Raoult's Law

Raoult's Law is an important concept in chemistry that deals with the connection between vapour pressure and the makeup of ideal liquid mixtures. It was introduced by the French chemist François-Marie Raoult in 1887. This law helps us understand how the pressure of a specific part in a mixture relates to its proportion in the overall mixture. In simpler terms, Raoult's Law sheds light on how the pressure of a substance in a mix is connected to how much of it is in the whole mix. This law is also considered one of the laws of thermodynamics.

Imagine a steaming cup of coffee. What causes that enticing aroma to waft up your nose? It's the magic of vapour pressure, the pressure exerted by the vapourised molecules escaping from the liquid. But what happens when you add sugar to your coffee? Does the steam change? The answer lies in a fundamental law of physical chemistry called Raoult's Law. Let us learn more about Raoult’s law, understand its principles and applications, and study its limitations in this article.

Understanding the Lingo:

Before we dive deep, let's break down some key terms:

• Solution: A homogeneous mixture of two or more substances.

• Solute: The substance dissolved in the solvent.

• Solvent: The substance that dissolves the solute.

• Mole fraction: The ratio of the moles of a component to the total moles in the solution.

• vapour pressure: The pressure exerted by the vapour of a substance in equilibrium with its liquid or solid form.

What is Raoult’s Law?

Raoult’s law states that a solvent’s partial vapour pressure in a solution is equal or the same as the vapour pressure of the pure solvent multiplied by its mole fraction in the solution. This means, that when you add something to a liquid, like salt to water, it makes the freezing point lower and the boiling point higher compared to the liquid by itself. The amount of change depends on how much of the added stuff (solute) is in the mixture.

Mathematically, Raoult’s law equation is given by the following formula.

Psolution = Xsolvent.P0Solvent

Where,

Psolution = Vapour pressure of the solution

Xsolvent = Mole fraction of the solvent

P0Solvent = Vapour pressure of the pure solvent

Note:

Partial vapour pressure: When multiple liquids are mixed, each contributes to the total pressure exerted by the vapour above the mixture. This contribution from each liquid is called its partial vapour pressure.

Mole fraction: This represents the number of moles of a component relative to the total number of moles in the mixture. It's a dimensionless quantity between 0 and 1.

Understanding the Implications:

1. Lower the mole fraction, lower the partial pressure: As the mole fraction of a component decreases (more of the other component is present), its partial pressure also drops. This explains why adding salt to water reduces the overall vapour pressure of the solution – fewer water molecules are available to exert their vapour pressure.

2. Ideal vs. Real Solutions: Raoult's Law strictly applies to ideal solutions. These are hypothetical mixtures where intermolecular forces between different molecules are identical to those between like molecules, and molar volumes are the same. In real solutions, deviations from ideality occur due to differing attractive/repulsive forces, leading to slight variations in partial pressures.

3. Colligative Properties: Raoult's Law forms the foundation for understanding various colligative properties, such as boiling point elevation, freezing point depression, and osmotic pressure. These properties depend solely on the number of solute particles present (not their identity), and Raoult's Law helps us explain how the presence of solute molecules affects these thermodynamic parameters.

At Equilibrium, Raoult's law states that:

When things balance out, Raoult's law tells us that the pressure of a substance (let's call it A) in a mixture equals the product of its vapour pressure at that temperature and its fraction in the liquid. Similarly, for another substance (let's call it B), its pressure is the product of its vapour pressure at that temperature and its fraction in the liquid.

So, when you have both A and B in a mix, the total pressure is the sum of their individual pressures (this is known as Dalton's Law). In simpler terms, it's like adding up the pressures each substance would exert on its own.

$P_A=P_A^{\circ} x_A, P_B=P_B^{\circ} x_B$

Where 

$P_A$ - Partial pressure of $A$.

$\mathrm{P}_{\mathrm{A}}$ - Vapour pressure of $\mathrm{A}$ at that temperature.

