Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 8

What is the vapor pressure of water at \(100^{\circ} \mathrm{C} ?\) How do you know?

Short Answer

Expert verified
The vapor pressure of water at 100°C is approximately 758.3 mmHg. This value is obtained using the Antoine equation and the given constants for water, which relates the vapor pressure to temperature. At this temperature, water molecules have enough energy to escape into the vapor phase, and the vapor pressure is close to the standard atmospheric pressure, which is why water boils at 100°C.

Step by step solution

01

Understanding Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase (liquid or solid) at a given temperature in a closed system. In simple terms, it is the pressure at which liquid and vapor phase can coexist at a given temperature. The vapor pressure of a substance depends on its temperature: as the temperature increases, the vapor pressure increases.
02

Using a Vapor Pressure Table or Formula

To find the vapor pressure of water at 100°C (373.15 K), we can either consult a vapor pressure table for water or use the Antoine equation, which is a common empirical formula used to estimate vapor pressure. In this solution, we will use the Antoine Equation, given as: \(log_{10}P = A - \frac{B}{C + T}\) where: - P is the vapor pressure (in mmHg), - T is the temperature (in Celsius), - A, B, and C are constants specific to each substance. For water, A=8.07131, B=1730.63, and C=233.426.
03

Calculation

Now, we will use the Antoine equation with the given constants for water and the temperature (100°C) to calculate the vapor pressure: \(log_{10}P = 8.07131 - \frac{1730.63}{233.426 + 100}\) \(log_{10}P = 8.07131 - \frac{1730.63}{333.426}\) \(log_{10}P = 8.07131 - 5.1958\) \(log_{10}P = 2.87551\) Now, to find the vapor pressure, we raise 10 to the power of the result: \(P = 10^{2.87551}\) \(P \approx 758.3\ mmHg\)
04

Interpreting the Result

The vapor pressure of water at 100°C is approximately 758.3 mmHg. This means that at 100°C, water molecules in the liquid phase have enough energy to escape into the vapor phase, and the pressure exerted by the water vapor is 758.3 mmHg. This value also confirms our knowledge that water boils at 100°C at standard atmospheric pressure (760 mmHg), as the vapor pressure of water is very close to the atmospheric pressure at this temperature.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Selenium is a semiconductor used in photocopying machines. What type of semiconductor would be formed if a small amount of indium impurity is added to pure selenium?

General Zod has sold Lex Luthor what Zod claims to be a new copper-colored form of kryptonite, the only substance that can harm Superman. Lex, not believing in honor among thieves, decided to carry out some tests on the supposed kryptonite. From previous tests, Lex knew that kryptonite is a metal having a specific heat capacity of 0.082 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\( and a density of 9.2 \)\mathrm{g} / \mathrm{cm}^{3}$ Lex Luthor's first experiment was an attempt to find the specific heat capacity of kryptonite. He dropped a \(10 \mathrm{g} \pm 3 \mathrm{g}\) sample of the metal into a boiling water bath at a temperature of $100.0^{\circ} \mathrm{C} \pm 0.2^{\circ} \mathrm{C}$ . He waited until the metal had reached the bath temperature and then quickly transferred it to \(100 \mathrm{g} \pm\) 3 \(\mathrm{g}\) of water that was contained in a calorimeter at an initial temperature of \(25.0^{\circ} \mathrm{C} \pm 0.2^{\circ} \mathrm{C}\) . The final temperature of the metal and water was \(25.2^{\circ} \mathrm{C} .\) Based on these results, is it possible to distinguish between copper and kryptonite? Explain. When Lex found that his results from the first experiment were inconclusive, he decided to determine the density of the sample. He managed to steal a better balance and determined the mass of another portion of the purported kryptonite to be \(4 \mathrm{g} \pm 1 \mathrm{g} .\) He dropped this sample into water contained in a \(25-\mathrm{mL}\) graduated cylinder and found that it displaced a volume of \(0.42 \mathrm{mL} \pm 0.02 \mathrm{mL}\) . Is the metal copper or kryptonite? Explain. Lex was finally forced to determine the crystal structure of the metal General Zod had given him. He found that the cubic unit cell contained four atoms and had an edge length of \(600 . \mathrm{pm}\) . Explain how this information enabled Lex to identify the metal as copper or kryptonite. Will Lex be going after Superman with the kryptonite or seeking revenge on General Zod? What improvements could he have made in his experimental techniques to avoid performing the crystal structure determination?

The critical point of \(\mathrm{NH}_{3}\) is \(132^{\circ} \mathrm{C}\) and $111 \mathrm{atm},\( and the critical point of \)\mathrm{N}_{2}\( is \)-147^{\circ} \mathrm{C}\( and 34 \)\mathrm{atm}$ . Which of these substances cannot be liquefied at room temperature no matter how much pressure is applied? Explain.

The second-order diffraction \((n=2)\) for a gold crystal is at an angle of \(22.20^{\circ}\) for \(\mathrm{X}\) rays of 154 \(\mathrm{pm} .\) What is the spacing between these crystal planes?

You have three covalent compounds with three very different boiling points. All of the compounds have similar molar mass and relative shape. Explain how these three compounds could have very different boiling points.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free