(Solved): (b) The van der Waals equation has the form; \[ \left(p+\frac{a n^{2}}{V^{2}}\right)(V-n b)=n R T \ ...

(b) The van der Waals equation has the form; \[ \left(p+\frac{a n^{2}}{V^{2}}\right)(V-n b)=n R T \] (i) How does this equation differ from the ideal gas equation? (2 marks) (ii) Explain the meaning of the two expressions in parentheses (brackets) in this equation. (4 marks) (iii) Use the van der Waals equation to calculate the pressure of \( 5.0 \mathrm{~mol} \) of a gas confined to a volume of \( 3.5 \mathrm{~L} \) at \( 30^{\circ} \mathrm{C} \). Is it larger or smaller than the pressure obtained from the ideal gas equation? The van der Waals coefficients of the gas are \( a=5.507 \mathrm{dm}^{6} \) atm \( \mathrm{mol}^{-2}, b=0.0651 \mathrm{dm}^{3} \mathrm{~mol}^{-1} \). (6 marks) (a) Draw each of the molecules below and classify them as polar or non-polar. Indicate the overall dipole moment of any polar molecules with an arrow: (i) \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{~F} \) (ii) \( \mathrm{CH}_{4} \) (iii) \( \mathrm{H}_{2} \mathrm{~S} \) (6 marks) (b) The Lennard-Jones potential (as given below) combines two energy terms: \[ V(r)=4 \varepsilon\left\{\left(\frac{r_{0}}{r}\right)^{12}-\left(\frac{r_{0}}{r}\right)^{6}\right\} \] (i) Indicate, qualitatively, at what separation distance in the Lennard-Jones potential a species has a) a repulsive force acting on it; b) an attractive force; c) no force. (3 marks) (ii) Two atoms are separated by a distance of \( 3.80 \AA \), which coincides with the \( r_{0} \) value of their LennardJones potential. If their separation distance is decreased to \( 3.70 \AA \), does the intermolecular potential between the molecules become more negative or more positive? Justify your answer. (2 marks)