Final answer:
To calculate the molecular mass of the gas in the flask, we use the ideal gas law PV = nRT to first find the number of moles n. Then, we divide the mass of the gas (0.977 g) by the number of moles to determine the molecular mass.
Step-by-step explanation:
To calculate the molecular mass of the gas, 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, R is the gas constant, and T is the temperature. Given that P = 1.0 ATM, V = 0.3 L, and T = 300K, and knowing that the mass of the gas is 0.977g, we can solve for n (the number of moles) and then calculate the molecular mass (M).
The molar volume of an ideal gas at STP conditions (0°C and 1 ATM) is 22.41 L/mol. Since the conditions vary here, we adjust the ideal gas equation to find the amount of gas under the given conditions.
First, calculate moles n from the ideal gas law:
n = PV / RT
Where:
- P is the pressure in atm (1.0 atm)
- V is the volume in liters (0.3 L)
- R is the ideal gas constant (0.0821 L·atm/K·mol)
- T is the temperature in Kelvin (300K)
Thus:
n = (1.0 atm)(0.3 L) / (0.0821 L·atm/K·mol)(300K)
Next, determine the molecular mass M by the mass of gas over the number of moles n:
M = mass / n
M = 0.977 g / n
Doing the math, you find n and then calculate the molecular mass M. This will give you the molecular mass of the gas collected in the flask.