Standard Deviation Formula:
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Definition: This calculator determines the standard deviation (σ) of molecular spreading due to diffusion over time.
Purpose: It helps scientists and engineers quantify how much a band of molecules will spread due to random diffusion processes.
The calculator uses the formula:
Where:
Explanation: The standard deviation grows with the square root of time, showing how diffusion causes increasing spreading over time.
Details: Understanding diffusive spreading is crucial in fields like chromatography, chemical engineering, and biological transport processes.
Tips: Enter the diffusion coefficient (typically 10⁻⁹ to 10⁻¹¹ m²/s for liquids) and diffusion time. All values must be > 0.
Q1: What does the standard deviation represent in diffusion?
A: It quantifies the root-mean-square distance molecules spread from their origin due to random motion.
Q2: How does temperature affect the results?
A: Higher temperatures increase the diffusion coefficient (D), leading to faster spreading.
Q3: Why is there a factor of 2 in the formula?
A: The factor accounts for diffusion occurring in all spatial dimensions (1D, 2D, or 3D).
Q4: What are typical diffusion coefficient values?
A: In liquids: ~10⁻⁹ m²/s for small molecules, ~10⁻¹¹ m²/s for proteins. In gases: ~10⁻⁵ m²/s.
Q5: Can this be used for non-Fickian diffusion?
A: No, this formula applies only to normal Fickian diffusion where σ ∝ √t.