Phase Equilibria

The phase diagram of water is an important topic in physical chemistry as it provides insight into the states of water under various temperature and pressure conditions. A phase diagram illustrates the conditions of temperature and pressure at which distinct phases occur and coexist at equilibrium.

In the context of the question, we are asked to identify the correct phase diagram of water from given options. The correct answer is usually characterized by a few distinctive features specific to water:

• Water's solid-liquid boundary line (line between solid and liquid phases) has a negative slope, unlike most other substances. This indicates the unusual behavior of water where ice melts under increased pressure.
• There is a triple point where all three phases (solid, liquid, and gas) coexist in equilibrium.
• The critical point marks the end of the liquid-gas boundary line and indicates the conditions above which distinct liquid and gas phases do not exist.

The correct phase diagram for water will accurately represent these features. Here is the phase diagram identified as correct from the options provided:

This diagram shows the negative slope of the solid-liquid boundary and the coexistence of the three phases at the triple point, which are typical characteristics of water's phase diagram.

Understanding the phase diagram of water is crucial because it explains various anomalous properties of water, such as why ice floats on liquid water and how it behaves under high pressure.

The problem given is related to colligative properties in physical chemistry, specifically Raoult's Law, which is used to determine the vapor pressure of solutions.

Raoult's Law states that the vapor pressure of a solution, , is directly proportional to the mole fraction of the solvent in the solution. When a non-volatile solute is dissolved in a solvent, the vapor pressure of the solution decreases compared to the vapor pressure of the pure solvent, . The relationship is given by:

where is the mole fraction of the solvent.

The difference in vapor pressure between the pure solvent and the solution is given by:

This difference can be further expressed as:

Dividing by the vapor pressure of the pure solvent , we have:

The term is equivalent to the mole fraction of the solute in the solution, as the sum of the mole fractions in a solution must equal 1:

Therefore,

Hence, the expression is equal to the mole fraction of the solute.

The correct option is: mole fraction of the solute.

For an ideal solution, the total vapour pressure is given by Raoult’s Law, which states:

P_total = P_benzene + P_toluene

Where:

• P_benzene = P_{0 benzene} · X_benzene
• P_toluene = P_{0 toluene} · X_toluene

Here, P_{0 benzene} and P_{0 toluene} are the vapour pressures of pure benzene and toluene, and X_benzene and X_toluene are the mole fractions of benzene and toluene, respectively.

The mole fraction of benzene X_benzene is related to the total vapour pressure by the equation:

P_total = P_{0 benzene} · X_benzene + P_{0 toluene} · (1 − X_benzene)

Substitute the given values into the equation:

0.3 = 0.5 · X_benzene + 0.2 · (1 − X_benzene)

Simplify and solve for X_benzene:

0.3 = 0.5 · X_benzene + 0.2 − 0.2 · X_benzene

0.3 − 0.2 = 0.5 · X_benzene − 0.2 · X_benzene

0.1 = 0.3 · X_benzene

X_benzene =

Thus, the mole fraction of benzene in the mixture is 0.34.