Solve Gas Laws Confusion - P, V, T & n

[ghostanime2001]

Hey guys ! I am confused when textbooks say that P (pressure), V (volume), T (temperature), n (moles) or any combinations of these be CONSTANTS. Especially when it comes down to the three gas laws. I don't understand what some variable being a constant means :( and hence the immense confusion when I'm trying to understand these laws.

 

[Studiot]

Hello ghost,

Gasses have a number of interdependent mechanical and thermal properties that are set by circumstances. That is they depend upon both the external world and the gas itself.
These properties include the temperature (T) the pressure (P) and the volume (V) and density (ρ)

There are also properties which are inherent in the particular sample of gas itself and not dependent on the external world.
These include the mass (m), molecular weight (M), number of moles (n), and so on. Some of these will be constant eg the molecular weight of oxygen is a fixed number, 32.

Over the centuries, various individual laws linking all these properties have been developed and these are what you ar now studying.

Important ones are

Boyles Law, Charles, Law, Avogadro's Law, the ideal gas law which is a combination of Boyles and Charles laws.

Taking the last one.

PV = nRT

One variable, number of moles, is set by the sample of gas itself
n = number of moles = mass / molecular weight.

By changing the environment we can change or fix the other three variables, P, V and T.

However we do not have total freedom to set all three. They interact so that changing one changes at least one of the others.
The equation describes this interaction.

So if we have a balloon of gas and heat it up (raise the temperature) it expands. That is the volume increases.
However we have not heated the whole atmosphere around the balloon so we have not changed the pressure upon it. That is we have held the pressure constant.
The equation tells us that if we double the temperature we must multiply the other side by 2 to compensate ie double the volume.

Alternatively we could heat the same amount of gas in a rigid container (pressure vessel).
And yes, you guessed it, we have now held the volume constant so the factor of 2 is now applied to the pressure, which must therefore double.

Does this help?

 

[ghostanime2001]

This reminds me when I was studying grade 9 functions ex. constant functions, linear etc.. I think you mean that every interval of time the value remains the same. So I guess, drawing a mental picture in my head, the pressure or volume doesn't change, it remains what it is from the environment. But I don't understand how if something is constant it is eliminated from the ideal gas law and simplified to give all the relationships expressed through the gas laws.

 

[Studiot]

Constants aren't eliminated, they have a definite value.

If, however, they remain unchanged when we change the circumstances from state1 to state2, then the diffeerence or change = 0

That is in our rigid container if V₂ = V₁

Then ΔV = V₂ - V₁ = 0

 

[Borek]

$$\frac{PV}{nT} = R$$

For every sample of the ideal gas $\frac{PV}{nT}$ has exactly the same value. That means when preparing a gas sample you have only a limited number of degrees of freedom - you can select any three parameters, but the fourth one will be a function of these three. $\frac{PV}{nT}$ is a constant.

In other cases we are limiting number of parameters we change. For example when we say PV=const we mean - if we keep nT constant (for example we can do experiments without allowing gas to escape nor enter the vessel, and we allow it to have the same temperature all the time), PV is a constant as well. Or when we say $\frac V T = const$ we mean it is constant as long as $\frac P n$ doesn't change (again, many ways to design an experiment this way).

 

[ghostanime2001]

I understand how setting up the experiments makes variables unchanged but I just don't understand the mathematics of it.

 

[Borek]

Now I don't understand what is the problem:

PV=k

You measure P, V and calculate the product. Then you change pressure, measure P, V - and product stays the same.