Final answer:
To calculate the initial number of moles of gas, we can use the proportion of initial volume to final volume with the initial and final moles of gas. Assuming constant pressure and temperature, we find that the initial number of moles is approximately 0.04244 mol.
Step-by-step explanation:
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
In this problem, we are given the initial and final volumes (275.2 mL and 519.9 mL), as well the number of moles of gas (0.07995 mol). Since pressure and temperature are not given, we cannot directly calculate the initial number of moles of gas. Therefore, we will assume that the pressure and temperature remain constant throughout the process, and use the initial and final volumes to calculate the initial number of moles of gas.
We can set up the following proportion:
initial volume / final volume = initial moles / final moles
Plugging in the given values, we get:
275.2 mL / 519.9 mL = initial moles / 0.07995 mol
Solving for the initial moles, we get:
initial moles = (275.2 mL / 519.9 mL) * 0.07995 mol
initial moles ≈ 0.04244 mol
Therefore, the initial number of moles of gas in the system is approximately 0.04244 mol.