Answer:
[tex]v^{VdW}=0.0704\frac{L}{mol}[/tex]
[tex]v^{ideal}=0.05816\frac{L}{mol}[/tex]
Differences:
- The gas is at a very high pressure, which causes strong nonidealities.
- Attraction and repulsion actually phenomena exist among molecules, which is not considered by the ideal gas equation.
Explanation:
Hello,
In this case, the VdW equation takes the typical form:
[tex]p=\frac{RT}{v-b}-\frac{a}{v^2}[/tex]
Whereas [tex]a[/tex] and [tex]b[/tex] are referred to the attraction and repulsion effect, in such a way, for neon, such values are 0.208 bar*L²/mol² and 0.01672 L/mol respectively. However, with the given information, the polynomic form of the VdW equation is:
[tex]v^3-(\frac{RT}{P}+b)v^2+\frac{a}{p} v-\frac{ab}{p} =0[/tex]
Which in terms of the molar volume becomes:
[tex]v^3-(\frac{0.083\frac{bar*L}{mol*K}*355.0K}{506.625bar}+0.01672\frac{L}{mol} )v^2+(\frac{0.208\frac{bar*L^2}{mol^2} }{506.625bar})v-\frac{0.208\frac{bar*L^2}{mol^2}*0.01672\frac{L}{mol}}{506.625bar} =0[/tex]
[tex]v^3-0.07488v^2+0.0004106v-0.000006865=0[/tex]
Thus, by solving via solver the roots, two are imaginary and the feasible molar volume is:
[tex]v^{VdW}=0.0704\frac{L}{mol}[/tex]
Now, the volume obtained from the ideal gas equation is:
[tex]v^{ideal}=\frac{RT}{p}=\frac{0.083\frac{bar*L}{mol*K}*355.0K}{506.625bar} =0.05816\frac{L}{mol}[/tex]
In this case, the two values are different because:
- The gas is at a very high pressure, which causes strong nonidealities.
- Attraction and repulsion actually phenomena exist among molecules, which is not considered by the ideal gas equation.
Best regards.
Answer:
Ideal gas: V = 0.05826L
Van der Waals: V = 0.071L
Explanation:
Given Data:
Number of Mole = 1.000
Pressure = 500atm
temperature = 355.0k
R = 0.082057L atm mol^-1K^-1
1. Using the ideal gas equation, the volume can be calculated as;
PV = nRT
V = nRT/P
= (1 * 0.082057 * 355)/500
= 29.130/500
V = 0.05826L
2. Using the van der Waals equation to calculate the volume; we have
[P + (n²a/V²)](V-nb) = nRT
For neon gas,
a = 0.2135
b = 0.01709
Substituting, we have
[500 + (1² * 0.2135/V²)] (V-1 * 0.01709) = 1 * 0.082057 * 355
[ 500 + (0.2135/V²)] ( V- 0.01709) = 29.130
V = 0.071L
The ideal gas molecules do not interact with each other but the real gas molecules interact. Therefore, the difference in volume is due to interaction between atoms of real gas but not in the ideal gas.
