Basic Diffusion Rate Calculator
Calculate the rate of diffusion based on amount and time elapsed.
Graham's Law: Time Comparison
Calculate how long Substance B takes to diffuse compared to Substance A based on Molar Mass.
How to Calculate Rate of Diffusion with Time
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) from a region of higher concentration to a region of lower concentration. In chemistry and physics, calculating the rate at which this occurs is crucial for understanding reaction kinetics, gas behavior, and biological transport mechanisms.
1. The Basic Diffusion Rate Formula
The most fundamental way to calculate the rate of diffusion is by observing the change in a quantity over a specific period of time. The general formula is:
Rate = Amount Diffused / Time Elapsed
Where:
- Amount Diffused: This can be the volume of gas (mL or L), the number of moles (mol), or the distance traveled by a precipitate in a tube (cm or m).
- Time Elapsed: The duration over which the diffusion occurred (usually in seconds or minutes).
For example, if 50 mL of gas diffuses through a porous membrane in 25 seconds, the rate is 50 mL / 25 s = 2 mL/s.
2. Calculating Diffusion Time Using Graham's Law
When dealing with gases, Graham's Law of Effusion/Diffusion provides a way to compare the rates and times of two different gases based on their molar masses. This is particularly useful when you know the diffusion time of one gas and want to predict the time for another.
Because lighter gases move faster, they take less time to diffuse. Therefore, the time taken is proportional to the square root of the molar mass:
Time B / Time A = √(Molar Mass B / Molar Mass A)
Example Calculation:
Let's say Oxygen gas ($O_2$, molar mass 32 g/mol) takes 100 seconds to diffuse through a tiny hole. How long will it take for Hydrogen gas ($H_2$, molar mass 2 g/mol) to diffuse through the same hole?
- Time A ($O_2$) = 100s
- Mass A ($O_2$) = 32
- Mass B ($H_2$) = 2
- Calculation: Time B = 100 × √(2 / 32) = 100 × √(0.0625) = 100 × 0.25 = 25 seconds.
The hydrogen diffuses 4 times faster, so it takes only 1/4th of the time.
Factors Affecting Rate of Diffusion
While the mathematical formulas provide exact numbers, several physical factors influence the actual rate in a real-world setting:
- Temperature: Higher temperatures increase the kinetic energy of particles, thereby increasing the rate of diffusion and decreasing the time required.
- Concentration Gradient: The steeper the gradient (difference in concentration), the faster the diffusion.
- Medium: Diffusion happens fastest in gases, slower in liquids, and slowest in solids due to particle density.