Molar volume \( (V_m) \) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with \( V_m \) as the variable. The ratio (in \( \mathrm{mol\ dm^{-3}} \)) of the coefficient of \( V_m^{2} \) to the coefficient of \( V_m \) for a gas having van der Waals constants \( a = 6.0 \) \( \mathrm{dm^{6}\ atm\ mol^{-2}} \) and \( b = 0.060 \) \( \mathrm{dm^{3}\ mol^{-1}} \) at \( 300 \) \( \mathrm{K} \) and \( 300 \) \( \mathrm{atm} \) is __________.
Use: Universal gas constant \( (R) = 0.082 \) \( \mathrm{dm^{3}\ atm\ mol^{-1}\ K^{-1}} \)
