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Determination of Entropy using Sackur-Tetrode Equation Calculator

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Distinguishable Particles Indistinguishable Particles

✖Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joulekelvin−1mole−1.ⓘ Universal Gas Constant [R]			+10% -10%
✖Relative Atomic Mass, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant.ⓘ Relative Atomic Mass [A_r]			+10% -10%
✖Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.ⓘ Temperature [T]			+10% -10%
✖Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.ⓘ Pressure [p]			+10% -10%
✖Standard Pressure is equal to 1 atm (101.325 kilopascals).ⓘ Standard Pressure [p°]			+10% -10%

✖Standard Entropy (S°) is the absolute entropy of a pure material at 25°C (298 K) and 1 atm pressure.ⓘ Determination of Entropy using Sackur-Tetrode Equation [S°_m]

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Determination of Entropy using Sackur-Tetrode Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure))
S°_m = R*(-1.154+(3/2)*ln(A_r)+(5/2)*ln(T)-ln(p/p°))
This formula uses 1 Functions, 6 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Standard Entropy - (Measured in Joule per Kelvin) - Standard Entropy (S°) is the absolute entropy of a pure material at 25°C (298 K) and 1 atm pressure.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
Relative Atomic Mass - Relative Atomic Mass, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant.
Temperature - (Measured in Kelvin) - Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Standard Pressure - (Measured in Pascal) - Standard Pressure is equal to 1 atm (101.325 kilopascals).

STEP 1: Convert Input(s) to Base Unit

Universal Gas Constant: 8.314 --> No Conversion Required
Relative Atomic Mass: 4 --> No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Pressure: 1.123 Atmosphere Technical --> 110128.6795 Pascal (Check conversion here)
Standard Pressure: 1.000000001 Atmosphere Technical --> 98066.5000980665 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S°_m = R*(-1.154+(3/2)*ln(A_r)+(5/2)*ln(T)-ln(p/p°)) --> 8.314*(-1.154+(3/2)*ln(4)+(5/2)*ln(300)-ln(110128.6795/98066.5000980665))

Evaluating ... ...

S°_m = 125.282785161331

STEP 3: Convert Result to Output's Unit

125.282785161331 Joule per Kelvin --> No Conversion Required

FINAL ANSWER

125.282785161331 ≈ 125.2828 Joule per Kelvin <-- Standard Entropy

(Calculation completed in 00.004 seconds)

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Determination of Entropy using Sackur-Tetrode Equation

LaTeX Go Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure))

Total Number of Microstates in All Distributions

LaTeX Go Total Number of Microstates = ((Total Number of Particles+Number of Quanta of Energy-1)!)/((Total Number of Particles-1)!*(Number of Quanta of Energy!))

Translational Partition Function

LaTeX Go Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)

Translational Partition Function using Thermal de Broglie Wavelength

LaTeX Go Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3

Determination of Entropy using Sackur-Tetrode Equation Formula

LaTeX Go

Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure))
S°_m = R*(-1.154+(3/2)*ln(A_r)+(5/2)*ln(T)-ln(p/p°))

What is Statistical Thermodynamics?

Statistical thermodynamics is a theory that uses molecular properties to predict the behavior of macroscopic quantities of compounds. While the origins of statistical thermodynamics predate the development of quantum mechanics, the modern development of statistical thermodynamics assumes that the quantized energy levels associated with a particular system are known. From these energy-level data, a temperature-dependent quantity called the partition function can be calculated. From the partition function, all of the thermodynamic properties of the system can be calculated. Statistical thermodynamics has also been applied to the general problem of predicting reaction rates. This application is called transition state theory or the theory of absolute reaction rates.

How to Calculate Determination of Entropy using Sackur-Tetrode Equation?

Determination of Entropy using Sackur-Tetrode Equation calculator uses Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure)) to calculate the Standard Entropy, The Determination of Entropy using Sackur-Tetrode Equation formula is defined as an expression for the entropy of a mono atomic ideal gas. Standard Entropy is denoted by S°_m symbol.

How to calculate Determination of Entropy using Sackur-Tetrode Equation using this online calculator? To use this online calculator for Determination of Entropy using Sackur-Tetrode Equation, enter Universal Gas Constant (R), Relative Atomic Mass (A_r), Temperature (T), Pressure (p) & Standard Pressure (p°) and hit the calculate button. Here is how the Determination of Entropy using Sackur-Tetrode Equation calculation can be explained with given input values -> 150.3074 = 8.314*(-1.154+(3/2)*ln(4)+(5/2)*ln(300)-ln(110128.6795/98066.5000980665)).

FAQ

What is Determination of Entropy using Sackur-Tetrode Equation?

The Determination of Entropy using Sackur-Tetrode Equation formula is defined as an expression for the entropy of a mono atomic ideal gas and is represented as S°_m = R*(-1.154+(3/2)*ln(A_r)+(5/2)*ln(T)-ln(p/p°)) or Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure)). Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1, Relative Atomic Mass, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant, Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed & Standard Pressure is equal to 1 atm (101.325 kilopascals).

How to calculate Determination of Entropy using Sackur-Tetrode Equation?

The Determination of Entropy using Sackur-Tetrode Equation formula is defined as an expression for the entropy of a mono atomic ideal gas is calculated using Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure)). To calculate Determination of Entropy using Sackur-Tetrode Equation, you need Universal Gas Constant (R), Relative Atomic Mass (A_r), Temperature (T), Pressure (p) & Standard Pressure (p°). With our tool, you need to enter the respective value for Universal Gas Constant, Relative Atomic Mass, Temperature, Pressure & Standard Pressure 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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