Ch.12 - Liquids, Solids & Intermolecular Forces

Problem 91

Chapter 12, Problem 91

The vapor pressure of water at 25 °C is 23.76 torr. If 0.25 g of water is enclosed in a 1.50-L container, will any liquid be present? If so, what mass of liquid?

Verified step by step guidance

Calculate the number of moles of water using the formula: \( n = \frac{m}{M} \), where \( m \) is the mass of water (0.25 g) and \( M \) is the molar mass of water (18.02 g/mol).

Use the ideal gas law to calculate the pressure exerted by the water vapor if all the water were to vaporize: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume (1.50 L), \( n \) is the number of moles calculated in step 1, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin (25 °C = 298 K).

Convert the calculated pressure from atm to torr (1 atm = 760 torr) to compare with the given vapor pressure of water at 25 °C (23.76 torr).

Compare the calculated vapor pressure with the given vapor pressure of water. If the calculated pressure is greater than 23.76 torr, not all water will vaporize, and some liquid will remain.

If liquid remains, calculate the mass of water that remains as liquid by determining the difference between the initial mass and the mass that would vaporize to reach the equilibrium vapor pressure.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. For water at 25 °C, the vapor pressure is 23.76 torr, meaning that at this temperature, water molecules escape into the vapor phase until this pressure is reached. Understanding vapor pressure is crucial for determining whether liquid water will remain in a closed container.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this scenario, it can be used to calculate the number of moles of water vapor that can exist in the 1.50-L container at the given vapor pressure. This helps in assessing whether the amount of water vapor exceeds the capacity of the container, indicating if any liquid water will remain.

Phase Equilibrium

Phase equilibrium occurs when the rates of evaporation and condensation of a substance are equal, resulting in a stable amount of liquid and vapor. In this case, if the amount of water vapor produced from the 0.25 g of water exceeds the vapor pressure of 23.76 torr, the system will reach equilibrium with some liquid remaining. Understanding this concept is essential for predicting the presence of liquid water in the container.

Recommended video:

Guided course

03:22

Phase Changes in Diagrams

Related Practice

Textbook Question

Explain the observed trend in the melting points of the hydrogen halides.

HI -50.8 °C

HBr -88.5 °C

HCl -114.8 °C

HF -83.1 °C

views

Textbook Question

Explain the observed trend in the boiling points of these compounds.

H₂Te -2 °C

H₂Se -41.5 °C

H₂S -60.7 °C

H₂O 100 °C

Textbook Question

The vapor pressure of CCl₃F at 300 K is 856 torr. If 3.5 g of CCl₃F is enclosed in a 1.0-L container, will any liquid be present? If so, what mass of liquid?

Textbook Question

A sample of steam with a mass of 0.552 g and at a temperature of 100 °C condenses into an insulated container holding 4.25 g of water at 5.0 °C. Assuming that no heat is lost to the surroundings, what is the final temperature of the mixture?