If 0.896g of a gas occupies a 250mL flask at 20 degree celcius and 760 mmHg of pressure, what is the molar mass of the gas?
Use PV = nRT; calculate n = moles.
Then moles = grams/molar mass. You have moles and grams, solve for molar mass
To determine the molar mass of a gas, we need to use the ideal gas law equation, which 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)
First, we need to convert the given data into the appropriate units:
- Pressure: 760 mmHg = 760/760 = 1 atm
- Volume: 250 mL = 250/1000 = 0.25 L
- Temperature: 20 degrees Celsius = 20 + 273.15 = 293.15 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (1 atm * 0.25 L) / (0.0821 L·atm/mol·K * 293.15 K)
Calculating:
n ≈ 1.06 x 10^-2 mol
Finally, we can calculate the molar mass by dividing the mass of the gas (0.896 g) by the number of moles (n):
Molar mass = mass / moles
Molar mass ≈ 0.896 g / (1.06 x 10^-2 mol)
Calculating the molar mass:
Molar mass ≈ 84.53 g/mol
Therefore, the molar mass of the gas is approximately 84.53 g/mol.