Concept explainers
The Dieterici equation of state for one mole of gas is
Where a and b are constants determined experimentally. For NH3(g), a = 10.91 atm. L2 and b = 0.0401 L. Plot the pressure of the gas as the volume of 1.00 mol of NH3(g) expands from 22.4 L to 50.0 L at 273 K, and numerically determine the work done by the gas by measuring the area under the curve.
Interpretation:
The Dieterici equation of state for one mole of gas is
Where a and b are constants determined experimentally. For NH3(g), a = 10.91 atm. L2 and b = 0.0401 L. The pressure of the gas as the volume of 1.00 mol of NH3(g) expands from 22.4 L to 50.0 L at 273 K is to be plotted and numerically the work done by the gas by measuring the area under the curve is to be determined.
Concept introduction:
The ideal gas law considered the molecules of a gas as point particles with perfectly elastic collisions among them in nature. This works importantly well for gases at dilution and at low pressure in many experimental calculations. But the gas molecules are not performing as point masses, and there are situations where the properties of the gas molecules have measurable effect by experiments. Thus, a modification of the ideal gas equation was coined by Johannes D. van der Waals in 1873 to consider size of molecules and the interaction forces among them. Berthelot modified the van der Waals equation as modified Berthelot model of state and further changes was made, and the equation was provided as Dieterici equation of state. The significant advantages of this equation, such as a more realistic critical compressibility factor are documented.
Answer to Problem 2.91E
The Dieterici equation of state for one mole of gas is
Explanation of Solution
The Dieterici equation of state for one mole of gas is
Given,
a = 10.91 atm. L2
b = 0.0401 L
volume of gas initial = 22.4 L
volume of gas final = 50.0 L
temperature of system = 273 K
pressure at 22.4 L is calculated as,
∴ pressure at 22.4 L = 0.9794 atm
Similarly, pressure at 50 L is calculated as follows;
∴ pressure at 50 L = 0.4435 atm
From the graph the pressure difference can be calculated as;
0.5359 atm.
the work done by the gas by measuring the area under the curve is determined as;
Thus, the pressure of the gas is plotted against volume and the work done in expansion is calculated.
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