A gaseous compound has a density of 0.355 g/L at 17 degree celcius and 189 mmHg. What is the molar mass of the compound?
Use PV = nRT which can be re-arranged to
PV = (g/M)RT where M is the molar mass. Since density = g/L, we can substitute to make it
PVM = gRT and
PM = (g/V)RT.
Solve for M
thank you
To find the molar mass of the compound, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (convert mmHg to atm)
V = volume in L
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin (convert degrees Celsius to Kelvin)
First, we need to convert the given values to the appropriate units:
Pressure: 189 mmHg = 189/760 atm (since 1 atm = 760 mmHg) = 0.249 atm
Temperature: 17 degrees Celsius = 17 + 273.15 Kelvin = 290.15 K
Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the values:
n = (0.249 atm) * (V / 0.355 g/L) / (0.0821 L.atm/mol.K) * (290.15 K)
We have the density (0.355 g/L), but we need the volume. However, since the density is given, we can rewrite it as:
density = mass / volume
mass = density * volume
Since the density is 0.355 g/L, the mass of the compound in one liter is 0.355 grams. So, the numerator becomes:
mass = 0.355 g/L * V
Substituting the mass into the equation:
n = (0.249 atm) * (0.355 g/L * V) / (0.0821 L.atm/mol.K) * (290.15 K)
Notice that the units of L, atm, g, and K cancel out, leaving us with:
n = (0.249 * 0.355 * V) / (0.0821 * 290.15)
Now, we can solve for the number of moles (n) using the given density:
0.355 * V = n
Substituting into the equation:
n = (0.249 * (0.355 * V)) / (0.0821 * 290.15)
Simplifying:
n = (0.0879952 * V) / 23.84861515
Since the molar mass of the compound is the mass per mole, we can rewrite the molar mass equation as:
Molar mass (g/mol) = mass (g) / moles (mol)
Therefore, the molar mass of the compound is given by:
Molar mass = (0.355 g/L * V) / [(0.249 * (0.355 * V)) / (0.0821 * 290.15)]
Note that the volume (V) of the gas is a variable that was not provided in the question. You would need the volume of the gas in order to calculate the molar mass.