Final answer:
To calculate the molar mass of the gas, the student must use the Ideal Gas Law to find the number of moles, and then divide the mass of the gas sample by the number of moles.
Step-by-step explanation:
To determine the molar mass of the unknown gas given the sample's mass, volume, temperature, and pressure, we apply the Ideal Gas Law, which is PV = nRT where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. To find the number of moles (n), we rearrange the equation: n = PV / RT. We then use the number of moles and the mass of the gas sample to find the molar mass (MM) with the formula: MM = mass/n.
Given:
- Pressure (P) = 0.850 atm
- Volume (V) = 2.4 L
- Temperature (T) = 287 K
- Mass of the gas sample = 0.622 grams
- Gas constant (R) = 0.0821 L atm / (mol K)
We calculate the number of moles (n):
n = (0.850 atm * 2.4 L) / (0.0821 L atm / (mol K) * 287 K)
Then we use this value to find the molar mass (MM):
MM = 0.622 grams / n
After calculating n and MM, we deduce the molar mass of the gas, which we can then compare to known substances to possibly identify the gas.