Question

A solution contains 4.08 g of chloroform \(\left(\mathrm{CHCl}_{3}\right)\) and 9.29 g of acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right) .\) The vapor pressures at \(35^{\circ} \mathrm{C}\) of pure chloroform and pure acetone are 295 torr and 332 torr, respectively. Assuming ideal behavior, calculate the vapor pressures of each of the components and the total vapor pressure above the solution. The experimentally measured total vapor pressure of the solution at \(35^{\circ} \mathrm{C}\) is 312 torr. Is the solution ideal? If not, what can you say about the relative strength of chloroformactone interactions compared to the acetone-acetone and chloroform-chloroform interactions?

Short answer

After calculating the mole fractions and applying Raoult's Law, if the total calculated vapor pressure equals 312 torr, the solution is ideal. If it differs, the strength of chloroform-acetone versus pure component interactions determine if the deviation from ideality is positive or negative.

Step-by-step solution

Determine Molar Amounts

First, calculate the number of moles of chloroform (\(n_{\text{CHCl}_3}\)) and acetone (\(n_{\text{C}_3\text{H}_6\text{O}}\)) using the formula: moles = mass / molar mass. The molar mass of chloroform is 119.38 g/mol and that of acetone is 58.08 g/mol. Thus, for chloroform, it is \(n_{\text{CHCl}_3} = \frac{4.08 \text{ g}}{119.38 \text{ g/mol}}\) and for acetone, \(n_{\text{C}_3\text{H}_6\text{O}} = \frac{9.29 \text{ g}}{58.08 \text{ g/mol}}\).

Calculate Mole Fractions

Then, calculate mole fractions (\(X\)) of chloroform (\(X_{\text{CHCl}_3}\)) and acetone (\(X_{\text{C}_3\text{H}_6\text{O}}\)) using their respective moles and the total moles: \(X = \frac{\text{moles of component}}{\text{total moles}}\).

Calculate Vapor Pressures of Components

Use Raoult's Law to calculate the partial vapor pressures of chloroform (\(P_{\text{CHCl}_3}\)) and acetone (\(P_{\text{C}_3\text{H}_6\text{O}}\)), which states that \(P_{\text{component}} = X_{\text{component}} \times P^\text{o}_{\text{component}}\), where \(P^\text{o}_{\text{component}}\) is the vapor pressure of the pure component.

Calculate the Total Vapor Pressure

The total vapor pressure above the solution \(P_{\text{total}}\) is the sum of the vapor pressures of the individual components, given by \(P_{\text{total}} = P_{\text{CHCl}_3} + P_{\text{C}_3\text{H}_6\text{O}}\).

Compare with Experimental Vapor Pressure

To determine if the solution behaviours ideally, compare the calculated total vapor pressure \(P_{\text{total}}\) with the experimental value. If they are equal, the solution is ideal. If not, \the solution exhibits non-ideal behaviour.

Analyze Deviation from Ideality

If the solution is not ideal, determine whether the vapor pressure is greater or less than the calculated value. If it's greater, chloroform-acetone interactions are weaker than the pure component interactions, leading to a positive deviation. If it's less, the interactions are stronger, causing a negative deviation.

Key concepts

Raoult's Law

Understanding Raoult's Law is essential for calculating vapor pressures in mixtures. This law connects the vapor pressure of a component in a solution to the vapor pressure of the pure component and its concentration in the mixture. Specifically, Raoult's Law states that the partial vapor pressure of each component in an ideal solution is directly proportional to the mole fraction of that component in the solution.

Mathematically, Raoult's Law is expressed as:

\( P_\text{component} = X_\text{component} \times P^\circ_\text{component} \)

where \( P_\text{component} \) is the partial vapor pressure of the component, \( X_\text{component} \) is the mole fraction, and \( P^\circ_\text{component} \) is the vapor pressure of the pure component. This law assumes that the mixture exhibits ideal behavior, which means that intermolecular forces between different components are similar to those within pure substances.

In the context of the given exercise, using Raoult's Law helps to predict the vapor pressures of chloroform and acetone in the solution if they were to behave ideally.

Mole Fraction

The mole fraction is a way of expressing the concentration of a component in a solution. It is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. The greater the mole fraction, the larger the proportion of the component present.

Here's how to calculate the mole fraction:

\( X_\text{component} = \frac{n_\text{component}}{n_\text{total}} \)

where \( n_\text{component} \) represents the moles of the component and \( n_\text{total} \) is the sum of moles of all components.

For the exercise in question, you would compute the mole fractions of chloroform and acetone individually to use in Raoult's Law. It's a crucial step because the mole fraction directly affects calculations of partial vapor pressures, and thus the overall pressure of the solution.

Ideal Solution Behavior

An ideal solution is a hypothetical scenario where there are no changes in enthalpy or volume when two or more substances are mixed. In terms of vapor pressure, it represents a condition where the solution obeys Raoult's Law throughout the entire range of concentrations. Ideal solutions have two main characteristics: the intermolecular forces between different components are equal to those in the pure substances, and the solution follows a linear mixing rule without heat being absorbed or evolved.

Therefore, when a solution is described as 'ideal', the total vapor pressure can be found through a straightforward summation of the individual vapor pressures calculated using each component's mole fraction. The exercise compares the experimentally measured total vapor pressure to what Raoult's Law predicts to assess if the solution behaves ideally. If there is a discrepancy between the experimental and calculated values, it signals non-ideal behavior.

Partial Vapor Pressure

Partial vapor pressure refers to the pressure exerted by a single component in a mixture of liquids or solutions. When you have multiple volatile substances mixed together, each contributes to the total vapor pressure in accordance to its proportion in the mixture. Raoult's Law helps us to calculate what this contribution should be for each substance, assuming ideal mixing.

To find the partial vapor pressure using Raoult's Law, multiply the mole fraction of the component by the vapor pressure of that component in its pure state, as shown earlier. These partial pressures add up to give the total vapor pressure of the mixture:

\( P_\text{total} = \sum P_\text{component} \)

In our exercise, calculating the partial vapor pressures of chloroform and acetone, and summing them provides the expected total vapor pressure of the ideal solution. Comparing this calculated value to the experimental measurement can provide insight into the solution's departure from ideal behavior.