use the ideal gas law (pV = nRT) to derive as many gas laws as you can

Question

derive: Boyle's Law, Charles' Law, Gay Lussac's Law, Avogadro's Law and Combined gas Law.

Answer 1

PV = nRT ... ideal gas law

If you have two conditions for the gas, the initial condition and the final condition, you would have...

P₁V₁ = n₁RT₁ for the initial condition and

P₂V₂ = n₂RT₂ for the final condition

And since R is the gas CONSTANT, it will not vary (it's a constant), so we can write ...

P₁V₁ = n₁T₁ for the initial condition and

P₂V₂ = n₂T₂ for the final condition

Finally, we can relate these as follows:

P₁V₁ / n₁T₁ = P₂V₂ / n₂T₂

If the number of moles (n) is constant, we have ..,

P₁V₁ / T₁ = P₂V₂ / T₂ ... COMBINED GAS LAW

From this, we can derive Boyles law and Charles law ...

If T (temperature) is constant, we have

P₁V₁ = P₂V₂ ... BOYLE'S LAW

If P (pressure) is constant, we have

V₁ / T₁ = V₂ / T₂ ... CHARLES' LAW

If V (volume) is constant, we have

P₁ / T₁ = P₂ / T₂ ... GAY LUSSAC'S LAW

If T and P are constant, and the number of moles (n) changes, we have

V₁/n₁ = V₂/n₂ ... AVOGADRO'S LAW