Why is the universal gas constant a constant?

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opus
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The ideal gas law is given as ##PV=nRT## where ##R## is said to be the universal gas constant equal to ##0.082056\frac{L⋅atm}{mol⋅K}##. ##R## is said to be a constant, and thus cannot change even if we change the values of ##P,V,n,T##.
I don't see how this is possible, because the way we found ##R## to begin with is to take certain values of ##P,V,n,T## and then solve for ##R##. So it seems like if we were to change any of them, ##R## would need to change as well.
 

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  • #2
phyzguy
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The ideal gas law is given as ##PV=nRT## where ##R## is said to be the universal gas constant equal to ##0.082056\frac{L⋅atm}{mol⋅K}##. ##R## is said to be a constant, and thus cannot change even if we change the values of ##P,V,n,T##.
I don't see how this is possible, because the way we found ##R## to begin with is to take certain values of ##P,V,n,T## and then solve for ##R##. So it seems like if we were to change any of them, ##R## would need to change as well.

The point is that you can't change just one of P,V,n,T without one of the others changing. Suppose I take a fixed quantity of gas in a container of fixed size, for example. If I heat it up to change T, P will change as well by the same fraction. So if you take some other set of P,V,n,T and solve for R, you will always get the same R. This is what the ideal gas law says, and it is true to a high degree of accuracy in most circumstances.
 
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kuruman
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Boyle's law says that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.
Charles' law says that for a fixed amount of an ideal gas kept at a fixed pressure, temperature and volume are directly proportional.
These are experimental observations. You put them together to get the ideal gas law that for a fixed amount of an ideal gas the product of pressure and volume are proportional to the temperature. This means you can write pV = C T, where C is the constant of proportionality that contains the fixed amount of gas. If you express this amount of gas as number of molecules N, then C = Nk, where k is the Boltzmann constant. If you express this amount of gas as number of moles n, then C = nR, where R is the gas constant.
 
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without one of the others changing
Ohh ok. That was a key part I missed. So then if we change one, there will be a corresponding change in the others so that ##R## remains the same no matter what we change? So for example, according to Charle's Law, at a constant pressure, temperature and volume are directly proportional. So if I increase the temperature, the volume will increase proportionally and as such, ##R## would remain the same?
 
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opus
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Boyle's law says that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.
Charles' law says that for a fixed amount of an ideal gas kept at a fixed pressure, temperature and volume are directly proportional.
These are experimental observations. You put them together to get the ideal gas law that for a fixed amount of an ideal gas the product of pressure and volume are proportional to the temperature. This means you can write pV = C T, where C is the constant of proportionality that contains the fixed amount of gas. If you express this amount of gas as number of molecules N, then C = Nk, where k is the Boltzmann constant. If you express this amount of gas as number of moles n, then C = nR, where R is the gas constant.
Ok that makes more sense too in knowing that the Ideal Gas Law is a combination of those. I was confused at seeing things like "at a constant pressure" for Charle's Law because I couldn't imagine how you could increase the temperature without affecting the pressure. So then, are the individual laws such as Charles', Boyle's, Gay-Lussac's not very useful, but when combined into the Ideal Gas Law, then we can start to do something useful?
 
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kuruman
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Ok that makes more sense too in knowing that the Ideal Gas Law is a combination of those. I was confused at seeing things like "at a constant pressure" for Charle's Law because I couldn't imagine how you could increase the temperature without affecting the pressure. So then, are the individual laws such as Charles', Boyle's, Gay-Lussac's not very useful, but when combined into the Ideal Gas Law, then we can start to do something useful?
Yes.
 
  • #8
Borek
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I was confused at seeing things like "at a constant pressure" for Charle's Law because I couldn't imagine how you could increase the temperature without affecting the pressure.

If you work with a syringe and you don't block the piston movement you can safely assume the pressure inside is always identical to the pressure outside. As long as the pressure outside doesn't change (which is true if you do the experiment reasonably fast) you work at a "constant pressure", no matter if you heat or cool the gas inside the syringe.
 
  • #9
opus
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If you work with a syringe and you don't block the piston movement you can safely assume the pressure inside is always identical to the pressure outside. As long as the pressure outside doesn't change (which is true if you do the experiment reasonably fast) you work at a "constant pressure", no matter if you heat or cool the gas inside the syringe.
Cool! That makes sense. I don't have to take the Chem lab so I haven't had any experimental experiences like that. Kind of a bummer!
 

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