A container of volume V = 103 cm3 has a mass of 30.0042 g when evacuated. When the container is filed with an unknown gas of pressure p = 4.72 atm at temperature T = 20oC, the mass of the system increases to 30.9508 g. Assuming that the unknown gas behaves like an ideal gas, calculate from these data the average molar mass of the unknown gas.
To calculate the average molar mass of the unknown gas, we can use the ideal gas law equation:
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)
We need to convert the given volume from cm3 to liters and the temperature from degrees Celsius to Kelvin.
Given:
V = 103 cm3 = 103/1000 = 0.103 L
P = 4.72 atm
T = 20°C = 20 + 273.15 = 293.15 K
Mass of container when empty = 30.0042 g
Mass of container filled with gas = 30.9508 g
First, we need to find the mass of the gas alone:
Mass of gas = Mass of system - Mass of container
Mass of gas = 30.9508 g - 30.0042 g = 0.9466 g
Next, we can calculate the number of moles of the gas using the molar mass of the gas.
Number of moles = Mass of gas (in grams) / Molar mass
To calculate the molar mass, we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
Substituting the given values into the equation:
n = (4.72 atm) * (0.103 L) / (0.0821 L∙atm/mol∙K) * (293.15 K)
Simplifying:
n = 2.083 mol
Now, we can calculate the average molar mass of the gas:
Molar mass = Mass of gas (in grams) / Number of moles
Molar mass = 0.9466 g / 2.083 mol
Calculating:
Molar mass ≈ 0.4549 g/mol
Therefore, the average molar mass of the unknown gas is approximately 0.4549 g/mol.
To calculate the average molar mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure of the gas (in atm)
V = Volume of the container (in liters)
n = Number of moles of the gas
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature of the gas (in Kelvin)
First, let's convert the given volume from cm^3 to liters:
V = 103 cm^3 = 103/1000 = 0.103 L
Next, convert the given pressure from atm to Pascals (Pa):
P = 4.72 atm × 101325 Pa/atm = 478984.6 Pa
Now, let's convert the given temperature from Celsius to Kelvin:
T = 20°C + 273.15 = 293.15 K
Using the ideal gas law equation, we can rearrange it to solve for the number of moles (n) of the gas:
n = (PV) / (RT)
Plug in the given values:
n = (478984.6 Pa × 0.103 L) / (0.0821 L·atm/(mol·K) × 293.15 K)
n ≈ 1.776 moles
Now, let's calculate the mass of the gas using the given mass of the system:
Mass of the gas = Mass of the system - Mass of the container
Mass of the gas = 30.9508 g - 30.0042 g = 0.9466 g
Finally, the molar mass is calculated by dividing the mass of the gas by the number of moles:
Molar mass = Mass of the gas / Number of moles
Molar mass = 0.9466 g / 1.776 mol
Molar mass ≈ 0.533 g/mol
Therefore, the average molar mass of the unknown gas is approximately 0.533 g/mol.