Final answer:
To identify the compound from a 50.0 g sample with 2.20 x 10^23 molecules, the molar mass of the compound is calculated and compared to that of the given options. The molar mass is found to be approximately 137 g/mol, indicating that PCl3 is the most likely compound.
Step-by-step explanation:
To determine which compound could be represented by a 50.0 g sample containing 2.20 x 1023 molecules, we need to calculate the molar mass of the compound. The sample is smaller than a mole, given that one mole of any substance contains Avogadro's number of particles, which is approximately 6.02 x 1023. Using the formula:
Molar mass of compound = (mass of the sample in grams) / (number of moles in the sample)
We can compute the number of moles in the sample:
Number of moles = (number of molecules) / (Avogadro's number)
Thus:
Number of moles = (2.20 x 1023) / (6.02 x 1023 mol-1) ≈ 0.365 moles
Now, we calculate the molar mass:
Molar mass = (50.0 g) / (0.365 moles) ≈ 137 g/mol
Now, we compare this value to the molar masses of the options provided:
- NH3: 17.03 g/mol
- NF3: 71.00 g/mol
- PCl5: 208.24 g/mol
- PCl3: 137.33 g/mol
- PH3: 34.00 g/mol
The molar mass closest to our calculated molar mass of 137 g/mol is PCl3, making it the most likely compound.