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Answer in Brief

Derive an Ideal gas equation. Mention the terms involved in it.

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#### Solution

According to Boyle’s law,

V ∝ `1/"P"` (at constant T and n) .…(1)

According to Charles’ law,

V ∝ T (at constant P and n) .…(2)

According to Avogadro’s law,

V ∝ n (at constant P and T) .…(3)

Combining relations (1), (2), and (3), we get

V ∝ `("nT")/"P"`

Converting this proportionality into an equation by introducing a constant of proportionality (‘R’ known as gas constant), we get

∴ V = `("nRT")/"P"`

On rearranging the above equation, we get

PV = nRT

where,

P = Pressure of gas,

V = Volume of gas,

n = number of moles of gas,

R = Gas constant,

T = Absolute temperature of gas.

This is the ideal gas equation or equation of state.

Concept: Deviation from Ideal Behaviour

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