how does boyle's law relate to the ideal gas equation?

Question

This is also known as PERVERT. This relates all 3 ideal gas laws

Answer 1

Boyle's law states that

p1v1=p2v2

provided that amount of gas, and temperature remains constant.

How does this relate to pv = nrt?

Well, the truth is that pv = nrt is all you need. All these silly contrived laws - gay-lussac, boyle, and all that nonsense are made to honor scientists (with the unfortunate effect of confusing students).

The basic idea is this

(PV)/(NRT)initial = (PV)/(NRT)final

Now we know that for boyle'ls law the amount of gas is the same so Ninitial = Nfinal. And the temperature is the same Tinitial = Tfinal.

So, if we multiply both sides of the above equation by T (which are the same on both sides - initial and final values are equal) we get this equation:

PV/NR initial = PV/NR final

Because N and R are the same on both sides too we can simplify to this:

PVinitial = PVfinal

Basically, you are just cancelling things that remain the same on either side of the universal gas law.

Answer 2

Boyle's regulation states that "at a persevering with temperature the quantity of a fastened quantity of gasoline is inversely proportional to the utilized tension". that's often represented by using V = c (a million/P) the place c represents a persevering with. Rearrange this equation and you get PV = c (a persevering with). Your equation (PV=nRT) is prevalent by way of fact the "appropriate gasoline regulation". The variable "n" is the quantity of the gasoline expressed as moles. The variable "T" is easily the temperature. you could evaluate this equation to be an extension of Boyle's regulation the place the temperature is unique and the quantity of gasoline is unique. the fee of "R" is the "gasoline consistent". staring at Boyle's regulation, PV=c, the fee of "c" and be seen to equivalent "nRT".