A series of measurements are made in order to determine the molar mass of an unknown gas. First, a large flask is evacuated and found to weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31°C and reweighed; its mass is now 137.456 g. Finally, the flask is filled with water at 31°C and found to weigh 1067.9g. The density of water at this temperature is 0.997 g/mL. Assuming that the ideal-gas equation applies, what is the molar mass of the unknown gas?
The difference in weight tells you the mass M of the gas in the flask. The water filling tells you volume V of the flask. You are told what the gas pressure P and temperature T are.
PV = nRT tell you the number of moles n of the gas. R is the molar gas cosntant.
The molar mass is M/n.
Crank out the numbers.
137.86L
I don't know
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.