# Ideal gas equation derivation proportionality [duplicate]

While deriving the Ideal gas Equation using Boyle's, Charles', and Avogadro Laws, how are each of the laws, which have different proportionality constants and different quantities as constant combined? (eg: Boyle's law which assumes the temperature and moles of gas to be constant, but in Charles' law temperature changes. How is it possible?)

• If you consider the ideal gas state equation $pV=nRT$, and if you keep either of the 3 state variables p,V,T constant, involving its value into the equation constant, you get each of the respective original gas laws. – Poutnik Aug 23 '20 at 16:13
• Related question: chemistry.stackexchange.com/questions/58330/…. – Mathew Mahindaratne Aug 23 '20 at 16:52

I understand your concern because this is the way it is taught in South Asian schools and colleges and even general chemistry texts taught elsewhere are silent about it. They state all the individual gas laws using a proportionality sign "$$\propto$$" and magically all gas laws are combined and that becomes $$R$$- the universal gas constant. This is done in a single paragraph.