Final answer:
The molar mass of the unknown gas, calculated using the Ideal Gas Law, is found to be 312.5 g/mol when pressure, volume, and temperature are properly converted to their respective standard units.
Step-by-step explanation:
To calculate the molar mass of the unknown gas given its pressure, volume, and temperature, we will use the Ideal Gas Law equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
First, we need to convert pressure to atmospheres (1 atm = 760 mmHg), volume to liters if not already, temperature to Kelvin (K = °C + 273.15), and the mass to grams. The Ideal Gas Law needs all units in this standard form.
- Pressure: 35.8 mmHg / 760 mmHg/atm = 0.0471 atm
- Volume: already in liters (20.0 L)
- Temperature: 25 °C + 273.15 = 298.15 K
The ideal gas constant (R) = 0.0821 L atm/mol K.
Next, solve for n (number of moles) using the rearranged Ideal Gas Law equation:
n = PV / RT = (0.0471 atm x 20.0 L) / (0.0821 L atm/mol K x 298.15 K) = 0.00320 mol
Finally, to find the molar mass (MM), we use the mass of the sample (m) divided by the number of moles (n):
MM = m / n = 1.00 g / 0.00320 mol = 312.5 g/mol