Question

At \(35^{\circ} \mathrm{C}\) the vapor pressure of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\), is 360 torr, and that of chloroform, \(\mathrm{CHCl}_{3}\), is 300 torr. Acetone and chloroform can form weak hydrogen bonds between one another as follows: A solution composed of an equal number of moles of acetone and chloroform has a vapor pressure of 250 torr at \(35^{\circ} \mathrm{C}\). (a) What would be the vapor pressure of the solution if it exhibited ideal behavior? (b) Use the existence of hydrogen bonds between acetone and chloroform molecules to explain the deviation from ideal behavior. (c) Based on the behavior of the solution, predict whether the mixing of acetone and chloroform is an exothermic \(\left(\Delta H_{\mathrm{soln}}<0\right)\) or endothermic \(\left(\Delta H_{\text {soln }}>0\right)\) process.

Short answer

The ideal vapor pressure of the solution is 330 torr, but the actual vapor pressure is 250 torr, indicating a deviation from ideal behavior. This deviation is due to the hydrogen bonding between acetone and chloroform molecules, which makes it more difficult for them to escape into the vapor phase. The mixing process is exothermic (\(\Delta H_{\mathrm{soln}} < 0\)) because the formation of hydrogen bonds releases energy.

Step-by-step solution

(a) Calculate the Ideal Vapor Pressure of the Solution

To find out if the solution exhibits ideal behavior, first, we need to calculate the ideal vapor pressure of the solution. We will use Raoult's Law to do this, which states: \[P_{solution}^{ideal} = X_{acetone} P_{acetone}^{pure} + X_{chloroform} P_{chloroform}^{pure}\] Where \(P_{solution}^{ideal}\) is the ideal vapor pressure of the solution, \(X_{acetone}\) and \(X_{chloroform}\) are the mole fractions of acetone and chloroform in the solution, and \(P_{acetone}^{pure}\) and \(P_{chloroform}^{pure}\) are the vapor pressures of pure acetone and chloroform, respectively. Since the solution contains an equal number of moles of acetone and chloroform, we can say that: \(X_{acetone} = X_{chloroform} = 0.5\) Now, we plug in the given vapor pressure values and the mole fractions to calculate the ideal vapor pressure: \(P_{solution}^{ideal} = 0.5 \times 360\,\text{torr} + 0.5 \times 300\,\text{torr}\)

(a) Calculate and Compare the Ideal and Actual Vapor Pressures

Now let's calculate the ideal vapor pressure and compare it to the actual vapor pressure: \(P_{solution}^{ideal} = 0.5 \times 360\,\text{torr} + 0.5 \times 300\,\text{torr} = 330\,\text{torr}\) The actual vapor pressure of the solution, as given in the exercise, is \(250\,\text{torr}\). Since the actual vapor pressure of the solution is less than the ideal vapor pressure, the solution deviates from the ideal behavior.

(b) Explain the Deviation from Ideal Behavior Due to Hydrogen Bonds

The deviation from ideal behavior might be due to intermolecular interactions between the molecules of acetone and chloroform. In this case, weak hydrogen bonds can form between the acetone and chloroform molecules, as given in the exercise. These hydrogen bonds change the distribution of the molecules in the solution, leading to a deviation from the ideal behavior predicted by Raoult's Law, which assumes no intermolecular interactions between the solute and solvent molecules. Since the hydrogen bonding between acetone and chloroform molecules reduces the vapor pressure compared to the ideal case, we can conclude that these interactions make it more difficult for the molecules to escape into the vapor phase.

(c) Predict if the Mixing Process is Exothermic or Endothermic

The mixing process can be exothermic or endothermic depending on the energy changes associated with the intermolecular interactions in the solution. The formation of hydrogen bonds between acetone and chloroform molecules would release energy. Therefore, the overall effect of these hydrogen bond formations would be a decrease in the energy of the system. Since the energy of the system decreases upon mixing, the mixing process is exothermic, i.e., \(\Delta H_{\mathrm{soln}} < 0\).

Key concepts

Raoult's Law

Raoult's Law is crucial for understanding the behavior of solutions in chemistry. It relates the vapor pressure of a solution to the concentration of its components. Specifically, it states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent. The formula for Raoult's Law is
\[ P_{solution} = X_{solvent} P_{solvent}^{pure} \]
where \( P_{solution} \) is the vapor pressure of the solution, \( X_{solvent} \) is the mole fraction of the solvent, and \( P_{solvent}^{pure} \) is the vapor pressure of the pure solvent. This law assumes that the solution behaves ideally, meaning that the solute and solvent interact similarly to how the solvent molecules interact with each other. When solutions deviate from this ideal behavior, typically due to strong solute-solvent interactions, Raoult's Law no longer accurately predicts the vapor pressure.

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including attractions and repulsions. These forces are crucial in determining the physical properties of substances, like boiling points, melting points, and solubility. There are several types of intermolecular forces, including dipole-dipole interactions, London dispersion forces, and hydrogen bonding. London dispersion forces are the weakest and result from transient dipoles that occur due to moment-to-moment fluctuations in electron distribution. Dipole-dipole interactions occur between molecules with permanent dipoles. Hydrogen bonding, which is a stronger type of dipole-dipole interaction, occurs when a hydrogen atom bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine is attracted to another electronegative atom in a different molecule.

Hydrogen Bonding

Hydrogen bonding is a special type of intermolecular force that occurs when a hydrogen atom covalently bound to a highly electronegative atom, such as oxygen or nitrogen, experiences an attraction to another electronegative atom in a nearby molecule. While weaker than a covalent or ionic bond, hydrogen bonds are stronger than van der Waals forces and have a significant impact on the physical properties of substances. For example, hydrogen bonding is responsible for water's high boiling and melting points compared to other molecules of similar size. It also affects the behavior of solutions; in the exercise provided, the hydrogen bonding between acetone and chloroform leads to a lower vapor pressure than expected, as these bonds need additional energy to break and allow the molecules to escape into the vapor phase.

Ideal vs. Non-Ideal Solutions

Solutions can be classified as ideal or non-ideal based on how the solute and solvent interact. Ideal solutions follow Raoult's Law without deviation because the intermolecular forces between solute and solvent are nearly identical to those present in the pure substances. No new types of interactions are formed, and the enthalpy change of mixing is close to zero.

Non-ideal solutions, on the other hand, exhibit behavior that deviates from Raoult's Law. This happens when solute-solvent interactions differ significantly from the original intermolecular forces in the pure substances. If the interactions are stronger in the solution, the vapor pressure decreases, and if they are weaker, the vapor pressure increases compared to what Raoult's Law would predict. Non-ideal behavior also indicates that the enthalpy change upon mixing is not zero, signifying that new interactions, which might be either stronger or weaker, are influencing the system's energy.

Exothermic and Endothermic Processes

Chemical and physical processes can either absorb or release energy, and they are classified accordingly. An exothermic process releases energy to the surroundings, typically in the form of heat, and is characterized by a negative enthalpy change \(\Delta H < 0\). Combustion is a common example of an exothermic reaction.

An endothermic process, on the other hand, absorbs energy from the surroundings, and is evidenced by a positive enthalpy change \(\Delta H > 0\). The process of evaporation is an example of an endothermic process where liquid absorbs energy to become gas. In the context of the exercise, when acetone and chloroform are mixed and hydrogen bonds form between them, energy is released as heat. Consequently, the solution gets warmer, and thus, the process is exothermic.