/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 28 The pressure on \(0.850\) mol of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 28

The pressure on \(0.850\) mol of neon gas is increased from \(1.25\) atm to \(2.75\) atm at \(100^{\circ} \mathrm{C}\). Assuming the gas to be ideal, calculate \(\Delta S\) for this process.

Short Answer

Expert verified
The change of entropy (\(\Delta S\)) for this isothermal process can be calculated using the formula \(\Delta S = nR * \ln(P2/P1)\), where n = 0.850 mol, R = 0.0821 L * atm / (mol * K), P1 = 1.25 atm, and P2 = 2.75 atm. Plugging in the values, we get \(\Delta S \approx 0.0550\) L * atm / K.

Step by step solution

01

Identify the given parameters

We are given the following parameters: - Number of moles (n) = 0.850 mol - Initial pressure (P1) = 1.25 atm - Final pressure (P2) = 2.75 atm - Temperature (T) = 100掳C Since all calculations must be in Kelvin, we need to convert the temperature from Celsius to Kelvin: T = 100掳C + 273.15 = 373.15 K
02

Use the formula for the entropy change of an ideal gas during an isothermal process

Now we'll use the formula for the entropy change during an isothermal process: 螖S = nR * ln(P2/P1) Where n = 0.850 mol, R = 0.0821 L * atm / (mol * K), P1 = 1.25 atm, and P2 = 2.75 atm.
03

Calculate the entropy change

Plug the values into the formula: 螖S = (0.850 mol) * (0.0821 L * atm / (mol * K)) * ln(2.75 atm / 1.25 atm) 螖S 鈮� 0.0698 * ln(2.2) 螖S 鈮� 0.0698 * 0.7885 螖S 鈮� 0.0550 L * atm / K The entropy change (螖S) for this process is approximately 0.0550 L * atm / K.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ideal Gas
An ideal gas is a theoretical concept that represents a gas composed of many randomly moving particles that are not subject to any force except during elastic collisions. The ideal gas law, which is a cornerstone in understanding ideal gases, is expressed as:\[ PV = nRT \]Here, \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
  • The concept of an ideal gas helps us model real gases under many conditions though no real gas perfectly fits these criteria.
  • Neon, like other noble gases, behaves very closely to an ideal gas at standard temperature and pressure.
Even though ideal gases are a simplification, using this model allows us to predict the behavior of gases under various situations. It is particularly useful in calculations involving entropy changes during different gas processes.
Isothermal Process
An isothermal process occurs at a constant temperature. In such a process, the system exchanges heat with its surroundings to maintain the temperature constant despite changes in volume and pressure. In the realm of gases, particularly ideal gases, the work done and the heat exchange during an isothermal process are intimately linked.
  • For an isothermal process involving an ideal gas, the change in internal energy is zero. This is due to the direct relation of internal energy with temperature, which remains unchanged.
  • Entropy change in an isothermal process can be calculated using the formula:\[ \Delta S = nR \ln\left( \frac{P_2}{P_1} \right) \]This equation reflects how entropy is influenced by the pressure ratio when the temperature holds steady.
Understanding isothermal processes is crucial for analyzing systems where temperature remains constant, such as in the given example that calculates the entropy change (\( \Delta S \)) of neon gas during such a process at 100掳C.
Neon Gas
Neon gas, a member of the noble gas family, is famous for its lack of color, taste, and distinct chemical inertness due to its full electron shells. This makes neon excellent for uses such as in neon signs and high-voltage indicators.
  • Due to its monoatomic nature and noble gas characteristics, neon behaves almost ideally under standard conditions, which aids in applying the ideal gas law accurately.
  • In the condition described in the exercise, neon's properties allow for an effective demonstration of entropy calculations in isothermal processes for an ideal gas.
While neon is often used in visual technologies, its gaseous properties make it a great candidate for educational purposes in physics and chemistry, especially in demonstrating theoretical concepts like those involving entropy changes in ideal gases.

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

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of \(88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}\). The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: $$ \begin{array}{lrl} \hline \text { Substance } & \begin{array}{l} \text { Normal Boiling } \\ \text { Point }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{l} \Delta H_{\text {vap }} \\ \text { (kJ/mol) } \end{array} \\ \hline \text { Acetone, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO} & 56.1 & 29.1 \\ \text { Dimethyl ether, }\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O} & -24.8 & 21.5 \\ \text { Ethanol } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & 78.4 & 38.6 \\ \text { Octane, } \mathrm{C}_{8} \mathrm{H}_{18} & 125.6 & 34.4 \\ \text { Pyridine, } \mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N} & 115.3 & 35.1 \\\ \hline \end{array} $$ (a) Calculate \(\Delta \mathrm{S}_{\mathrm{vap}}\) for each of the liquids. Do all of the liquids obey Trouton's rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix \(\mathrm{B}\), check the accuracy of your conclusion. (d) Chlorobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(131.8^{\circ} \mathrm{C}\). Use Trouton's rule to estimate \(\Delta H_{\text {vap }}\) for this substance.

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from \(300 \mathrm{~K}\) to \(200 \mathrm{~K}\). (a) Describe how this change might be carried out while keeping the volume of the gas constant. (b) Describe how it might be carried out while keeping the pressure of the gas constant. (c) Does the change in \(\Delta E\) depend on the particular pathway taken to carry out this change of state? Explain.

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\) (c) Ethyl alcohol evaporates from a beaker. (d) \(\mathrm{A}\) diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\).

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(g)\) (b) \(\mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\) Explain.

Consider what happens when a sample of the explosive TNT (Section 8.8: "Chemistry Put to Work: Explosives and Alfred Nobel") is detonated. (a) Is the detonation a spontaneous process? (b) What is the sign of \(q\) for this process? (c) Can you determine whether \(w\) is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of \(\Delta E\) for the process? Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Making Measurements

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

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.