Mass of an unknown gas of 50 mL volume at 25 degrees C. and 740 mm of Hg pressure was 0.056 g. The molecular mass of this gas is...
PV = nRT and solve for n = mol gas.
Then n = grams/molar mass
Solve for molar mass.
Don't forget T must be in kelvin and P: must be in atm. 740 mm = 740/760 atm
To find the molecular mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas
Given:
P = 740 mm Hg
V = 50 mL (which is equivalent to 0.05 L)
T = 25 degrees C (which is equivalent to 298 K)
m = mass of the gas = 0.056 g
First, we need to convert the pressure from mm Hg to atm since the ideal gas constant R is in atm. To do this, we divide the pressure in mm Hg by 760:
P = 740 mm Hg / 760 mm Hg/atm
P = 0.974 atm
Next, we can rearrange the ideal gas law equation to solve for n (number of moles):
n = PV / RT
Substituting the given values:
n = (0.974 atm) * (0.05 L) / [(0.0821 L*atm/(mol*K)) * (298 K)]
Simplifying:
n = 0.05207 mol
Finally, to find the molecular mass of the gas, we divide the mass (m) by the number of moles (n):
Molecular mass = m / n
Molecular mass = 0.056 g / 0.05207 mol
Molecular mass ≈ 1.074 g/mol
Therefore, the approximate molecular mass of the unknown gas is 1.074 g/mol.