Final answer:
The molecule with the smallest molecular dipole moment is H2 because it is a homonuclear diatomic molecule with no difference in electronegativity, resulting in a zero dipole moment.
Step-by-step explanation:
The molecule predicted to have the smallest molecular dipole moment among HI, HCl, H2, and HBr is H2. This is because H2 is a homonuclear diatomic molecule, meaning it consists of two identical atoms. Therefore, there is no difference in electronegativity between the hydrogen atoms, and as a result, the dipole moment is zero. In contrast, HI, HCl, and HBr are heteronuclear diatomic molecules which have a positive dipole moment due to the difference in electronegativity between the hydrogen atom and the halogen atom. However, the difference in electronegativity is greater in HCl as compared to HI, leading to a larger dipole moment. For HBr, the dipole moment is also significant but typically smaller than that of HCl due to intermediate electronegativity difference. Given the electronegativity values (XH = 2.20; XCl = 3.16; XCl-XH = 0.96), HCl has a relatively large dipole moment. The bond dipole moment for HCl is known to be 1.08 D, and for HI, it is 0.44 D, thus showing that HI is less polar than HCl.