Final answer:
By applying the Ideal Gas Law, the molar mass of the unknown gas is determined, leading to the identification of SO2 as the most likely chemical formula for the sulfur oxide gas in the flask.
Step-by-step explanation:
To determine the most likely chemical formula for the unknown sulfur oxide gas (SOx), we can apply the Ideal Gas Law, which is PV = nRT. Knowing the conditions given (1 atm of pressure, 25.0 °C which is 298.15 K when converted to Kelvins, and a volume of 0.5 L), we can solve for moles (n) using R = 0.0821 atm·L/mol·K.
First, we calculate the number of moles (n) using the Ideal Gas Law:
n = PV / RT
n = (1 atm) × (0.5 L) / (0.0821 atm·L/mol·K × 298.15 K)
This calculation yields a value of approximately 0.0204 moles of the gas.
To find the molar mass (M) of the unknown gas, we use the mass of the gas sample (m) and the number of moles (n) calculated:
M = m / n
M = 1.636 g / 0.0204 mol
M = 80.2 g/mol
As sulfur has a molar mass of approximately 32 g/mol, the most likely chemical formula for a sulfur oxide with a molar mass around 80 g/mol is SO2 (sulfur dioxide), as this would have a molar mass of 32 g/mol + (2 × 16 g/mol) = 64 g/mol, which is reasonably close to the calculated molar mass.
Given the evidence and calculation, SO2 is the most likely candidate for the unknown sulfur oxide gas.