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# The ideal gas law (PV = nRT)

The ideal gas law (PV = nRT) relates the macroscopic properties of ideal gases. An ideal gas is a gas in which the particles (a) do not attract or repel one another and (b) take up no space (have no volume). No gas is truly ideal, but the ideal gas law does provide a good approximation of real gas behavior under many conditions. Created by Sal Khan.

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• Can't you derive the equation from Boyle's, Charles's, and Avogadro's law? Since volume is proportional to temperature, pressure, and moles, can you say that by adding proportionality constant R you can relate these in PV=nRT?
• Yes. The Ideal gas equation is a synthesis of all three laws. Ya science!!
• Why does temperature always have to be converted to Kelvin??
• You have to convert to Kelvin because Celsius is a relative scale. Specifically, 0°C is NOT the point of no heat. Instead, 0°C was set as a convenient point for humans (specifically it is the temperature where water freezes at standard pressure). Likewise, doubling a temperature in Celsius is not doubling the heat (again, because the 0 is not an absolute 0).

But, to do these calculations, you must have an absolute scale. 0 must mean no heat. A doubling of the temperature must mean a doubling of the heat. Thus, you use Kelvin because 0K is the point of no heat. When you double a temperature on the Kelvin scale you really are doubling the heat.

Example: On the Celsius scale, if you double 1°C you would get 2°C -- which is hardly any warmer. The temperature that actually has twice as much heat as 1°C is 275°C (rounded to the nearest degree). On the Kelvin scale, you have this problem corrected.
• If ideal gas laws are applicable only for 'ideal' gases , then why study them at all if there exists no such 'ideal' gas ?
• Two reasons:
1) Lots of gases approximate ideal gases as long as the temperature is high and the pressure is low
2) You have to walk before you can run.
• True or False: If one gas is more dense than another, it's because it has more molecules at 22.4L of the gas at stp.

I don't get it.... where is this explained?
If you solve the Ideal Gas equation for n (the number of particles expressed as moles) you get:
n = PV/RT

Thus, at STP, the same volume of all gases have the same number of molecules (provided the conditions are suitable for the Ideal Gas Law to apply).

A more dense gas has more MASSIVE molecules, but the same number of particles as compared to a less dense gas under the same temperature, pressure and volume.

So, in summary, the Ideal Gas Law states that under the same temperature, pressure and volume all gases contain the same number of molecules (but not the same mass).

Reminder: The Ideal Gas law does not apply when the temperature and pressure are near the point of transforming into a liquid or solid.
• what is the value of R in the equation??
• R can have multiple values depending on the units of the other variables.
If pressure is in atm, R = 0.0821
If pressure is in kPa, R = 8.314

There are lots of other options, but those are the most common units of R. Hope that helps!
• Why do you need to put in R in the equation?
• R is the constant that makes the equation true, kind of like when you use pi to find the circumference, area of a circle or volume of a sphere.
• My teacher told me that an ideal gas is one that follows Boyle's law, Charles' law and Avogadro's law strictly is an Ideal Gas and it is hypothetical but Sal says something else for describing the ideal gas. Help!! :|
• The Ideal Gas is a model that GREATLY simplifies the math necessary for describing the behavior of real gases. As Andrew M mentioned, if the temperature is high enough and the pressure low enough that the gas is nowhere near liquifying or solidifying, then real gases usually behave close enough to ideal gases that we can use the Ideal Gas law.

If you go through the very difficult math for the equations for real gases, you generally get an answer only a fraction of a percent different from the much easier math of the Ideal Gas Law. However, if the temperature and/or pressure is close to where the gas becomes a liquid or a solid, then the Ideal Gas Law will give you VERY wrong answers. In those cases you have to use the much more difficult mathematics for the real gas equations of state. But, except when we have to, we don't use the other equations of state because they are so hard to work with. Most of the time an error of less than 0.5% is acceptable and we use the Ideal Gas Law.

Just for reference, one of the better equations of state that does much better at predicting the behavior of gases as they begin to condense into liquids is the Peng–Robinson equation. You may learn about it at this link http://kshmakov.org/fluid/note/3/
I think you will quickly see why we avoid that level of complexity whenever we can.
• what is the difference between ideal gas and normal gasses and noble gasses??
• An ideal gas is just that, "ideal", it does not really exist. Instead, it is an approximation that comes very close to the way that most real gases behave near conditions found in Earth's environment. Many times, the approximation is so close to reality that we can just ignore the error because it will be so slight we can barely detect the error at all.

The reason we use such approximations is that calculations closer to reality get EXTREMELY complicated and very hard to understand. So we use the Ideal Gas Law any time we possibly can.

There are, however, situations (mostly when the gas is near condensing into a liquid) that the Ideal Gas Law gives such poor approximations that we cannot use it and must go with something more complex.
• What is the equation PV=nTR?
• This equation is the ideal gas law. It explains the relationship between the different conditions and amounts of the ideal gas.
P = pressure
V = volume
n = moles of gas
T = temperature (in Kelvin)
R = ideal gas constant