusion Matters
Effusion is the process by which gas molecules escape through a tiny hole into a vacuum. Graham's Law relates the rates of effusion of two gases to their molar masses, showing that lighter gases effuse faster than heavier ones.
Graham's Law Formula

Effusion in Action

  • Helium effuses faster than Oxygen due to its lower molar mass.
  • Hydrogen, being the lightest, has the highest effusion rate.

Step-by-Step Guide to Using the Calculator

  • Input Required Data
  • Choose Calculation Type
  • Interpret Results
Enter the molar masses and effusion rates as needed. The calculator will solve for the unknown using Graham's Law or the basic rate formula (V/t).
How to Use the Tool

Practical Usage

  • Calculate the rate ratio for two gases.
  • Find the unknown rate or molar mass.

Real-World Applications of Gas Effusion

  • Industrial Gas Separation
  • Laboratory Analysis
  • Educational Demonstrations
Effusion principles are used in isotope separation, leak detection, and identifying unknown gases in labs. Understanding effusion helps in designing efficient chemical processes.
Effusion in Industry and Science

Applications

  • Uranium enrichment uses effusion.
  • Effusion helps detect gas leaks.

Common Misconceptions and Correct Methods

  • Effusion vs. Diffusion
  • Unit Consistency
  • Input Accuracy
Effusion is not the same as diffusion. Always use consistent units for rates and molar masses. Double-check your inputs for accuracy to avoid calculation errors.
Avoiding Mistakes

Tips

  • Mixing up effusion and diffusion leads to wrong results.
  • Using different units for r₁ and r₂ causes errors.

Mathematical Derivation and Examples

  • Graham's Law Derivation
  • Sample Calculations
  • Interpreting Results
Graham's Law is derived from the kinetic theory of gases. The calculator applies the square root relationship between rates and molar masses for accurate results.
Worked Examples

Math in Action

  • Given M₁=4, M₂=32, r₁/r₂=2.
  • If r₁=1.5, M₁=28, M₂=32, r₂≈1.4.