What is vapour pressure and how does it relate to solutions?

Vapour pressure is the pressure exerted by the vapour in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. For solutions, when a non-volatile solute is added to a volatile solvent, the vapour pressure of the solution is observed to be lower than that of the pure solvent. This is because the solute particles occupy a portion of the surface area, reducing the number of solvent molecules available to escape into the vapour phase, thus decreasing the rate of evaporation and leading to a lower equilibrium vapour pressure.

What is Raoult's Law for solutions containing non-volatile solutes?

Raoult's Law states that for a solution containing a non-volatile solute, the partial vapour pressure of the solvent in the solution is directly proportional to its mole fraction in the solution. Mathematically, it's expressed as $P_A = x_A P_A^0$, where $P_A$ is the vapour pressure of the solvent in the solution, $x_A$ is the mole fraction of the solvent, and $P_A^0$ is the vapour pressure of the pure solvent at the same temperature. This law forms the basis for understanding the colligative property of vapour pressure lowering.

Why is the lowering of vapour pressure considered a colligative property?

The lowering of vapour pressure is a colligative property because it depends solely on the number of solute particles present in the solution, irrespective of their chemical nature or identity. Whether you add 1 mole of glucose or 1 mole of urea to the same amount of solvent, the extent of vapour pressure lowering will be approximately the same, provided both are non-volatile and do not dissociate. This characteristic is shared with other colligative properties like boiling point elevation, freezing point depression, and osmotic pressure.

How can the molar mass of a non-volatile solute be determined using vapour pressure lowering?

The relative lowering of vapour pressure is equal to the mole fraction of the solute ($x_B$). This relationship, $rac{P_A^0 - P_A}{P_A^0} = x_B$, can be expanded. Since $x_B = rac{n_B}{n_A + n_B}$ and $n = rac{ ext{mass}}{ ext{molar mass}}$, we can substitute these to get $rac{P_A^0 - P_A}{P_A^0} = rac{w_B/M_B}{w_A/M_A + w_B/M_B}$. For dilute solutions, this simplifies to $rac{P_A^0 - P_A}{P_A^0} approx rac{w_B M_A}{M_B w_A}$. By measuring the vapour pressures and knowing the masses and molar mass of the solvent, the molar mass of the solute ($M_B$) can be calculated.

What are ideal and non-ideal solutions in the context of Raoult's Law?

An ideal solution is one that obeys Raoult's Law over the entire range of concentrations and temperatures. In an ideal solution, the intermolecular forces between solute-solvent particles (A-B) are similar to those between solute-solute (B-B) and solvent-solvent (A-A) particles. Non-ideal solutions, on the other hand, deviate from Raoult's Law. They can show positive deviation (vapour pressure higher than predicted, weaker A-B interactions) or negative deviation (vapour pressure lower than predicted, stronger A-B interactions). Most real solutions are non-ideal to some extent, but dilute solutions often approximate ideal behavior.

Vapour Pressure of Solutions of Solids in Liquids

Chemistry

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Vapour pressure of a solution containing a non-volatile solute in a volatile solvent is always lower than that of the pure solvent at the same temperature. This phenomenon is quantitatively described by Raoult's Law, which states that for a solution of a non-volatile solute, the partial vapour pressure of each volatile component (solvent) in the solution is directly proportional to its mole fracti…

Quick Summary

When a non-volatile solid is dissolved in a volatile liquid, the vapour pressure of the resulting solution is always lower than that of the pure solvent at the same temperature. This phenomenon occurs because the solute particles occupy a portion of the liquid's surface, reducing the number of solvent molecules that can escape into the vapour phase.

Raoult's Law quantifies this observation, stating that the partial vapour pressure of the solvent in the solution ( $P_A$ ) is directly proportional to its mole fraction ( $x_A$ ) in the solution, given by $P_A = x_A P_A^0$ , where $P_A^0$ is the vapour pressure of the pure solvent.

The difference, $P_A^0 - P_A$ , is the lowering of vapour pressure. The relative lowering of vapour pressure, $rac{P_A^0 - P_A}{P_A^0}$ , is equal to the mole fraction of the solute ( $x_B$ ). This property is colligative, meaning it depends only on the number of solute particles, not their identity.

This principle is crucial for determining the molar mass of unknown non-volatile solutes and forms the basis for understanding other colligative properties.

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Key Concepts

Raoult's Law for Non-volatile Solutes

Raoult's Law is a cornerstone for understanding the vapour pressure of solutions. When a non-volatile solute…

Relative Lowering of Vapour Pressure

The relative lowering of vapour pressure is a particularly important aspect of Raoult's Law because it…

Molar Mass Determination from Vapour Pressure Lowering

One of the most practical applications of the relative lowering of vapour pressure is the determination of…

Vapour Pressure Lowering —

P_A < P_A^0

for solution with non-volatile solute.

Raoult's Law —

P_A = x_A P_A^0

Lowering of VP —

Delta P = P_A^0 - P_A

Relative Lowering of VP —

\frac{Delta P}{P_A^0} = \frac{P_A^0 - P_A}{P_A^0} = x_B

Mole Fraction of Solute —

x_B = \frac{n_B}{n_A + n_B}

Molar Mass Determination (dilute soln) —

\frac{P_A^0 - P_A}{P_A^0} \approx \frac{w_B M_A}{M_B w_A}

Colligative Property — Depends on number of solute particles, not nature.

Non-volatile Solute — Does not vaporize significantly.

To remember Raoult's Law for non-volatile solutes and its effect: 'VAPOUR LOWERS, SOLUTE SHARES'

VAPOUR LOWERS — Vapour pressure of solution is lower than pure solvent.

SOLUTE SHARES — Solute particles 'share' the surface, reducing solvent escape.

LAW —

P_A = x_A P_A^0

(Pressure of A = mole fraction of A * pure pressure of A)

RELATIVE —

\frac{Delta P}{P_A^0} = x_B

(Relative lowering = mole fraction of Solute B)