Isothermal compressibility K of an ideal gas is defined as K-1-V - V- P T-n What is the isothermal compressibility factor for an ideal gas at 1-0 atm -

We know that at constant T amp; n, PV = C(Constant) (According to Boyles law) V=C/P or ( ∂ V/∂ P )_T.n = C/P^2= V/P [ ∵ V=C/P ] ∴ K= 1/V ( ∂ V/∂ P )_T.n =1/ ...

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Standard XII

Chemistry

Van der Waal's Forces

Isothermal co...

Question

Isothermal compressibility (K) of an ideal gas is defined as $K = - \frac{1}{V} {(\frac{\partial V}{\partial P})}_{T . n}$
What is the isothermal compressibility factor for an ideal gas at 1.0 atm ? ___

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Solution

We know that at constant T & n, PV = C(Constant) (According to Boyles law)
$V = \frac{C}{P} o r {(\frac{\partial V}{\partial P})}_{T . n} = - \frac{C}{P^{2}} = - \frac{V}{P} [∵ V = \frac{C}{P}]$
$∴ K = - \frac{1}{V} {(\frac{\partial V}{\partial P})}_{T . n} = \frac{1}{P} = 1 a t m^{- 1}$

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Isothermal compressibility (K) of an ideal gas is defined as K=−1V(∂V∂P)T.n What is the isothermal compressibility factor for an ideal gas at 1.0 atm ? ___

We know that at constant T & n, PV = C(Constant) (According to Boyles law) V=CP or (∂V∂P)T.n=−CP2=−VP[∵V=CP] ∴ K=−1V(∂V∂P)T.n=1P=1 atm−1

Isothermal compressibility (K) of an ideal gas is defined as $K = - \frac{1}{V} {(\frac{\partial V}{\partial P})}_{T . n}$
What is the isothermal compressibility factor for an ideal gas at 1.0 atm ? ___

We know that at constant T & n, PV = C(Constant) (According to Boyles law)
$V = \frac{C}{P} o r {(\frac{\partial V}{\partial P})}_{T . n} = - \frac{C}{P^{2}} = - \frac{V}{P} [∵ V = \frac{C}{P}]$
$∴ K = - \frac{1}{V} {(\frac{\partial V}{\partial P})}_{T . n} = \frac{1}{P} = 1 a t m^{- 1}$