What is the correct interpretation of the equation for real gases involving virial coefficients?

The equation for real gases that involves virial coefficients is expressed in the form ( pV = nRT(1 + B/V_m + ...) ), where ( p ) is the pressure, ( V ) is the volume, ( n ) is the number of moles, ( R ) is the ideal gas constant, ( T ) is the temperature, ( B ) is the second virial coefficient, and ( V_m ) is the molar volume.

This equation serves as a correction to the ideal gas law (which is given by ( pV = nRT )), accounting for the deviations of real gases from ideal behavior due to intermolecular forces and the volume occupied by the gas particles. The term ( B/V_m ) represents how these factors influence the pressure-volume relation for gases at different conditions.

In real scenarios, as pressure increases or when the gas is at a low temperature, the effects described by the virial coefficients become significant, and this equation becomes crucial for accurately describing gas behavior. The inclusion of the term ( B/V_m ) (and potentially higher-order terms in the series) allows for a more accurate depiction of how real gases behave compared to the assumptions made in