Non-steady state diffusion Calculator

✖The Initial concentration is the abundance of a constituent divided by the total volume of a mixture before diffusion or reaction.ⓘ Initial Concentration [C₀]			+10% -10%
✖Surface concentration represents the concentration of diffusing species at the surface.ⓘ Surface concentration [C_s]			+10% -10%
✖Distance (length) across which the diffusion is taking place.ⓘ Distance [d]			+10% -10%
✖Diffusion coefficient is the proportionality factor D in Fick's law .ⓘ Diffusion Coefficient [D]			+10% -10%
✖Diffusion Time represents the total time in which the diffusion was taking place.ⓘ Diffusion Time [t]			+10% -10%

✖Concentration at x Distance represents the concentration of the diffusing species at a distance of x from the surface.ⓘ Non-steady state diffusion [C_x]

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Formula

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Non-steady state diffusion

Formula

`"C"_{"x"} = "C"_{"0"}+("C"_{"s"}-"C"_{"0"})*(1-erf("d"/(2*sqrt("D"*"t"))))`

Example

`"0.701888"="0.3mol/L"+("0.7"-"0.3mol/L")*(1-erf("0.01m"/(2*sqrt("800m²/s"*"1000s"))))`

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Non-steady state diffusion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time))))
C_x = C₀+(C_s-C₀)*(1-erf(d/(2*sqrt(D*t))))
This formula uses 2 Functions, 6 Variables

Functions Used

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

Variables Used

Concentration at x Distance - Concentration at x Distance represents the concentration of the diffusing species at a distance of x from the surface.
Initial Concentration - (Measured in Mole per Cubic Meter) - The Initial concentration is the abundance of a constituent divided by the total volume of a mixture before diffusion or reaction.
Surface concentration - Surface concentration represents the concentration of diffusing species at the surface.
Distance - (Measured in Meter) - Distance (length) across which the diffusion is taking place.
Diffusion Coefficient - (Measured in Square Meter Per Second) - Diffusion coefficient is the proportionality factor D in Fick's law .
Diffusion Time - (Measured in Second) - Diffusion Time represents the total time in which the diffusion was taking place.

STEP 1: Convert Input(s) to Base Unit

Initial Concentration: 0.3 Mole per Liter --> 300 Mole per Cubic Meter (Check conversion here)
Surface concentration: 0.7 --> No Conversion Required
Distance: 0.01 Meter --> 0.01 Meter No Conversion Required
Diffusion Coefficient: 800 Square Meter Per Second --> 800 Square Meter Per Second No Conversion Required
Diffusion Time: 1000 Second --> 1000 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_x = C₀+(C_s-C₀)*(1-erf(d/(2*sqrt(D*t)))) --> 300+(0.7-300)*(1-erf(0.01/(2*sqrt(800*1000))))

Evaluating ... ...

C_x = 0.701887933909575

STEP 3: Convert Result to Output's Unit

0.701887933909575 --> No Conversion Required

FINAL ANSWER

0.701887933909575 ≈ 0.701888 <-- Concentration at x Distance

(Calculation completed in 00.004 seconds)

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< 9 Composition and Diffusion Calculators

Atom percent to mass percent

Go Mass Percent of First Element = Atomic percent of first element*Atomic mass of first element*100/(Atomic percent of first element*Atomic mass of first element+(100-Atomic percent of first element)*Atomic mass of second element)

Atom percent

Go Atomic percent of first element = 100*Mass Percent of First Element*Atomic mass of second element/(Mass Percent of First Element*Atomic mass of second element+(100-Mass Percent of First Element)*Atomic mass of first element)

Non-steady state diffusion

Go Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time))))

Volume percent to mass percent

Go Mass percent of first phase = Volume percent of first phase*Density of the first phase*100/(Volume percent of first phase*Density of the first phase+(100-Volume percent of first phase)*Density of the second phase)

Mass percent to volume percent

Go Volume percent of first phase = Mass percent of first phase*Density of the second phase*100/(Mass percent of first phase*Density of the second phase+(100-Mass percent of first phase)*Density of the first phase)

Entropy of mixing

Go Entropy of mixing = 8.314*(Mole fraction of element A*ln(Mole fraction of element A)+(1-Mole fraction of element A)*ln(1-Mole fraction of element A))

Equilibrium Vacancy Concentration

Go Number of vacancies = Number of atomic sites*exp(-Activation energy for vacancy formation/([BoltZ]*Temperature))

Temperature dependent diffusion coefficient

Go Diffusion Coefficient = Pre-exponential factor*e^(-Activation energy for diffusion/(Universal Gas Constant*Temperature))

Diffusion Flux

Go Diffusion flux = Diffusion Coefficient*(Concentration difference/Distance)

Non-steady state diffusion Formula

Assumptions used for solving the diffusion equation

This solution is for a semi-infinite solid in which the surface concentration is held constant. Frequently, the source of the diffusing species is a gas phase, the partial pressure of which is maintained at a constant value. Furthermore, the following assumptions are made:
1. Before diffusion, there is a uniform initial concentration
2. The value of x at the surface is zero and increases with distance into the solid.
3. The time is taken to be zero the instant before the diffusion process begins.

How to Calculate Non-steady state diffusion?

Non-steady state diffusion calculator uses Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))) to calculate 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 calculate Non-steady state diffusion using this online calculator? To use this online calculator 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. Here is how the Non-steady state diffusion calculation can be explained with given input values -> 0.701888 = 300+(0.7-300)*(1-erf(0.01/(2*sqrt(800*1000)))).

FAQ

What is Non-steady state diffusion?

Non-steady state diffusion represents the time dependent diffusion of species, a transient diffusion state and is represented as C_x = C₀+(C_s-C₀)*(1-erf(d/(2*sqrt(D*t)))) or Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))). The Initial concentration is the abundance of a constituent divided by the total volume of a mixture before diffusion or reaction, Surface concentration represents the concentration of diffusing species at the surface, Distance (length) across which the diffusion is taking place, Diffusion coefficient is the proportionality factor D in Fick's law & Diffusion Time represents the total time in which the diffusion was taking place.

How to calculate Non-steady state diffusion?

Non-steady state diffusion represents the time dependent diffusion of species, a transient diffusion state is calculated using Concentration at x Distance = Initial Concentration+(Surface concentration-Initial Concentration)*(1-erf(Distance/(2*sqrt(Diffusion Coefficient*Diffusion Time)))). To calculate Non-steady state diffusion, you need Initial Concentration (C₀), Surface concentration (C_s), Distance (d), Diffusion Coefficient (D) & Diffusion Time (t). With our tool, you need to enter the respective value for Initial Concentration, Surface concentration, Distance, Diffusion Coefficient & Diffusion Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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