$x_A$ - Mole fraction of $A$ in the liquid state.

Similarly, $\mathrm{P}_{\mathrm{B}}, \mathrm{P}_{\mathrm{B}}^{\circ} \mathrm{X}_{\mathrm{B}}$

Hence,

$ P_T=P_A+P_B$ (according to Dalton's Law)

$ =P_A^{\circ} x_A+P_B^{\circ} x_B$ (applying Raoult's law for both A and B)

$ =P_A^{\circ}+x_B\left(P_B^{\circ}-P_A^{\circ}\right)$

In even simpler words, it's saying that the total pressure is the sum of the individual pressures, where each pressure is the product of the vapour pressure and the fraction of that substance in the liquid.

Importance of Raoult’s Law

Imagine you have a closed box filled with a smelly liquid. As time goes by, some of the liquid turns into smelly gas, creating a balance where gas particles are constantly escaping and returning to the liquid's surface. The pressure caused by these gas particles is called vapour pressure.

Now, if you pour another liquid into the box, its particles will mix with the first liquid's particles on the surface. Each liquid has some molecules that are energetic enough to turn into gas. Since we now have fewer of the first liquid's molecules on the surface, there will be fewer gas particles and, as a result, lower vapour pressure.

If the second liquid can also turn into gas, its molecules will add to the gas in the box, but there will still be fewer of them compared to if it was just that liquid alone. This combined pressure from both liquids is called partial pressure, and it follows Raoult's law, depending on how much of each liquid is in the mix.

PA ∝ XA , PB ∝ XB  = XAP’A= XBP’B

Where P’ is the mole fractions of the components

Example:

1. Imagine a solution with 60% water (X₁ = 0.6) and 40% ethanol (X₂ = 0.4). The vapour pressure of pure water is 23.76 kPa, and that of pure ethanol is 7.9 kPa. 

Solution: Using Raoult's Law, we can calculate the partial pressures of both components:

P_water = 23.76 kPa * 0.6 = 14.26 kPa

P_ethanol = 7.9 kPa * 0.4 = 3.16 kPa

Therefore, the total vapour pressure of the solution would be the sum of these partial pressures: 14.26 kPa + 3.16 kPa = 17.42 kPa. This is lower than the vapour pressure of pure water (23.76 kPa) due to the presence of ethanol molecules.

Key points to remember:

Raoult's Law applies to ideal solutions where intermolecular forces between different components are similar to those between like molecules, and molar volumes are the same. Non-ideal solutions deviate from Raoult's Law due to differences in intermolecular forces.

The law finds various applications, including:

• Calculating boiling points and freezing points of solutions

• Understanding distillation processes

• Explaining colligative properties like osmotic pressure

Visualising Raoult's Law:

Imagine a container filled with a solution of water and sugar. Water molecules (blue) and sugar molecules (red) are present in the liquid phase. Some water molecules escape into the vapour phase, exerting a partial pressure (P₁). However, due to the presence of sugar molecules, fewer water molecules can escape compared to pure water. Therefore, P₁ is less than the vapour pressure of pure water.

Limitations of Raoult’s Law

The limitations of Raoult’s Law are as follows.

• Raoult's law works well for ideal solutions, where the gas phase behaves like a mix of ideal gases. But ideal solutions are uncommon and hard to find.

• Chemical components in ideal solutions must be identical.

• In real-life mixtures, liquids often don't have the same attractive forces, causing deviations from Raoult's law.

• This means the actual behavior of the solution might not match what Raoult's law predicts.

Applications of Raoult's Law:

• Predicting boiling and freezing points of solutions: Knowing the mole fraction of a solute, we can calculate the change in boiling and freezing points of a solution compared to the pure solvent. This is crucial in various industrial processes and scientific experiments.

• Concentration determination: By measuring the vapour pressure lowering of a solution, we can indirectly determine the concentration of the solute. This technique is used in analytical chemistry and pharmaceutical applications.

