The vapor pressure of pure water at 25°C is 24.0 mm Hg. What is the expected vapor pressure at 25°C — Solutions Chemistry Question

STEPS:

1. Identify the Underlying Chemistry Concept: This problem tests the application of Raoult's Law, which describes the vapor pressure of an ideal solution. For a solution containing a nonvolatile solute, the vapor pressure of the solution is determined solely by the solvent's ability to escape into the gas phase.
2. Recall the Equation for Raoult's Law: The vapor pressure of the solution ($P_{solution}$) is equal to the mole fraction of the solvent ($X_{solvent}$) multiplied by the vapor pressure of the pure solvent ($P^\circ_{solvent}$):
$$P_{solution} = X_{solvent} \times P^\circ_{solvent}$$
3. Extract the Provided Data: From the question, identify the specific values needed for the calculation:
* Vapor pressure of pure water ($P^\circ_{H_2O}$) = $24.0\text{ mm Hg}$
* Mole fraction of water ($X_{H_2O}$) = $0.900$
4. Perform the Calculation: Substitute the values into the equation:
$$P_{solution} = 0.900 \times 24.0\text{ mm Hg}$$
To solve without a calculator, recognize that $0.9 \times 24$ is the same as $24 - (0.1 \times 24)$, which is $24 - 2.4 = \mathbf{21.6\text{ mm Hg}}$.
5. Conclusion: The expected vapor pressure of the solution is $21.6\text{ mm Hg}$, which matches choice C.

WHY_OTHERS_WRONG:

• A) $1.48\text{ mm Hg}$: This value is likely a distractor resulting from a miscalculation or an incorrect manipulation of the variables provided.
• B) $2.40\text{ mm Hg}$: This represents the vapor pressure lowering ($\Delta P$), calculated by multiplying the mole fraction of the *solute* ($1 - 0.9 = 0.1$) by the pure vapor pressure ($0.1 \times 24 = 2.4$). While this is the amount the pressure dropped, the question asks for the final pressure of the solution.
• D) $24.0\text{ mm Hg}$: This is the vapor pressure of the pure solvent. According to colligative property principles, the presence of a nonvolatile solute will always result in a vapor pressure lower than that of the pure substance.
• E) $26.7\text{ mm Hg}$: This value is higher than the vapor pressure of the pure solvent. A nonvolatile solute cannot increase the vapor pressure of the solvent; only a volatile solute with a higher vapor pressure than water could do so.