what is the molar mass of a gaseous organic compound with a density of 3.38 g/L at 40oC and a pressure of 1.97 atm?
Didn't Dr Russ work a problem just like this for you earlier? or almost like it anyway.
I would do this.
PV = nRT
n = moles = g/M where M = molar mass
PVM = gRT, then we can rearrange to
PM=(g/v)RT and g/v is grams/volume or density.Solve for M.
Thank you sir
To find the molar mass of a gaseous organic compound, we need to use the ideal gas law equation and the formula:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the density from grams per liter (g/L) to grams per mole (g/mol). Since density is mass/volume, the mass of 1 liter of the compound would be 3.38 grams.
Now, we need to find the volume for 1 mole of the compound. To do this, we'll use the Ideal Gas Law equation rearranged to solve for volume:
V = (nRT) / P
Here, we know:
P = 1.97 atm (pressure)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 40 + 273 = 313 K (temperature in Kelvin), since 40oC is equivalent to 313 K.
Now, let's plug these values into the equation:
V = (n * 0.0821 * 313) / 1.97
We need to solve for n, so rearrange the formula:
n = (V * P) / (R * T)
Now, substitute in the values:
n = (1 * 1.97) / (0.0821 * 313)
Calculate n:
n ≈ 0.075
Now that we have the number of moles (n), we need to determine the molar mass (M) of the compound. The molar mass is the mass of one mole of substance.
Molar mass (M) = Mass (m) / Moles (n)
Given the mass is 3.38 grams (density of the compound), and n is 0.075 moles, we can calculate M:
M = 3.38 / 0.075
M ≈ 45.07 g/mol
Therefore, the molar mass of the gaseous organic compound is approximately 45.07 g/mol.