Advanced Graham's Law Diffusion Calculator

Calculator Form

Use equal temperature and pressure conditions for valid Graham's Law comparisons.

Calculation mode

Gas 1 name

Gas 2 name

Molar mass of Gas 1 (g/mol)

Molar mass of Gas 2 (g/mol)

Rate unit

Known rate of Gas 1

Known rate of Gas 2

Elapsed time

Time unit

Distance output unit

Optional notes

Mode guidance: Compare rates and compare times need both molar masses. Unknown-rate modes need both molar masses and one known rate. Unknown-molar-mass modes need one known molar mass and both rates. Distance mode uses Gas 1 rate plus elapsed time.

Example Data Table

These sample pairs demonstrate relative diffusion behavior under equal conditions.

Gas 1	Gas 2	Molar Mass 1 (g/mol)	Molar Mass 2 (g/mol)	Rate Ratio r1/r2	Time Ratio t1/t2
Hydrogen	Oxygen	2.016	32.00	3.9841	0.2510
Helium	Carbon Dioxide	4.00	44.01	3.3160	0.3016
Ammonia	Hydrogen Chloride	17.03	36.46	1.4632	0.6834
Methane	Sulfur Dioxide	16.04	64.07	1.9989	0.5003

Formula Used

Graham's Law states that a gas diffusion or effusion rate is inversely proportional to the square root of its molar mass when temperature and pressure remain the same.

r1 / r2 = √(M2 / M1)

Here, r represents diffusion or effusion rate and M represents molar mass in g/mol.

t1 / t2 = √(M1 / M2)

For equal travel distance, the heavier gas needs more time. Time ratio is the inverse of the rate ratio.

M1 = M2 × (r2 / r1)²

Use this rearranged equation when Gas 1 molar mass is unknown.

M2 = M1 × (r1 / r2)²

Use this rearranged equation when Gas 2 molar mass is unknown.

Distance = Rate × Time

This relation is useful when the calculator operates in distance mode using a known rate and elapsed time.

How to Use This Calculator

Select the calculation mode matching your chemistry problem.
Enter names for Gas 1 and Gas 2 for cleaner output labels.
Provide molar masses, known rates, or elapsed time as needed.
Choose suitable rate, time, and distance units.
Press Calculate Now to show results below the header and above the form.
Inspect the result table and Plotly graph.
Use the CSV button for spreadsheet-ready output.
Use the PDF button to download a clean summary report.

FAQs

1) What does Graham's Law calculate?

It compares gas diffusion or effusion speeds using molar mass. Lighter gases move faster under the same temperature and pressure conditions.

2) What is the difference between diffusion and effusion?

Diffusion is gas mixing through space or another gas. Effusion is gas escape through a tiny opening. Graham's Law is commonly used for both ideal comparisons.

3) Why must temperature and pressure stay the same?

The law compares gases fairly only under identical conditions. Changing temperature or pressure affects particle speed and can distort the simple square-root relationship.

4) Can this calculator solve unknown molar mass?

Yes. Enter one known molar mass and both rates. The calculator rearranges Graham's Law to estimate the missing molar mass directly.

5) Which units should I use for rate?

Use any supported rate unit consistently. The ratio calculation is unit-independent as long as both gas rates use the same unit system.

6) Why does a heavier gas diffuse more slowly?

Heavier particles have greater molar mass, so their relative motion is slower in the square-root relationship. That reduces diffusion or effusion speed.

7) Can I use this for equal-distance travel time?

Yes. Choose the time comparison mode. The calculator returns the relative time needed by each gas to cover the same path length.

8) What does the graph show?

The graph visualizes either relative rates, relative times, molar masses, or distance over time. It helps you compare outcomes instantly.