Problem 26 - Chemistry and Chemical Reactivity

Question

Pure iodine \((105 \mathrm{g})\) is dissolved in \(325 \mathrm{g}\) of \(\mathrm{CCl}_{4}\) at \(65^{\circ} \mathrm{C} .\) Given that the vapor pressure of \(\mathrm{CCl}_{4}\) at this temperature is \(531 \mathrm{mm} \mathrm{Hg},\) what is the vapor pressure of the \(\mathrm{CCl}_{4}-\mathrm{I}_{2}\) solution at \(65^{\circ} \mathrm{C} ?\) (Assume that \(\mathrm{I}_{2}\) does not contribute to the vapor pressure.)

Step-by-Step Solution

Answer

The vapor pressure of the \(\mathrm{CCl}_4-\mathrm{I}_2\) solution is less than 531 mmHg.

Step 1: Calculate the Moles of CCl4

First, we need to calculate the number of moles of \(\mathrm{CCl}_4\). The molar mass of \(\mathrm{CCl}_4\) is calculated as follows: \(M = 12.01 + 4 \times 35.45 = 153.81\ \text{g/mol}\). Using this, calculate moles, \(n = \frac{325}{153.81}\).

Step 2: Calculate Moles of I2

Next, calculate the number of moles of \(\mathrm{I}_2\). The molar mass of \(\mathrm{I}_2\) is \(253.8\ \text{g/mol}\). Therefore: \(n = \frac{105}{253.8}\).

Step 3: Calculate Mole Fraction of CCl4

Use the moles of \(\mathrm{CCl}_4\) (denote it as \(n_{CCl_4}\)) and \(\mathrm{I}_2\) (denote it as \(n_{I_2}\)) to find the mole fraction of \(\mathrm{CCl}_4\) in the solution. The mole fraction \(X_{CCl_4} = \frac{n_{CCl_4}}{n_{CCl_4} + n_{I_2}}\).

Step 4: Use Raoult's Law to Find the Vapor Pressure of Solution

According to Raoult's Law, the vapor pressure of the solution \(P_{solution}\) is given by \(P_{solution} = X_{CCl_4} \times P^{\circ}_{CCl_4}\), where \(P^{\circ}_{CCl_4}\) is the pure solvent vapor pressure (given as 531 mmHg). Insert \(X_{CCl_4}\) to find the vapor pressure of the solution.

Key Concepts

Vapor Pressure

Vapor pressure is a crucial concept in understanding how substances behave in a mixture, like in our chemical solution example. It refers to the pressure exerted by a vapor in equilibrium with its liquid or solid form. This is especially important in mixtures because the presence of additional compounds, like iodine in our scenario, affects the overall vapor pressure.
The vapor pressure of a solution is typically less than that of the pure solvent—here, carbon tetrachloride (CCl extsubscript{4}). This reduction is due to the solute molecules, which aren't contributing to the vapor pressure like the solvent does. By understanding vapor pressure changes, we can predict how solutions will behave, especially regarding evaporation and boiling points.

Mole Fraction

The mole fraction is a way to express the concentration of components in a mixture, particularly in a chemical solution. It is calculated by dividing the number of moles of a given component by the total number of moles in the solution.
In the given problem, we need to determine the mole fraction of CCl extsubscript{4} to apply Raoult's Law properly. For example, if we know the moles of CCl extsubscript{4} and iodine (I extsubscript{2}), we can calculate the mole fraction of CCl extsubscript{4} as follows:

• Calculate moles of CCl extsubscript{4} and I extsubscript{2}
• Use the formula: \( X_{CCl_4} = \frac{n_{CCl_4}}{n_{CCl_4} + n_{I_2}} \)

This mole fraction is pivotal for determining how much the iodine affects the vapor pressure of the solution.

Molar Mass

Molar mass is the mass of one mole of a given substance and is expressed in g/mol. It is an essential factor in calculating the number of moles, which are used to find mole fractions, as we saw earlier. In our exercise, calculating the molar mass allows us to determine how much carbon tetrachloride and iodine we have in terms of moles.
For instance, to find the molar mass of carbon tetrachloride (CCl extsubscript{4}), we add the atomic masses of its composite elements:

• One carbon (C): 12.01 g/mol
• Four chlorine (Cl): 4 × 35.45 g/mol = 141.80 g/mol

Thus, the molar mass of CCl extsubscript{4} is 153.81 g/mol. Similarly, the molar mass of iodine (I extsubscript{2}) is 253.8 g/mol. This information helps us convert mass into moles, a step crucial for solving many chemistry-related problems.

Chemical Solution

A chemical solution is a homogenous mixture composed of two or more substances. It is fundamental to understand how these mixtures behave because the properties of a solution differ from those of its individual components.
In a solution like our iodine and carbon tetrachloride mixture, each component contributes to the overall properties but often doesn't behave as it would in its pure state. Raoult's Law helps explain this by showing how the presence of a non-volatile solute reduces the vapor pressure of the solvent.
In our specific example, pure CCl extsubscript{4} has its vapor pressure, but this decreases when iodine is added because the iodine molecules occupy space that would otherwise be available to vapor-forming CCl extsubscript{4} molecules. As a result, this solution's behavior is predicted efficiently by understanding each component's role in the mixture.