To determine the boiling point of the solution consisting of phenol and ethanol, we need to calculate the vapor pressure of the solution at 1 atm and then find the boiling point corresponding to that vapor pressure.
First, let's calculate the mole fraction of ethanol and phenol in the solution:
Mole fraction (X) = (moles of component) / (total moles of all components)
To find the moles of ethanol (C2H5OH), we can use the given mass and molar mass:
Moles of ethanol = (mass of ethanol) / (molar mass of ethanol)
= (250 g) / (46.07 g/mol) [Molar mass of ethanol = 46.07 g/mol]
= 5.426 mol
Similarly, to find the moles of phenol (C6H6O):
Moles of phenol = (mass of phenol) / (molar mass of phenol)
= (35 g) / (94.11 g/mol) [Molar mass of phenol = 94.11 g/mol]
= 0.372 mol
Next, calculate the total moles of the solution:
Total moles of solution = moles of ethanol + moles of phenol
= 5.426 mol + 0.372 mol
= 5.798 mol
Now, we can calculate the mole fraction of ethanol and phenol in the solution:
Mole fraction of ethanol = (moles of ethanol) / (total moles of solution)
= 5.426 mol / 5.798 mol
= 0.936
Mole fraction of phenol = (moles of phenol) / (total moles of solution)
= 0.372 mol / 5.798 mol
= 0.064
Using Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the product of the mole fraction of that component and its vapor pressure in the pure state, we can calculate the vapor pressure of the solution.
Vapor pressure of solution = (mole fraction of ethanol) * (vapor pressure of ethanol) + (mole fraction of phenol) * (vapor pressure of phenol)
The vapor pressure of ethanol is given as 0.308 atm.
The vapor pressure of phenol can be found using its vapor pressure at boiling point (assuming it behaves ideally):
Vapor pressure of phenol = 1 atm
Now, calculate the vapor pressure of the solution:
Vapor pressure of solution = (0.936) * (0.308 atm) + (0.064) * (1 atm)
= 0.287 atm + 0.064 atm
= 0.351 atm
Finally, to find the boiling point of the solution at atmospheric pressure of 1 atm, we consult a vapor pressure versus temperature chart for ethanol.
From the chart, we find that at 1 atm, the boiling point of ethanol is approximately 78.3°C.
Therefore, the boiling point of the solution consisting of 35 g of phenol in 250 g of ethanol is around 78.3°C.