Question

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plz derive ideal gas equation

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Answer 1

$\huge\mathfrak\red{Answer :}$

$\textbf{Ideal Gas Equation :}$

A gas that follows Boyle's Law, Charles Law and Avogadro's Law strictly is called an Ideal Gas.

By combination of all these three laws, we get a combined gas equation, called ideal gas equation...

Boyles law... at constant T and n;

$V$ $\alpha$ $\dfrac{1}{P}$ ....(1)

Charles Law.... at constant P and n;

$V$ $\alpha$ $T$ ....(2)

Avogadro's Law... at constant P and T;

$V$ $\alpha$ $n$ ....(3)

Here;

P = Pressure of gas.

V = Volume of gas.

n = Number of moles of gas.

T = Temperature of gas.

R = Gas constant.

By combination of equation (1), (2) and (3) we get;

$V$ $\alpha$ $\dfrac{nT}{P}$

$V$ = $R\times\:\dfrac{nT}{P}$

$\textbf{PV\:=\:nRT}$

[Which is ideal gas equation]

Answer 2

☆ According to Boyle's Law,

v∝1p when  T & n constant.


☆ According to Charle's Law,

v∝T when  p & nconstant.


☆ According to Avogadro's Law,

v∝n when  p & Tconstant

According theory of variation,

v∝nT/P


We can write this in this form, 

v=R⋅nTp

⇒pv = nRT.
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