To determine the molar mass of the unknown gas, we can use the ideal gas law equation along with the given information. The ideal gas law equation is:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
Let's break down the problem step by step:
Step 1: Convert the given pressures and temperature from torr and °C to atm and Kelvin.
- Pressure: 735 torr = 735/760 atm (since 1 atm = 760 torr)
- Temperature: 31°C = 31 + 273.15 K (Kelvin = °C + 273.15)
Step 2: Calculate the volume of the flask.
To calculate the volume, we need to subtract the initial weight of the flask from the final weight after it was filled with the gas. Since the density of water is given and the flask is filled with water, we can use the density to convert the weight of water to volume.
Initial weight = 134.567 g
Final weight = 137.456 g
Weight of water = Final weight - Initial weight = 137.456 g - 134.567 g = 2.889 g
Density of water = 0.997 g/mL
Volume of water = Weight of water / Density of water = 2.889 g / 0.997 g/mL = 2.900 mL
(Note: The volume of the gas is the same as the volume of water since the flask is filled with water before being filled with gas.)
Convert mL to liters: 2.900 mL = 2.900/1000 L = 0.002900 L
Step 3: Plug in the values into the ideal gas law equation.
PV = nRT
(735/760) * 0.002900 L = n * 0.0821 L.atm/mol.K * (31 + 273.15) K
Simplify and solve for n (number of moles):
n = (735/760) * 0.002900 L / (0.0821 L.atm/mol.K * 304.15 K)
n ≈ 0.00108 moles
Step 4: Calculate the molar mass.
Molar mass = mass of the gas / number of moles
Molar mass = (137.456 g - 134.567 g) / 0.00108 moles
Molar mass ≈ 268 g/mol
Therefore, the molar mass of the unknown gas is approximately 268 g/mol.