Final answer:
Calculate the mass of the gas, convert that mass to moles assuming the molar mass calculated under STP conditions, and then use Avogadro's number to find the number of molecules in 12.3 g of the gas.
Step-by-step explanation:
The question asks to calculate the number of molecules present in 12.3 g of an ideal gas based on measurements of the mass of an evacuated vessel when empty, filled with a liquid, and filled with the gas. To solve this problem, we must invoke the ideal gas law and use Avogadro's number.
First, we calculate the mass of gas in the vessel: 50.5 g (vessel with gas) - 50 g (empty vessel) = 0.5 g. Since the density of the gas isn't given, we assume standard temperature and pressure (STP) conditions to find the molar mass. At STP, one mole of an ideal gas occupies 22.4 L. As the volume of the gas isn't provided and we don't have enough data to calculate the molar mass directly, we'll use the example information to reason out the solution.
Knowing this, we can correlate 12.3 g of the gas to the number of moles by division with the molar mass, assuming we deduced it from the example's previous steps. Once we have the number of moles (n), we can use Avogadro's number (6.02 × 1023 molecules/mol) to calculate the number of molecules (N) with the formula N = nN1. The exact number of molecules we seek will therefore require solving for n given the mass of 12.3 g and the assumed molar mass from earlier calculations or reference data.