A volatile liquid was allowed to evaporate in a 43.298g flask that has a total volume of 253 mL. The temp of the water bath wad 100 °C at the atmospheric pressure of 776 torr. The mass of the flask and condensed vaporous was 44.173g. Calculate the molar mass of the liquid
To calculate the molar mass of the liquid, we need to use the ideal gas law equation, which relates the pressure, volume, temperature, and amount of gas. The equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin. The conversion is done by adding 273.15 to the Celsius temperature.
T = 100 °C + 273.15 = 373.15 K
Next, we need to calculate the number of moles of the vaporized liquid. We can use the difference in mass before and after the liquid evaporated.
Mass of liquid evaporated = mass of flask and condensed vapor - mass of empty flask
Mass of liquid evaporated = 44.173 g - 43.298 g = 0.875 g
To convert this mass to moles, we use the molar mass of the liquid. Let's assume the molar mass is M.
moles = mass / molar mass
moles = 0.875 g / M
Now, we can substitute the values into the ideal gas law equation:
PV = nRT
P = 776 torr (convert to atm by dividing by 760 torr/atm) = 1.021 atm
V = 253 mL (convert to L by dividing by 1000 mL/L) = 0.253 L
n = 0.875 g / M
R = 0.0821 L·atm/mol·K
T = 373.15 K
Plugging in the values:
(1.021 atm)(0.253 L) = (0.875 g / M)(0.0821 L·atm/mol·K)(373.15 K)
Simplifying:
0.258 L·atm = (0.0718 g / M)(30.703 L·atm/mol·K)
Now, solve for M:
M = (0.0718 g / M)(30.703 L·atm/mol·K) / 0.258 L·atm
To get the molar mass, we need to rearrange the equation and solve for M:
Multiply both sides by M:
M^2 = (0.0718 g)(30.703 L·atm/mol·K) / (0.258 L·atm)
Divide both sides by (0.0718 g)(30.703 L·atm/mol·K):
M^2 / [(0.0718 g)(30.703 L·atm/mol·K)] = 1 / (0.258 L·atm)
Take the square root of both sides:
M = √[1 / (0.258 L·atm)] × √[(0.0718 g)(30.703 L·atm/mol·K)]
Calculate the value of M using a calculator.
M ≈ 114 g/mol
Therefore, the molar mass of the liquid is approximately 114 g/mol.