Variables in Gas laws

[popcornfrenzy]

How are variables in the Gas laws are formulated in such way that show direct and inverse relationships?

Hi I'm a first year Environmental Science student I just want to ask how scientists were able to determine which is which like in Boyle's law, he determined that by multiplying the initial pressure and volume and making it equal to the change in pressure and volume produces an inverse relationship. I get that if you look for the missing variable; for example a high value for V2 in the equation P2= (P1)(V1) / V2 will produce a lower value for P2, but by looking at the formula P1V1 = P2V2 alone how was he able to determine that it would lead to inverse relationship. Taking note of the k = P1V1, without comparing the changes, how was he sure that just by multiplying both P1V1 will lead to the relationship. Same question for other gas laws such as the Charles's law that show direct relationship through the division of V and T. 

It might be a dumb question to ask sorry, it's just that I'm having a hard time comprehending these things. 

Edited March 23, 2021 by popcornfrenzy

[Sensei]

Experimentally.. e.g. have thermometer and manometer. Increase temperature with fixed volume (closed container) and observe readings from manometer..

[popcornfrenzy]

Oh thanks for the reply, I was wondering what is that J-shaped glass tube that Robert Boyle used in his experiment now I know that it's a manometer. Aside from that, determining relationships mathematically is purely based on logic? I think that's the reason why I can't understand it at first thank you so much.

Edited March 23, 2021 by popcornfrenzy

[Sensei]

Here you have nice explanations of various types of manometers with images:

https://www.engineeringclicks.com/manometer/

 

[studiot]

56 minutes ago, popcornfrenzy said:

How are variables in the Gas laws are formulated in such way that show direct and inverse relationships?

Hi I'm a first year Environmental Science student I just want to ask how scientists were able to determine which is which like in Boyle's law, he determined that by multiplying the initial pressure and volume and making it equal to the change in pressure and volume produces an inverse relationship. I get that if you look for the missing variable; for example a high value for V2 in the equation P2= (P1)(V1) / V2 will produce a lower value for P2, but by looking at the formula P1V1 = P2V2 alone how was he able to determine that it would lead to inverse relationship. Taking note of the k = P1V1, without comparing the changes, how was he sure that just by multiplying both P1V1 will lead to the relationship. Same question for other gas laws such as the Charles's law that show direct relationship through the division of V and T. 

It might be a dumb question to ask sorry, it's just that I'm having a hard time comprehending these things. 

First welcome to Science Forums.

It is not a dumb question, there are no dumb questions if honestly asked.
It is only dumb not to ask if you are unsure.

 

I think the key to your difficulty is introducing changes which is not appropriate in this case.
You directly with the variables of pressure and volume and mass.
As Sensei said, they can be directly measured or observed and are called observables.
As Boyle directly observed that as the pressure increases the volume decreases and vice versa.
So it is one of these quantities that is directly proportional and the other that is indirectly proportional.

It is true that for some theory you have to look at changes or differences and you may have already been told this.
This would be true, for instance of the variable height or height differences, which is an important variable in environmental theory.
That is because height is a different sort of variable from volume or mass or pressure.
With volume, mass and pressure you can have an actual zero ie no pressure, no mass or no volume perhaps because the is nothing there.

This is not true of height because you have to ask height above what ?

That is you are always measuring height difference.
For instance we often talk of height above sea level (altitude).

The result of this is that for something that changes proportionally to such a vaiable introduces a fixed constant and the equation is not y = mx but y = mx + c

Please ask if you want further explanation because this distinction will appear again and again in your studies.

 

Final note, you are allowed a total of 5 posts in your first 24 hours here as a spam prevention measure.
After that you can post away to your heart's content.

Hope this helps.
 

 

[swansont]

4 hours ago, popcornfrenzy said:

Oh thanks for the reply, I was wondering what is that J-shaped glass tube that Robert Boyle used in his experiment now I know that it's a manometer. Aside from that, determining relationships mathematically is purely based on logic? I think that's the reason why I can't understand it at first thank you so much.

It's based on the math analysis of data. You do a bunch of measurements where you change one variable (e.g. temperature) and then measure the effect on the one you measure, e.g. pressure. In this example, you know V is fixed, because you're using a rigid apparatus.

You look at the graph. You can fit a curve/line to the data (studiot gave the equation you would use for fitting a straight line) 

[popcornfrenzy]

Oh thanks to both of you, I further understand the role of the constant now in mathematical terms based on what you've written it Sir Studiot and thanks for further elaborating Sir Swansont. I think I need to polish my fundamentals especially on my math more now that I'm pursuing a science course. I'm planning to take chemistry for my MA and PhD so I really need to understand such basic concepts. Forgive me for lacking mathematical skills as I need to improve more on it. Also, Sir Studiot, I searched for the Environmental Theory is it by Florence Nightingale? is that what you're referring to? Forgive me for my English as I'm not yet quite proficient with it as a second language here in the Philippines. 

Also thanks for the warm welcome.

Edited March 24, 2021 by popcornfrenzy

[swansont]

I think you'll find having proficiency in math will help a lot with being able to work chemistry problems. Good luck!

[popcornfrenzy]

Thanks Sir