A vilatile liquid was allowed to evaporate in a 43.298 g flask that has a total volume of 252 ml. The temperature of the water bath was 100 degree Celsius at the atmospheric pressure of 776 torr. The mass of the flask and condensed vapor was 44.173 g.
Calculate the molar mass of the liquid?
Use PV = nRT to calculate n = number of moles.
Then moles = grams/molar mass. You have moles from the first equation and you have grams (from the difference if mass of the flask); calculate molar mass.
moles of gas = PV / RT
= 776 x .252 / 62.363 x (273+100) =0.00841 moles
which have mass of 44.173 - 43.298 g = 0.875g
molar mass = 0.875g / 0.00841 moles = 104.1 g/ mole
To calculate the molar mass of the liquid, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure in atm
V is the volume in liters
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100°C + 273.15 = 373.15 K
Now, we can calculate the number of moles:
PV = nRT
n = PV / RT
However, we first need to calculate the pressure in atm. We know that 1 atm equals 760 torr, so:
P(atm) = 776 torr / 760 torr/atm
P(atm) = 1.021 atm
Next, we need to convert the volume from ml to liters:
V(L) = V(ml) / 1000
V(L) = 252 ml / 1000 = 0.252 L
Now, we can substitute the values into the equation to find the number of moles:
n = PV / RT
n = (1.021 atm) * (0.252 L) / (0.0821 L·atm/mol·K * 373.15 K)
n ≈ 0.013 mol
Finally, we can calculate the molar mass of the liquid:
Molar mass(g/mol) = mass(g) / moles(mol)
Molar mass(g/mol) = (44.173 g - 43.298 g) / 0.013 mol
Molar mass(g/mol) ≈ 67.308 g/mol
Therefore, the molar mass of the liquid is approximately 67.308 g/mol.
To calculate the molar mass of the liquid, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (convert Torr to atm by dividing by 760: 776 torr / 760 torr/atm = 1.021 atm)
V = volume in liters (convert ml to liters: 252 ml / 1000 ml/L = 0.252 L)
n = number of moles (unknown)
R = ideal gas constant (0.0821 L · atm/(mol · K))
T = temperature in Kelvin (convert Celsius to Kelvin: 100°C + 273.15 = 373.15 K)
Rearranging the equation to solve for n:
n = PV / RT
Substituting the given values:
n = (1.021 atm)(0.252 L) / (0.0821 L · atm/(mol · K))(373.15 K)
Now we can calculate the number of moles (n).
Next, we need to determine the mass of the liquid. We can do this by subtracting the mass of the flask and condensed vapor from the total mass.
mass of liquid = mass of flask and condensed vapor - mass of flask
mass of liquid = 44.173 g - 43.298 g
Now we have the mass of the liquid.
Finally, we can calculate the molar mass of the liquid using the formula:
molar mass = mass of liquid / moles of liquid
Substitute the values we have calculated to find the molar mass.