Respuesta :
Explanation:
a). According to ideal gas equation, product of pressure and volume is equal to the product of number of moles, gas constant and temperature.
Mathematically, PV = nRT
Since, it is given that number of moles is 0.5 mol, volume is 1.0 L and temperature is [tex]25.08^{o}C[/tex]. Or in kelvin temperature will be (25.08 + 273) K = 298.08 K.
Therefore, to calculate the pressure put the given vaues in the ideal gas equation as follows.
PV = nRT
[tex]P \times 1.0 L[/tex] = 0.5 mol \times 0.0821 L atm/mol K \times 298.08 K[/tex]
P = 12.236 atm
= 12.24 atm (approx)
b). Vander waal equation is as follows.
[tex][P + a (\frac{n}{V})^{2}] (\frac{V}{n} - b)[/tex] = RT
For nitrogen gas, value of a is 1.370 and b is 0.0387. Therefore, putting the given values into Vander waal's equation as follows.
[tex][P + a (\frac{n}{V})^{2}] (\frac{V}{n} - b)[/tex] = RT
P = [tex]\frac{nRT}{(V - nb)} - \frac{n^{2}a}{V^{2}}[/tex]
P = [tex]\frac{0.5 mol \times 0.0821 atm L/mol K \times 298.08 K}{(1 L - (0.5 mol \times 0.0387))} - \frac{(0.5)^{2} \times 1.370}{(1 L)^{2}}[/tex]
P = 12.14 atm
c). Pressure calculated using ideal gas equation is 12.24 atm. Whereas pressure calculated using Vander waal's equation is 12.14 atm.
Pressure is the perpendicular amount of force applied to the area. Pressure according to the ideal gas law is 12.24 atm and according to the van der Waals is 12.14 atm.
What are the ideal gas and van der Waal equations?
Ideal gas law gives the relation of the pressure and volume of the hypothetical gas with the moles, gas constant and the temperature.
Van der Waals equation gives the relation of the two properties of the gas including attractive forces and the molar volume.
By the ideal gas equation, pressure can be given as,
[tex]\rm PV = nRT[/tex]
Where,
- Volume (V) = 1.0 L
- Moles (n) = 0.5 mol
- Temperature (T) = 298.08 K
Substituting values in the equation:
[tex]\begin{aligned}\rm P &= \rm \dfrac{nRT}{V}\\\\&= \dfrac{0.5 \times 0.0821 \times 298.08}{1.0}\\\\&= 12.24\;\rm atm\end{aligned}[/tex]
By the Vander Waal equation pressure can be given as:
[tex]\rm [P+a(\dfrac{n}{V})^{2}](\dfrac{V}{n} - b) = RT[/tex]
Where,
- Moles (n) = 0.5 mol
- Gas constant (R) = 0.0821 L atm/mol K
- Temperature (T) = 298.08 K
- Volume (V) = 1.0 L
- a= 1.370
- b = 0.0387
Substituting values in the equation:
[tex]\begin{aligned}\rm P &= \rm \dfrac{nRT}{(V-nb)} - \dfrac{n^{2}a}{V^{2}}\\\\&= \dfrac{0.5 \times 0.0821 \times 298.08 }{(1 -(0.5 \times 0.0387))} - \dfrac{(0.5)^{2} \times 1.370}{(1)^{2}}\\\\&= 12.14\;\rm atm\end{aligned}[/tex]
Pressure estimated by the ideal gas equation is 12.24 atm and that by the Vander wall equation is 12.14 atm.
Therefore, the pressure a. 12.24 atm and b. 12.14 atm.
Learn more about Vander wall and ideal gas equation here:
https://brainly.com/question/19166425
