Here is the question:
A sample of an unknown volatile liquid was injected into a Dumas flask (mflask=27.0928g. Vflask=.104L) and heated until no visible traces of the liquid could be found. The flask and its contents were then rapidly cooled and reweighed (mflask+vapor=27.4593g) The atmospheric pressure and temperature during the experiment were 0.976 atm and 18.0 °C, respectively. The unknown volatile liquid's molecular mass was __________.
I have not got any concrete homework done on this outside of guessing and checking can someone set up this equation for me or explain how this can be done?
Thank you that was exactly what I was looking for.
To determine the molecular mass of the unknown volatile liquid, we can use the Dumas Method. This method exploits the ideal gas law (PV=nRT) to calculate the number of moles (n) of the vapor and then relate it to the mass of the liquid.
1. Convert the given atmospheric pressure to Pascals (1 atm = 101325 Pa) and the temperature to Kelvin (18 °C + 273.15 = 291.15 K).
Atmospheric pressure = 0.976 atm = 0.976 × 101325 Pa
Temperature = 18.0 °C = 291.15 K
2. Determine the number of moles of air present in the flask (navg). Since the Dumas flask contained only air after heating, you can use the ideal gas law to solve for n using the given volume and conditions:
Pavg × Vflask = navg × R × T (R is the ideal gas constant)
Solve for navg:
navg = (Pavg × Vflask) / (R × T)
3. Determine the mass of air in the flask (mavg) using the equation:
mavg = navg × Mavg (Mavg is the molar mass of air)
4. Calculate the mass of the vaporized liquid using the difference in weights before and after vaporization:
mvapor = (mflask + vapor) - mflask
5. Finally, determine the number of moles of the vaporized liquid (nliquid) using the equation:
nliquid = mvapor / Mliquid (Mliquid is the molar mass of the unknown liquid)
6. Rearrange the equation to solve for the molecular mass of the unknown liquid:
Mliquid = mvapor / nliquid
Now, you can substitute the given values and constants into the equations and calculate the molecular mass of the unknown volatile liquid.
To determine the molecular mass of the unknown volatile liquid, you can use the Dumas method. This method relies on the principle of the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
1. Convert the temperature from Celsius to Kelvin: T(K) = T(°C) + 273.15.
In this case, the temperature is 18.0 °C, so T(K) = 18.0 + 273.15 = 291.15 K.
2. Calculate the number of moles of vapor using the ideal gas law equation: n = (PV) / (RT).
First, we need to determine the pressure of the vapor. Note that the atmospheric pressure is given as 0.976 atm, which is the pressure of the system before heating.
Since the volatile liquid vaporizes and fills the entire flask, the pressure inside the flask (P) after heating would be the same as the atmospheric pressure (Pa).
Now, substitute the values into the equation to solve for n. Remember to convert the volume from liters to cubic meters (1 L = 0.001 m³):
n = (Pa * V) / (R * T)
= (0.976 atm * 0.104 L) / (0.0821 L·atm/mol·K * 291.15 K)
= 0.0404 mol
3. Calculate the mass of the vaporized liquid by subtracting the mass of the empty flask from the mass of the flask containing the vapor:
m(vapor) = m(flask+vapor) - m(flask)
= 27.4593 g - 27.0928 g
= 0.3665 g
4. Finally, calculate the molecular mass of the volatile liquid by dividing the mass of the vaporized liquid by the number of moles:
Molecular mass = m(vapor) / n
= 0.3665 g / 0.0404 mol
≈ 9.06 g/mol
Therefore, the molecular mass of the unknown volatile liquid is approximately 9.06 g/mol.
Use n = PV/RT to get the number of moles in sample used.
Divide the grams of sample used by the number of moles to get the grams/mole which is the same as the molar mass. That is numerically the same as the molar mass.