At low pressure,the Van der Waals equation is | vedclass

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(A) The Van der Waals equation for $1 \ mol$ of gas is: $(P + \frac{a}{V_m^2})(V_m - b) = RT$. At low pressure,$V_m$ is very large,so $b$ is negligibl

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$Z = \frac{PV_m}{RT} = 1 - \frac{a}{V_m RT}$

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(A) The Van der Waals equation for $1 \ mol$ of gas is: $(P + \frac{a}{V_m^2})(V_m - b) = RT$. At low pressure,$V_m$ is very large,so $b$ is negligible compared to $V_m$ $(V_m - b \approx V_m)$. The equation becomes: $(P + \frac{a}{V_m^2})V_m = RT$. Expanding this: $PV_m + \frac{a}{V_m} = RT$. Dividing by $RT$: $\frac{PV_m}{RT} + \frac{a}{V_m RT} = 1$. Therefore,the compressibility factor $Z = \frac{PV_m}{RT} = 1 - \frac{a}{V_m RT}$.

At low pressure,the Van der Waals equation is reduced to:

Similar Questions

For one mole of a van der Waals gas when $b=0$ and $T=300 \ K$,the $PV$ vs. $1/V$ plot is shown below. The value of the van der Waals constant $a$ (in $\text{atm} \cdot \text{liter}^2 \cdot \text{mol}^{-2}$) is:

Which gas shows real behavior?

$1 \ mol$ of a real gas is kept at a high pressure of $100 \ bar$ at $300 \ K$. If the van der Waals constant $b$ is $0.005 \ L \ mol^{-1}$, what are the values of the compressibility factor $Z$ of the gas and the $\%$ deviation of volume from ideality?
$Z$ $\%$ Deviation

Which of the following formulae is used to determine the compressibility factor $(Z)$ for the measurement of deviation from ideal behavior?

In the van der Waals equation for real gases,which of the following terms represents the correction for intermolecular forces?

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