Question

Total vapour pressure of mixture of 1 mole of volatile component \(A\left(P_{A}^{\circ}=100 \mathrm{~mm} \mathrm{Hg}\right.\) ) and 3 mole of volatile component \(B\left(P_{B}^{\circ}=80 \mathrm{~mm} \mathrm{Hg}\right.\) ) is \(90 \mathrm{~mm} \mathrm{Hg}\). For such case: (a) there is positive deviation from Raoult's law (b) boiling point has been lowered (c) force of attraction between \(A\) and \(B\) is smaller than that between \(A\) and \(A\) or between \(B\) and \(B\) (d) all the above statements are correct

Short answer

There is a positive deviation from Raoult's Law, which indicates that the force of attraction between A and B is smaller than the intraspecific attractions, resulting in a lowered boiling point; hence, all the statements are correct.

Step-by-step solution

Understanding Raoult's Law

Raoult's Law states that the partial vapor pressure of a component in a mixture is proportional to its mole fraction in the mixture and its vapor pressure in pure form. The law is often considered for ideal solutions, where the interactions between different components are similar to the interactions between like components. The total vapor pressure of the mixture is the sum of the partial pressures of the components.

Calculating the Mole Fraction

Calculate the mole fraction of each component by dividing the number of moles of that component by the total number of moles in the mixture. For component A, with 1 mole out of the total of 4 moles, the mole fraction would be 0.25. For component B, with 3 moles out of 4, the mole fraction would be 0.75.

Calculating the Expected Vapor Pressure Using Raoult's Law

Using Raoult's Law, the expected vapor pressure of each component can be determined by multiplying the mole fraction of the component by its vapor pressure in pure form. For A, this would be \(0.25 \cdot 100 \, \text{mm Hg}\), and for B, this would be \(0.75 \cdot 80 \, \text{mm Hg}\). Sum these to find the expected total vapor pressure for an ideal solution.

Determining Deviation from Raoult's Law

Compare the calculated total vapor pressure from Step 3 with the given total vapor pressure. If there's a difference between them, the solution shows a deviation from Raoult's Law. If the actual pressure is higher than expected, the deviation is positive.

Analyzing the Deviation Type

If a positive deviation is observed, it indicates that the interactions between A and B are weaker than between A and A or B and B, affecting the boiling point. If the observed vapor pressure is higher than expected, the boiling point of the solution is lower than predicted by Raoult's Law for an ideal solution.

Key concepts

Vapor Pressure

Vapor pressure is a critical concept in understanding the behavior of liquids in mixtures. It is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The vapor pressure of a pure substance is constant at a fixed temperature, and when a substance is mixed with others to form a solution, its vapor pressure lowers due to the presence of other components.

When discussing vapor pressure in mixtures, it's essential to recognize that each component contributes to the total vapor pressure, based on its relative amount, or mole fraction, in the solution. An increase in the vapor pressure can lead to a lower boiling point, because the liquid will start to boil when its vapor pressure equals the external pressure. Learning to calculate vapor pressure is vital for predicting how solutions will behave under various conditions.

Non-Ideal Solution

A non-ideal solution is one where the components do not follow Raoult's Law precisely due to differing intermolecular forces between the molecules when mixed, compared to when they are in pure states. This variance can cause the actual vapor pressure to be different from what we would expect if the solution were ideal. In an ideal solution, the interactions between different molecules are identical to those within the same molecules, leading to vapor pressures that perfectly align with Raoult's Law.

In reality, most solutions exhibit some degree of non-ideality. Understanding this concept is crucial for scientists and engineers who work with solutions in various applications, such as in producing pharmaceuticals, where precise knowledge of vapor pressures is required to avoid undesired reactions or separations.

Positive Deviation from Raoult's Law

When we observe positive deviation from Raoult's Law, it indicates that the actual vapor pressure of the solution is higher than what the law predicts. This occurs when the intermolecular forces between unlike molecules in the mixture are weaker than those between like molecules. As a result, the molecules in the solution can escape into the vapor phase more easily, increasing the total vapor pressure.

Positive deviation can give us important information about the mixture, such as suggesting that the boiling point of the solution may be lower due to the higher vapor pressure. It is an indication that the components of the mixture are less attracted to each other than to their own kind, which is a valuable insight when predicting mixture behaviors and properties.

Mole Fraction Calculation

The mole fraction is a dimensionless quantity that represents the ratio of the number of moles of a component to the total number of moles of all components in the mixture. Calculating the mole fraction is fundamental when applying Raoult's Law as it defines the contribution of each component to the overall vapor pressure of the solution.

For example, in a mixture of two substances, if we have one mole of substance A and three moles of substance B, as in our exercise, the mole fraction of A is \(\frac{1}{1+3} = 0.25\) and for B, it is \(\frac{3}{1+3} = 0.75\). These mole fractions can be multiplied by the respective pure substances' vapor pressures to estimate their individual contributions to the total vapor pressure of the solution.

Boiling Point Alteration

Boiling point alteration is a phenomenon that occurs when the boiling point of a liquid changes due to the presence of other substances. According to Raoult's Law, adding a non-volatile solute to a solvent lowers the solvent's vapor pressure, leading to an increase in the boiling point, a phenomenon known as boiling point elevation.

However, in situations with a positive deviation from Raoult's Law, the weaker interactions within the mixture result in a lower vapor pressure, which means that the solution will boil at a lower temperature compared to the pure solvent. This is known as boiling point depression. Boiling point alteration is important in various applications, such as in cooking and in industrial processes where temperature control is crucial.