Van der Waals Graph: What is the Significance of PV & Trough?

In summary, this graph is used to compare gas behavior and to determine how far a gas deviates from ideal gas behavior.
  • #1
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For an assignment, I am graphing using the Van der Waals equation. I am meant to find graph PV (y-axis) over (P). However, I am not sure why. On the internet, most other graphs also use these axes. Why do you use PV though?

I am getting a graph that generally similar to those on the internet. Mine goes into a bit of a trough at then it escalates upwards. Could someone please also tell me what the trough indicates? i was thinking it had something to do with liquefying but I am not sure if that is true.
 
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  • #2
you mean this?

[URL]http://www.topcoaching.com/images/001/realGasBehaviour.jpg[/URL]

For an ideal gas, PV is constant. That's Boyle's law. You can use either PV or PV/RT for the y-axis, since the RT is constant given constant temperature. According to the PV=nRT equation, PV/RT = n which is a constant and has a value of 1 when you use one mole of gas.

For ideal gases, the PV against P graph is a horizontal line. This line is used as a benchmark for comparison. All real gases deviate from this line, and the extent of deviation from this line indicates how far a gas deviates from ideal gas behaviour. Implicitly, this means how strong the intermolecular forces are between the gas molecules - the greater the deviation, the stronger the intermolecular forces. (Recall: Ideal gases have negligible intermolecular forces.)

As the external pressure increases, the moleculars are more closely packed and therefore the intermolecular forces of attraction increases. The gas molecules pull one another closer due to attraction and therefore the gas appears to "shrink" (loosely speaking). Volume decreases more than increase in pressure and hence there is a net decrease in PV.

As the external pressure increases further, there will be a point where the gas cannot be compressed anymore and will start to push against the container wall. The pressure in the container therefore increase more than the decrease in volume and hence there is a net increase in PV.
 
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  • #3
Yes, this certainly clarifies a few things for me. Thanks for the time you put into the answer.

However, how come PV/P is used instead of volume? Wouldn't that have the same effect?
 
  • #4
I don't know the exact reason pressure is used instead of volume but I'm quite sure it has some practical reasons. This graph is plotted out empirically, i.e. with measurements at different pressure range. Pressure is more direct to measure than volume, with a pressure gauge rather than measuring the dimensions of the container separately and then doing some calculations depending on whether the container is spherical, cylinder and what not.
 
  • #5


I can provide some insight into the significance of PV and the trough in a Van der Waals graph. The Van der Waals equation is a mathematical model that describes the behavior of real gases, taking into account intermolecular forces and the volume occupied by gas particles. The equation is written as (P + a/V^2)(V - b) = RT, where P is pressure, V is volume, a and b are constants, R is the gas constant, and T is temperature.

The PV term in the equation represents the pressure-volume product, which is an important parameter in gas behavior. By plotting PV on the y-axis and P on the x-axis, we can observe the relationship between these two variables and how it changes with different conditions such as temperature and pressure.

The presence of a trough in the graph indicates a critical point, which is the point at which a gas can no longer be distinguished from its liquid state. This is due to the fact that at the critical point, the gas and liquid phases have the same density and can coexist in equilibrium. The trough in the graph represents the minimum value of PV at this critical point.

The critical point and the trough are important concepts in understanding the behavior of real gases, as they mark the transition between gas and liquid states. By studying the Van der Waals graph, we can gain insight into the properties of gases and how they behave under different conditions.

In conclusion, the PV axis is used in a Van der Waals graph because it represents an important parameter in gas behavior, and the trough indicates the critical point where a gas becomes indistinguishable from its liquid state. I hope this helps to clarify the significance of these elements in your graph.
 

1. What is the Van der Waals graph?

The Van der Waals graph is a plot of pressure (P) versus volume (V) for a given temperature (T). It is used to visualize the behavior of real gases, taking into account intermolecular forces that are not considered in the ideal gas law.

2. What is the significance of PV in the Van der Waals graph?

PV represents the product of pressure and volume, which is a constant value for a given amount of gas at a constant temperature. In the Van der Waals graph, it is used to plot the curve that represents the behavior of real gases, as it takes into account the volume occupied by the gas molecules themselves.

3. What does the trough in the Van der Waals graph represent?

The trough in the Van der Waals graph represents the region where the pressure and volume of a gas are at their lowest values. This is due to the attractive forces between gas molecules, which cause the volume to decrease and the pressure to decrease as well.

4. Why is temperature (T) included in the Van der Waals graph?

Temperature is included in the Van der Waals graph because it affects the behavior of gases. As temperature increases, the kinetic energy of gas molecules increases, resulting in more frequent collisions and a higher pressure. By including temperature, the Van der Waals graph can accurately depict the behavior of gases at different temperatures.

5. How is the Van der Waals graph different from the ideal gas law?

The ideal gas law assumes that gas molecules have no volume and do not interact with each other, which is not true for real gases. The Van der Waals graph takes into account intermolecular forces and the volume occupied by gas molecules, making it a more accurate representation of real gas behavior. It also has a slightly curved shape, while the ideal gas law line is straight.

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