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Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters Calculator

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✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]
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✖Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.ⓘ Molar Volume [Vm]
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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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✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [aPR]
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-10%
✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]
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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 of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters [Pc]
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Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters

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

Example
`"863128Pa"=((("[R]"*"85K")/("22.4m³/mol"-"0.12"))-(("0.1"*"2")/((("22.4m³/mol")^2)+(2*"0.12"*"22.4m³/mol")-(("0.12")^2))))/"3.675E^-5"`

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Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical Pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))))/Reduced Pressure
Pc = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pr
This formula uses 1 Constants, 7 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Molar Volume - (Measured in Cubic Meter per Mole) - Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
α-function - α-function is a function of temperature and the acentric factor.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
STEP 1: Convert Input(s) to Base Unit
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Molar Volume: 22.4 Cubic Meter per Mole --> 22.4 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> No Conversion Required
Reduced Pressure: 3.675E-05 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pc = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pr --> ((([R]*85)/(22.4-0.12))-((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2))))/3.675E-05
Evaluating ... ...
Pc = 863127.951850715
STEP 3: Convert Result to Output's Unit
863127.951850715 Pascal --> No Conversion Required
FINAL ANSWER
863127.951850715 ≈ 863128 Pascal <-- Critical Pressure
(Calculation completed in 00.004 seconds)
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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Critical Pressure » Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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6 Critical Pressure Calculators

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

Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters Formula

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

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 Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters?

Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters calculator uses Critical Pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))))/Reduced Pressure to calculate the Critical Pressure, The Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature. Critical Pressure is denoted by Pc symbol.

How to calculate Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters using this online calculator? To use this online calculator for Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters, enter Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Peng–Robinson Parameter a (aPR), α-function (α) & Reduced Pressure (Pr) and hit the calculate button. Here is how the Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters calculation can be explained with given input values -> 866238.4 = ((([R]*85)/(22.4-0.12))-((0.1*2)/((22.4^2)+(2*0.12*22.4)-(0.12^2))))/3.675E-05.

FAQ

What is Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters?
The Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature and is represented as Pc = ((([R]*T)/(Vm-bPR))-((aPR*α)/((Vm^2)+(2*bPR*Vm)-(bPR^2))))/Pr or Critical Pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))))/Reduced Pressure. Temperature is the degree or intensity of heat present in a substance or object, Molar Volume is the volume occupied by one mole of a real gas at standard temperature and pressure, Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, α-function is a function of temperature and the acentric factor & Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
How to calculate Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters?
The Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters formula is defined as minimum pressure required to liquify a substance at the critical temperature is calculated using Critical Pressure = ((([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2))))/Reduced Pressure. To calculate Critical Pressure of Real Gas using Peng Robinson Equation given Reduced and Actual Parameters, you need Temperature (T), Molar Volume (Vm), Peng–Robinson Parameter b (bPR), Peng–Robinson Parameter a (aPR), α-function (α) & Reduced Pressure (Pr). With our tool, you need to enter the respective value for Temperature, Molar Volume, Peng–Robinson Parameter b, Peng–Robinson Parameter a, α-function & Reduced Pressure 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 Critical Pressure?
In this formula, Critical Pressure uses Temperature, Molar Volume, Peng–Robinson Parameter b, Peng–Robinson Parameter a, α-function & Reduced Pressure. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Critical Pressure = 0.45724*([R]^2)*((Temperature/Reduced Temperature)^2)/Peng–Robinson Parameter a
  • Critical Pressure = 0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a
  • Critical Pressure = 0.07780*[R]*Critical Temperature/Peng–Robinson Parameter b
  • Critical Pressure = ((([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2))))/Reduced Pressure
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