A mixture of acetone and ethyl acetate of unknown ratio begins to boil at 65 degrees celcius (760 torr). What is the composition of this binary mixture in terms of the mole fraction of acetone and that of ethyl acetate?

Answer 1

To find the composition of the binary mixture in terms of mole fraction, we need to use the concept of Raoult's Law for liquid mixtures. Raoult's Law states that the vapor pressure of a component in a mixture is equal to the mole fraction of that component times its vapor pressure in the pure state.

Let x1 be the mole fraction of acetone (component 1) and x2 be the mole fraction of ethyl acetate (component 2). Given that the boiling point of the mixture is 65°C at 760 torr (1 atm), we can find the vapor pressures of the pure components at that temperature.

The normal boiling point of acetone is 56.05°C (329.20 K) and its vapor pressure at this temperature is 1 atm (760 torr). The normal boiling point of ethyl acetate is 77.1°C (350.25 K) and its vapor pressure at this temperature is also 1 atm (760 torr).

We can use the Antoine equation to find the vapor pressure of each component at 65°C:

log(P) = A - (B / (C + T))

For acetone:
A = 7.02447, B = 1161.0, C = 224

For ethyl acetate:
A = 7.03119, B = 1225.532, C = 202.487

Plugging the values at 65°C (338.15 K):

log(P1) = 7.02447 - (1161 / (224 + 338.15))
P1 = 242.7 torr

log(P2) = 7.03119 - (1225.532 / (202.487 + 338.15))
P2 = 76.4 torr

According to Raoult's Law:

Px = xi * Pxi

For acetone: P1 = x1 * P1
For ethyl acetate: P2 = x2 * P2

Since the total pressure is 760 torr:

P1 + P2 = 760
x1 * P1 + x2 * P2 = 760

We also know that the mole fractions should add up to 1:

x1 + x2 = 1

Solving the system of equations:

x1 * 242.7 + x2 * 76.4 = 760
x1 + x2 = 1

x2 = 1 - x1

Plugging the second equation into the first:

x1 * 242.7 + (1 - x1) * 76.4 = 760

Solving for x1:

x1 = (760 - 76.4) / (242.7 - 76.4)
x1 ≈ 0.8513

Now using the second equation:

x2 = 1 - 0.8513 = 0.1487

Therefore, the composition of the binary mixture is approximately 85.13% mole fraction of acetone and 14.87% mole fraction of ethyl acetate.