What is the molar mass of a compound if a gaseous sample has a density of 2.807 g/L at 18 °C and 728 torr?
P*molar mass = density*RT
Substitute an solv for molar mass.
12
To find the molar mass of a compound, we need to use the ideal gas law equation and rearrange it to solve for molar mass.
The ideal gas law equation is: PV = nRT
Where:
P = Pressure of the gas (in atm)
V = Volume of the gas (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, we need to convert the given density to the molar volume:
Density = mass/volume
Rearranging the equation:
Volume = mass/Density
Given:
Density = 2.807 g/L
Temperature = 18 °C (which needs to be converted to Kelvin)
To convert Celsius to Kelvin, use the formula:
T(K) = T(°C) + 273.15
Thus, temperature in Kelvin will be:
T = 18 °C + 273.15 = 291.15 K
Now, let's calculate the volume:
Volume = mass/Density = 1 g / 2.807 g/L = 0.356 L
Now, we can substitute the given values into the ideal gas law equation:
PV = nRT
(728 torr) * (0.356 L) = n * (0.0821 L·atm/mol·K) * (291.15 K)
Since we want to find the molar mass (in g/mol), we can rearrange the equation as follows:
n = (PV) / (RT)
Substituting the values and solving for n:
n = (728 torr * 0.356 L) / (0.0821 L·atm/mol·K * 291.15 K)
n = 8.9 x 10^-3 mol
Finally, to find the molar mass, we divide the mass of the compound by the number of moles:
Molar mass = mass / moles
Molar mass = 1 g / 8.9 x 10^-3 mol = 112.36 g/mol
Therefore, the molar mass of the compound is approximately 112.36 g/mol.