Question

derive ideal gas equation

Answer 1

P IS INVERSELY PROPORTIONAL TO V @CONST TEMP
VOLUME IS DIRECTLY PROPORTIONAL TO T
@CONST PRESSURE
VOLUME IS DIRECTLY PROPORTIONAL TO NUMBER OF MOLES
=>P ∝ 1/V=>V ∝ 1/P
=>V ∝ T
=>V ∝ n
=>V ∝ nT/P
=>V=RnT/P
here R IS KNOWN AS GAS CONSTANT
=>PV=nRT
HENCE PROVED

Answer 2

${\boxed{\tt{The\:Ideal\:Gas\:Equation\:!!}}}$

Answer:

A sample of Gas can be described in terms of its pressure, temperature (Kelvin), Volume, and the number of moles present. Anny three of these variables determine the fourth.

To sum up of the above gas laws in a general way, we have by

Boyle's Law = V is inversely proportional to 1/P (Constant T and n).

Avogadro's Law = V is directly proportional to n (Constant P and T).

Charles's Law = V is directly proportional to T (Constant P and n).

and therefore , V is directly proportional to nT/P

On rearranging PV is directly proportional to nT that is PV = bnT.

Explanation:

Where b is a proportionality constant. This constant depends on the units used for P, V and T in equation, and on the mass of the gas. If we choose one mole of gas at STP , the proportionality constant is the same for all gases.

The constant, b , is then represented by R, and is known as the ideal gas constant or universal gas constant.

The equation then becomes

PV = nRT Or PV/nT = R = Constant

The equation is known as the ideal gas equation or equation of state because the state of a substance in thermal equilibrium can be fixed by specifying any two of the three variables P, V and T.

The ideal Gas is one that obeys the gas law exactly.

In nature no gas is perfectly ideal the are real gases but behave as almost ideal under certain range of temperature and pressure.

The temperature range at which Boyle's Law is obeyed i.e., real haa behaves almost ideal over a wide range of pressure is called Boyle Temperature.

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