To calculate the number of molecules in a sample, we can use Avogadro's number, which represents the number of entities (atoms, molecules, ions, etc.) present in one mole of a substance. Avogadro's number is approximately 6.022 x 10^23 entities per mole.

The molar mass of dimethylmercury (CH3)2Hg is the sum of the atomic masses of its constituent atoms: 2(12.01 g/mol) for the two carbon atoms, 6(1.01 g/mol) for the six hydrogen atoms, and 1(200.59 g/mol) for the mercury atom. Therefore, the molar mass of dimethylmercury is approximately 230.64 g/mol.

Now, we can use the given mass of dimethylmercury (4.15 g) and its molar mass to determine the number of moles in the sample:

Moles of dimethylmercury = Mass / Molar mass

Moles of dimethylmercury = 4.15 g / 230.64 g/mol

Moles of dimethylmercury ≈ 0.0180 mol

Finally, we can multiply the moles of dimethylmercury by Avogadro's number to find the number of molecules in the sample:

Number of molecules = Moles × Avogadro's number

Number of molecules ≈ 0.0180 mol × 6.022 x 10^23 molecules/mol

Number of molecules ≈ 1.08 x 10^23 molecules

Therefore, a 4.15-g sample of dimethylmercury contains approximately 1.08 x 10^23 molecules.