• Understanding osmosis and separation processes: Raoult's law plays a vital role in comprehending osmotic pressure, a key factor in various separation techniques like reverse osmosis and dialysis.

Deviations from Raoult’s Law

Deviations from Raoult’s Law can be done if there are adhesive or cohesive forces between two liquids.

Negative Deviation

When the vapour pressure is lower than expected from the law, this results in a negative deviation. It occurs when forces between particles are stronger than those between particles in pure liquids. For instance, this behaviour is observed in a mixture of chloroform and acetone. In this case, hydrogen bonds cause deviation. A solution of hydrochloric acid and water is another example of this.

Positive Deviation

The positive deviation occurs when the cohesion between similar molecules exceeds adhesion between unlike molecules. The result is higher-than-expected vapour pressure. Both components of the mixture escape the solution more readily than if the components were pure. This behaviour is observed in mixtures of benzene and methanol, and mixtures of chloroform and ethanol.

Ideal vs. Non-ideal Solutions

Ideal solutions are best for Raoult’s law. "Perfect solutions have intermolecular interactions that are similar to those of pure components and show thermodynamics blending properties similar to those of perfect different gasses." There are numerous options for other concepts in Chemistry, this law is only applicable for ideal solutions. It still works well, however, for the dilute solutions insolvent. In actuality though, the calculation of Raoult's law for the extremely dilute solution will be greater with the decrease in pressure.

Why did Raoult's Law Work?

The concept or process of colligative properties if we look through the reviews of it we will come across that additional solute will fill the gaps between solvent particles to take up space while adding a solute lower vapor pressure to it. This results in lowering vapor pressure as less of the solvent will be able to break free to enter the gas phase and will be on the surface of the solvent. Raoult's Principle starts with a basic visual approach and progresses to a more comprehensive one on the basis of entropy. Let’s look below at the given approach in a simple way.

The number sticking onto the surface again is the same as an equilibrium here the set-up of the number of particles breaking away from the surface. When a liquid is in a sealed container remember that saturated vapor pressure is what you get.

To escape from the surface (e.g., 1 in 1000 or 1 in a million) a certain ratio of the solvent molecules will have sufficient energy. You are going to reduce the number which can run away at any point of given time if you reduce the solvent molecules on the surface. The vapor to stick to the surface again will not make any difference to the ability of molecules.  If the vapor comes into contact with such a portion of the interface that is covered by the solutes, it may cling to a solvent molecule. Otherwise, you would not have a solution in the first place if there is no obvious attraction between solvent and solute.

In the vapor, there will be less liquid particles. The net effect of this is that when an equilibrium is established it's hardly that they are going to break down. There is nothing like returning problems to them. The saturated vapor pressure is lower if there are fewer particles in the vapor at parity.

Raoult’s Law and its Relationship with Other Laws

We all know the ideal gas law is similar to that. The exception of this law is that it’s only applicable for ideal solutions. All have read ideal gas law and we know that it takes the assumption of gasses of ideal behavior that present between different molecules is zero or non-existent in intermolecular forces. Here in Raoult's Law, we assume that the existing intermolecular forces between similar and dissimilar molecules are equal.

It is sometimes applicable to non-ideal solutions too. This is however done by several incorporating factors where the interactions between several are considered of different substances.

If the proper ideal vapor and an ideal liquid consist of the perfectly ideal system we can further find a vital equation by combining Dalton's Law and Raoult's Law.

Conclusion

Raoult's Law is about how things ideally mix. In real solutions, intermolecular forces between different components can be stronger or weaker than those between like molecules. This can lead to deviations from the ideal behavior predicted by the law. For instance, when you mix ethanol and water, the real vapour pressure is a bit higher than what Raoult's Law says. This happens because the ethanol and water molecules form weak bonds with each other. Knowing about these differences is important when we use Raoult's Law in advanced ways, like in science or engineering.