Answer :
The Raoult's law states that the partial pressure of a volatile component in a solution is proportional to the mole fraction of the component in the solution. Therefore, the total vapor pressure above this solution is 171.5 torr.
Therefore, the total vapor pressure of the solution is given as; ptotal = p1 + p2, where p1 = mole fraction of component 1 × vapor pressure of pure component 1 and p2 = mole fraction of component 2 × vapor pressure of pure component 2From the given information; the number of moles of cyclohexane, n1 = 1.6 mol the number of moles of acetone, n2 = 2.0 mol the vapor pressure of cyclohexane, p∘cy = 97.6 torr the vapor pressure of acetone, p∘ac = 229.5 torr. Hence, the mole fraction of cyclohexane is given by: X1 = n1 / (n1 + n2)X1 = 1.6 / (1.6 + 2.0)X1 = 0.44.
Similarly, the mole fraction of acetone is given by: X2 = n2 / (n1 + n2)X2 = 2.0 / (1.6 + 2.0)X2 = 0.56Hence, the partial pressure of cyclohexane, p1 = X1 × p∘cy = 0.44 × 97.6 = 42.98 torr And the partial pressure of acetone, p2 = X2 × p∘ac = 0.56 × 229.5 = 128.52 torr. The total vapor pressure above the solution, ptotal = p1 + p2ptotal = 42.98 + 128.52ptotal = 171.5 torr.
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