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 very 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 \(\left(\Delta H_{\text {soln }}<0\right)\) or endothermic \(\left(\Delta H_{\text {soln }}>0\right)\) process.

Short answer

The vapor pressure of the ideal solution would be 330 torr, calculated using Raoult's Law. The deviation from ideal behavior is due to the presence of weak hydrogen bonds between acetone and chloroform molecules, causing a lower actual vapor pressure of 250 torr. Based on the solution's behavior, mixing acetone and chloroform is an exothermic process (\(\Delta H_\text{soln} < 0\)).

Step-by-step solution

Use the Raoult's Law to calculate the vapor pressure of an ideal solution

Raoult's Law states that the partial pressure of a component in an ideal solution is equal to the mole fraction of that component multiplied by the vapor pressure of the pure component. In this case, we have an equal number of moles of acetone and chloroform, so the mole fraction for each component is 0.5. We can use the given vapor pressures of the pure components at 35°C to calculate the partial pressures and add those together to get the total vapor pressure of the ideal solution: For acetone: \(P_{acetone} = X_{acetone} \times P°_{acetone} = 0.5 \times 360 \,\text{torr} = 180 \,\text{torr} \) For chloroform: \(P_{chloroform} = X_{chloroform} \times P°_{chloroform} = 0.5 \times 300 \,\text{torr} = 150 \,\text{torr}\) Now, we can add the partial pressures of acetone and chloroform to get the vapor pressure of the ideal solution: \(P_{ideal} = P_{acetone} + P_{chloroform} = 180 \,\text{torr} + 150 \,\text{torr} = 330 \,\text{torr} \) ##Step 2: Explain the deviation from ideal behavior##

Hydrogen bonding between acetone and chloroform

The actual vapor pressure of the solution is 250 torr, which is lower than the calculated vapor pressure of an ideal solution (330 torr). This deviation can be attributed to the existence of weak hydrogen bonds between acetone and chloroform molecules. The presence of hydrogen bonds between the molecules of the two components implies that there are additional intermolecular attractions in the solution, causing the molecules to be held together more strongly than in an ideal solution. This results in a lower vapor pressure for the solution, since more energy is required to overcome these intermolecular interactions and for the molecules to escape from the liquid to the vapor phase. ##Step 3: Predict the enthalpy change of mixing##

Determining the enthalpy change of mixing based on solution behavior

Since the solution exhibits a lower vapor pressure than expected for an ideal solution, this indicates that additional intermolecular interactions (hydrogen bonds) are present in the mixed solution. These additional interactions release energy when formed, suggesting that the process of mixing acetone and chloroform is exothermic (the energy released when new interactions are formed is greater than the energy needed to break the initial interactions in the pure components). Therefore, we can predict that the enthalpy change of mixing for acetone and chloroform is negative (\(\Delta H_\text{soln} < 0\)).

Key concepts

Understanding Vapor Pressure

Vapor pressure is a measure of a liquid's tendency to evaporate into a gas. It's determined by how many molecules escape from the liquid to create a saturated vapor above the liquid at a given temperature. The higher the vapor pressure, the more volatile the substance, indicating that it evaporates readily.

When considering an ideal solution, Raoult's Law provides that the total vapor pressure is the sum of the partial pressures of each component. The partial pressure is the product of the mole fraction of that component and its pure vapor pressure. In the context of our textbook example, for a mixture of acetone and chloroform in equal molar amounts, the expected vapor pressure would be calculated by adding the partial pressures, which are themselves half of the pure component vapor pressures. However, the actual pressure is lower due to deviations from ideality, which brings us to the role of intermolecular forces, specifically hydrogen bonding.

The Role of Hydrogen Bonding

Hydrogen bonding is a type of dipole-dipole interaction that occurs when a hydrogen atom, which is bonded to a highly electronegative atom such as nitrogen, oxygen or fluorine, is attracted to another electronegative atom. In the case of acetone and chloroform, although the hydrogen bonding is weak, it still impacts the behavior of the mixture.

These weak hydrogen bonds alter vapor pressure by stabilizing the liquid phase, effectively reducing the number of molecules that can escape into the vapor phase. The stronger the intermolecular forces within a liquid, the lower its vapor pressure will be at a given temperature. Thus, in our textbook exercise, the actual vapor pressure of 250 torr, compared to the expected 330 torr for an ideal solution, suggests that additional intermolecular forces—in this case, hydrogen bonds—are at play, holding the molecules of acetone and chloroform together more tightly than if they were in separate pure substances.

Predicting Enthalpy Change of Mixing

The enthalpy change of mixing, \( \Delta H_{\text{mix}} \), refers to the heat absorbed or released when substances are mixed. If heat is released during mixing, the process is exothermic \( \Delta H_{\text{mix}} < 0 \), indicating that the energy required to break original bonds is less than the energy released from forming new ones. When heat is absorbed, the process is endothermic \( \Delta H_{\text{mix}} > 0 \), meaning that it takes more energy to break the initial intermolecular forces than is released upon forming the new bonds.

In our textbook exercise, the mixture of acetone and chloroform has a lower vapor pressure than what Raoult's Law predicts for an ideal solution, demonstrating stronger intermolecular forces due to hydrogen bonding. This is indicative of an exothermic reaction—mixing acetone and chloroform releases heat, resulting in a negative enthalpy change of mixing. Essentially, the energy given off as the weak hydrogen bonds form is greater than what was used to separate the molecules initially.