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Real Gas Law
Storyboard 
In the case of an ideal gas, it is assumed that the molecules do not interact. If one wishes to model the behavior of a real gas in which there is interaction, one must consider the attraction between the molecules and the repulsion that prevent them from overlapping. The first has an effect above all on the edges of the system as it slows particles that move towards the edge. The attraction effectively reduces the pressure that the gas makes on the walls. On the other hand the repulsion acts as a reduction of the volume available to the particles creating a stiffness to compress it.
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Real Gas Law
Storyboard
In the case of an ideal gas, it is assumed that the molecules do not interact. If one wishes to model the behavior of a real gas in which there is interaction, one must consider the attraction between the molecules and the repulsion that prevent them from overlapping. The first has an effect above all on the edges of the system as it slows particles that move towards the edge. The attraction effectively reduces the pressure that the gas makes on the walls. On the other hand the repulsion acts as a reduction of the volume available to the particles creating a stiffness to compress it.
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Equations
The pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related through the following physical laws:
• Boyle's law
• Charles's law
• Gay-Lussac's law
• Avogadro's law
These laws can be expressed in a more general form as:
$\displaystyle\frac{pV}{nT}=cte$
This general relationship states that the product of pressure and volume divided by the number of moles and temperature remains constant:
When the pressure ($p$) behaves as an ideal gas, satisfying the volume ($V$), the number of moles ($n$), the absolute temperature ($T$), and the universal gas constant ($R_C$), the ideal gas equation:
and the definition of the molar concentration ($c_m$):
lead to the following relationship:
The number of moles ($n$) corresponds to the number of particles ($N$) divided by the avogadro's number ($N_A$):
If we multiply both the numerator and the denominator by the particle mass ($m$), we obtain:
$n=\displaystyle\frac{N}{N_A}=\displaystyle\frac{Nm}{N_Am}=\displaystyle\frac{M}{M_m}$
So it is:
The pressure ($p$) is associated with the volume ($V$), ERROR:6679, the absolute temperature ($T$), and the universal gas constant ($R_C$) through the equation:
Since ERROR:6679 can be calculated with the mass ($M$) and the molar Mass ($M_m$) using:
and obtained with the definition of the specific gas constant ($R_s$) using:
we conclude that:
Examples
Avogadro's Law states that the volume ($V$) and the number of moles ($n$) are directly proportional when the pressure ($p$) and the absolute temperature ($T$) are held constant.
This relationship can be expressed as follows, using the constant of Avogadro's principle ($C_a$):
The molar concentration ($c_m$) corresponds to ERROR:9339,0 divided by the volume ($V$) of a gas and is calculated as follows:
The molar concentration ($c_m$) can be calculated from the density ($\rho$) and the molar Mass ($M_m$) as follows:
The number of moles ($n$) is determined by dividing the mass ($M$) of a substance by its the molar Mass ($M_m$), which corresponds to the weight of one mole of the substance.
Therefore, the following relationship can be established:
The molar mass is expressed in grams per mole (g/mol).
The pressure ($p$), the volume ($V$), the absolute temperature ($T$), and the number of moles ($n$) are related by the following equation:
where the universal gas constant ($R_C$) has a value of 8.314 J/K mol.
The pressure ($p$) can be calculated from the molar concentration ($c_m$) using the absolute temperature ($T$), and the universal gas constant ($R_C$) as follows:
The pressure ($p$) is related to the mass ($M$) with the volume ($V$), the specific gas constant ($R_s$), and the absolute temperature ($T$) through:
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