In dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}(\mu=1.60 \mathrm{D})\), the dispersion force contribution to the intermolecular attractive forces is about five times larger than the dipole-dipole contribution. Compared to \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), would you expect the relative importance of the dipole-dipole contribution to increase or decrease (a) in dibromomethane \((\mu=1.43 \mathrm{D}),(\mathbf{b})\) in difluoromethane \((\mu=1.93 \mathrm{D}) ?\) Explain.

First, let's analyze the given values for CH2Cl2 to understand the question's context. We are given that the dispersion force contribution is about five times larger than the dipole-dipole contribution for dichloromethane (CH2Cl2). Thus, the ratio of dispersion force to dipole-dipole force for CH2Cl2 is: Dispersion Force / Dipole-Dipole Force = 5 Keep this in mind as we continue to analyze the other two compounds.

We are given the dipole moments for dibromomethane (CH2Br2) and difluoromethane (CH2F2) as 1.43 D and 1.93 D, respectively. Dipole moment for CH2Br2: \(\mu = 1.43 \,\mathrm{D}\) Dipole moment for CH2F2: \(\mu = 1.93 \,\mathrm{D}\) Higher dipole moments typically correlate with stronger dipole-dipole interactions. To determine which compound has a larger relative importance of the dipole-dipole contribution, we need to compare the ratios of the dispersion forces to the dipole-dipole contributions for each compound.

Let's analyze the dipole-dipole contribution of each compound in comparison to CH2Cl2. For CH2Br2: We can see that the dipole moment of CH2Br2 (1.43 D) is slightly lower than that of CH2Cl2 (1.60 D), which indicates that the strength of the dipole-dipole force contribution for CH2Br2 is expected to be weaker. As a result, it is likely that the dispersion force to dipole-dipole force ratio would be higher (more significant dispersion force contribution) for CH2Br2. Thus, the relative importance of dipole-dipole contribution for CH2Br2 decreases. For CH2F2: The dipole moment of CH2F2 (1.93 D) is higher than that of CH2Cl2 (1.60 D), indicating that the strength of the dipole-dipole force contribution for CH2F2 is likely to be stronger. Thus, the dispersion force to dipole-dipole force ratio would be lower (less significant dispersion force contribution) for CH2F2. So, the relative importance of dipole-dipole contribution for CH2F2 increases.

In conclusion, the relative importance of the dipole-dipole contribution to intermolecular attractive forces: (a) decreases for dibromomethane (CH2Br2) compared to dichloromethane (CH2Cl2) (b) increases for difluoromethane (CH2F2) compared to dichloromethane (CH2Cl2)