According to Raoult's law, the vapor pressure of a solution is proportional to the mole fraction of the solvent present in the solution. Since naphthalene is a nonvolatile solute, its mole fraction is negligible, and we can assume that the vapor pressure of the solution is equal to the vapor pressure of pure carbon disulfide, which is given as 355.6 torr.
To find the mole fraction of CS₂, we need to first calculate the moles of CS₂ present in the solution. The mass of CS₂ present in 155 ml of solution is:
mass of CS₂ = volume of solution x density of CS₂ = 155 ml x 1.261 g/ml = 195.76 g
The moles of CS₂ can be calculated as:
moles of CS₂ = mass of CS₂ / molar mass of CS₂ = 195.76 g / 76.14 g/mol = 2.569 mol
The mole fraction of CS₂ is then:
mole fraction of CS₂ = moles of CS₂ / total moles of solute and solvent = 2.569 mol / (2.569 mol + 0.0905 mol) [since weight of napthalene =11.60g, molar mass=128.2 g/mol, moles of napthalene=11.60/128.2=0.0905 mol] = 0.966
Finally, using Raoult's law, the vapor pressure of the solution is:
vapor pressure = mole fraction of CS₂ x vapor pressure of pure CS₂ = 0.966 x 355.6 torr = 343.2 torr
Therefore, the vapor pressure of the solution is 343.2 torr.