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Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters Calculator

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✖Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.ⓘ Critical Temperature [Tc]
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-10%
✖Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.ⓘ Reduced Temperature [Tr]
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-10%
✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume [Vm,r]
+10%
-10%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [Vm,c]
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-10%
✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [bPR]
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✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [Pr]
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✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure [Pc]
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✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]
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✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters [aPR]
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Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters

Formula
`"a"_{"PR"} = ((("[R]"*("T"_{"c"}*"T"_{"r"}))/(("V"_{"m,r"}*"V"_{"m,c"})-"b"_{"PR"}))-("P"_{"r"}*"P"_{"c"}))*((("V"_{"m,r"}*"V"_{"m,c"})^2)+(2*"b"_{"PR"}*("V"_{"m,r"}*"V"_{"m,c"}))-("b"_{"PR"}^2))/"α"`

Example
`"3.5E^6"=((("[R]"*("647K"*"10"))/(("11.2"*"11.5m³/mol")-"0.12"))-("3.675E^-5"*"218Pa"))*((("11.2"*"11.5m³/mol")^2)+(2*"0.12"*("11.2"*"11.5m³/mol"))-(("0.12")^2))/"2"`

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Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function
aPR = ((([R]*(Tc*Tr))/((Vm,r*Vm,c)-bPR))-(Pr*Pc))*(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2))/α
This formula uses 1 Constants, 9 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Critical Temperature - (Measured in Kelvin) - Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor.
Reduced Temperature - Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless.
Reduced Molar Volume - Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
Critical Molar Volume - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
α-function - α-function is a function of temperature and the acentric factor.
STEP 1: Convert Input(s) to Base Unit
Critical Temperature: 647 Kelvin --> 647 Kelvin No Conversion Required
Reduced Temperature: 10 --> No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Reduced Pressure: 3.675E-05 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
α-function: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
aPR = ((([R]*(Tc*Tr))/((Vm,r*Vm,c)-bPR))-(Pr*Pc))*(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2))/α --> ((([R]*(647*10))/((11.2*11.5)-0.12))-(3.675E-05*218))*(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2))/2
Evaluating ... ...
aPR = 3473992.97633715
STEP 3: Convert Result to Output's Unit
3473992.97633715 --> No Conversion Required
FINAL ANSWER
3473992.97633715 ≈ 3.5E+6 <-- Peng–Robinson Parameter a
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Peng Robinson Parameter » Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters

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6 Peng Robinson Parameter Calculators

Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters
Go Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function
Peng Robinson Parameter a, using Peng Robinson Equation
Go Peng–Robinson Parameter a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))/α-function
Peng Robinson Parameter b of Real Gas given Reduced and Actual Parameters
Go Peng–Robinson Parameter b = 0.07780*[R]*(Temperature/Reduced Temperature)/(Pressure/Reduced Pressure)
Peng Robinson parameter a, of Real Gas given Reduced and Actual Parameters
Go Peng–Robinson Parameter a = 0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/(Pressure/Reduced Pressure)
Peng Robinson Parameter b of Real Gas given Critical Parameters
Go Parameter b = 0.07780*[R]*Critical Temperature/Critical Pressure
Peng Robinson Parameter a, of Real Gas given Critical Parameters
Go Peng–Robinson Parameter a = 0.45724*([R]^2)*(Critical Temperature^2)/Critical Pressure

Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters Formula

Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function
aPR = ((([R]*(Tc*Tr))/((Vm,r*Vm,c)-bPR))-(Pr*Pc))*(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2))/α

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters?

Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters calculator uses Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function to calculate the Peng–Robinson Parameter a, The Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas. Peng–Robinson Parameter a is denoted by aPR symbol.

How to calculate Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters, enter Critical Temperature (Tc), Reduced Temperature (Tr), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson Parameter b (bPR), Reduced Pressure (Pr), Critical Pressure (Pc) & α-function (α) and hit the calculate button. Here is how the Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 3.5E+6 = ((([R]*(647*10))/((11.2*11.5)-0.12))-(3.675E-05*218))*(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2))/2.

FAQ

What is Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters?
The Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas and is represented as aPR = ((([R]*(Tc*Tr))/((Vm,r*Vm,c)-bPR))-(Pr*Pc))*(((Vm,r*Vm,c)^2)+(2*bPR*(Vm,r*Vm,c))-(bPR^2))/α or Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function. Critical Temperature is the highest temperature at which the substance can exist as a liquid. At this phase boundaries vanish, and the substance can exist both as a liquid and vapor, Reduced Temperature is the ratio of the actual temperature of the fluid to its critical temperature. It is dimensionless, Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature & α-function is a function of temperature and the acentric factor.
How to calculate Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters?
The Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas is calculated using Peng–Robinson Parameter a = ((([R]*(Critical Temperature*Reduced Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-(Reduced Pressure*Critical Pressure))*(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))/α-function. To calculate Peng Robinson Parameter a, using Peng Robinson Equation given Reduced and Critical Parameters, you need Critical Temperature (Tc), Reduced Temperature (Tr), Reduced Molar Volume (Vm,r), Critical Molar Volume (Vm,c), Peng–Robinson Parameter b (bPR), Reduced Pressure (Pr), Critical Pressure (Pc) & α-function (α). With our tool, you need to enter the respective value for Critical Temperature, Reduced Temperature, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b, Reduced Pressure, Critical Pressure & α-function and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Peng–Robinson Parameter a?
In this formula, Peng–Robinson Parameter a uses Critical Temperature, Reduced Temperature, Reduced Molar Volume, Critical Molar Volume, Peng–Robinson Parameter b, Reduced Pressure, Critical Pressure & α-function. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Peng–Robinson Parameter a = 0.45724*([R]^2)*(Critical Temperature^2)/Critical Pressure
  • Peng–Robinson Parameter a = 0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/(Pressure/Reduced Pressure)
  • Peng–Robinson Parameter a = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-Pressure)*((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))/α-function
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