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Non-steady state diffusion Formula

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Concentration at x Distance represents the concentration of the diffusing species at a distance of x from the surface. Check FAQs

C x = C 0 + (C s - C 0) \cdot (1 - e r f (\frac{d}{2 \cdot \sqrt{D \cdot t}}))

C_x - Concentration at x Distance?C₀ - Initial Concentration?C_s - Surface concentration?d - Distance?D - Diffusion Coefficient?t - Diffusion Time?

Non-steady state diffusion Example

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Here is how the Non-steady state diffusion equation looks like with Values.

Here is how the Non-steady state diffusion equation looks like with Units.

Here is how the Non-steady state diffusion equation looks like.

0.7019 = 0.3 + (0.7 - 0.3) \cdot (1 - e r f (\frac{0.01}{2 \cdot \sqrt{800 \cdot 1000}}))

0.7019 = 0.3mol/L + (0.7 - 0.3mol/L) \cdot (1 - e r f (\frac{0.01m}{2 \cdot \sqrt{800m²/s \cdot 1000s}}))

0.7019 = 0.3 + (0.7 - 0.3) \cdot (1 - e r f (\frac{0.01}{2 \cdot \sqrt{800 \cdot 1000}}))

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Non-steady state diffusion Solution

Follow our step by step solution on how to calculate Non-steady state diffusion?

FIRST Step Consider the formula

C x = C 0 + (C s - C 0) \cdot (1 - e r f (\frac{d}{2 \cdot \sqrt{D \cdot t}}))

Next Step Substitute values of Variables

∴

C x = 0.3mol/L + (0.7 - 0.3mol/L) \cdot (1 - e r f (\frac{0.01m}{2 \cdot \sqrt{800m²/s \cdot 1000s}}))

Next Step Convert Units

∴

C x = 300mol/m³ + (0.7 - 300mol/m³) \cdot (1 - e r f (\frac{0.01m}{2 \cdot \sqrt{800m²/s \cdot 1000s}}))

Next Step Prepare to Evaluate

∴

C x = 300 + (0.7 - 300) \cdot (1 - e r f (\frac{0.01}{2 \cdot \sqrt{800 \cdot 1000}}))

Next Step Evaluate

∴

C x = 0.701887933909575

LAST Step Rounding Answer

∴

C x = 0.7019

Non-steady state diffusion Formula Elements

Variables

Functions

Concentration at x Distance

Concentration at x Distance represents the concentration of the diffusing species at a distance of x from the surface.

Symbol: C_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Concentration at x Distance

Initial Concentration

The Initial concentration is the abundance of a constituent divided by the total volume of a mixture before diffusion or reaction.

Symbol: C₀

Measurement: Molar ConcentrationUnit: mol/L

Note: Value can be positive or negative.

Formulas to find Initial Concentration

Surface concentration

Surface concentration represents the concentration of diffusing species at the surface.

Symbol: C_s

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Surface concentration

Distance

Distance (length) across which the diffusion is taking place.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance

Diffusion Coefficient

Diffusion coefficient is the proportionality factor D in Fick's law .

Symbol: D

Measurement: DiffusivityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Diffusion Coefficient

Diffusion Time

Diffusion Time represents the total time in which the diffusion was taking place.

Symbol: t

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Diffusion Time

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

erf

The Gauss error function, denoted by erf, is a sigmoid function that occurs in statistics, probability, and partial differential equations.

Syntax: erf(Number)

Other formulas in Composition and Diffusion category

Go Diffusion Flux

J = D \cdot (\frac{ΔC}{d})

Go Mass percent to volume percent

V 1 = M 1 \cdot ρ 2 \cdot \frac{100}{M 1 \cdot ρ 2 + (100 - M 1) \cdot 𝜌 1}

Go Atom percent to mass percent

m 1 = X 1 \cdot A 1 \cdot \frac{100}{X 1 \cdot A 1 + (100 - X 1) \cdot A 2}

Go Entropy of mixing

ΔS mix = 8.314 \cdot (X A \cdot \ln (X A) + (1 - X A) \cdot \ln (1 - X A))

How to Evaluate Non-steady state diffusion?

Non-steady state diffusion evaluator uses Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))) to evaluate the Concentration at x Distance, Non-steady state diffusion represents the time dependent diffusion of species, a transient diffusion state. Concentration at x Distance is denoted by C_x symbol.

How to evaluate Non-steady state diffusion using this online evaluator? To use this online evaluator for Non-steady state diffusion, enter Initial Concentration (C₀), Surface concentration (C_s), Distance (d), Diffusion Coefficient (D) & Diffusion Time (t) and hit the calculate button.

FAQs on Non-steady state diffusion

What is the formula to find Non-steady state diffusion?

The formula of Non-steady state diffusion is expressed as Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))). Here is an example- 0.701888 = 300+(0.7-300)*(1-erf(0.01/(2*sqrt(800*1000)))).

How to calculate Non-steady state diffusion?

With Initial Concentration (C₀), Surface concentration (C_s), Distance (d), Diffusion Coefficient (D) & Diffusion Time (t) we can find Non-steady state diffusion using the formula - Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))). This formula also uses Square Root (sqrt), Gauss Error (erf) function(s).

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Non-steady state diffusion Formula

Non-steady state diffusion Example

Non-steady state diffusion Solution

Non-steady state diffusion Formula Elements

Other formulas in Composition and Diffusion category

How to Evaluate Non-steady state diffusion?

FAQs on Non-steady state diffusion

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