An ideal solution made up of benzene C6H6 and toluene C6H5CH3 has mole fraction of benzene as 0.025,0.5,0.75,1.0 at various concentration. calculate the molar fraction of toluene
Calculate the total vapour pressure of the solution at these concentration??
To calculate the molar fraction of toluene in the solution, subtract the mole fraction of benzene from 1.
Let's calculate the molar fractions of toluene for the given concentrations of benzene:
1. Concentration with mole fraction of benzene = 0.025:
Molar fraction of toluene = 1 - 0.025 = 0.975
2. Concentration with mole fraction of benzene = 0.5:
Molar fraction of toluene = 1 - 0.5 = 0.5
3. Concentration with mole fraction of benzene = 0.75:
Molar fraction of toluene = 1 - 0.75 = 0.25
4. Concentration with mole fraction of benzene = 1.0 (pure benzene):
Molar fraction of toluene = 1 - 1 = 0
Now, to calculate the total vapor pressure of the solution at these concentrations, we need to consider Raoult's Law, which states that the partial vapor pressure of a component in an ideal solution is directly proportional to the mole fraction of that component in the solution.
The vapor pressure of benzene (Pbenz) and toluene (Ptoluene) can be found in a reference table or literature. For example, at a given temperature, let's assume Pbenz = 100 mmHg and Ptoluene = 50 mmHg.
Using Raoult's Law, we can calculate the total vapor pressure (Ptotal) of the solution using the following formula:
Ptotal = Pbenz * Xbenz + Ptoluene * Xtoluene
1. Concentration with mole fraction of benzene = 0.025:
Ptotal = (100 mmHg * 0.025) + (50 mmHg * 0.975) = 2.5 mmHg + 48.75 mmHg ≈ 51.25 mmHg
2. Concentration with mole fraction of benzene = 0.5:
Ptotal = (100 mmHg * 0.5) + (50 mmHg * 0.5) = 50 mmHg + 25 mmHg = 75 mmHg
3. Concentration with mole fraction of benzene = 0.75:
Ptotal = (100 mmHg * 0.75) + (50 mmHg * 0.25) = 75 mmHg + 12.5 mmHg = 87.5 mmHg
4. Concentration with mole fraction of benzene = 1.0 (pure benzene):
Ptotal = (100 mmHg * 1) + (50 mmHg * 0) = 100 mmHg + 0 mmHg = 100 mmHg
Therefore, the total vapor pressures of the solution at various concentrations would be approximately:
- 51.25 mmHg,
- 75 mmHg,
- 87.5 mmHg, and
- 100 mmHg respectively.