Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 41

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is \(40 . \mathrm{cm}^{3} .\) If the combustion of this mixture releases \(950 . \mathrm{J}\) of energy, to what volume will the gases expand against a constant pressure of 650 . torr if all the energy of combustion is converted into work to push back the piston?

Short Answer

Expert verified
The gases expand to a final volume of approximately 40.11 cm³ when all the energy from the combustion is converted into work to push back the piston.

Step by step solution

01

Convert pressure to SI unit (Pascals)

Before calculating the work done, we need to convert the given pressure from torr to Pascals. We know that 1 torr = 133.322 Pa. So, the pressure in Pascals is: P = 650 torr × 133.322 Pa/torr = 86609.3 Pa
02

Calculate the initial volume in SI unit (cubic meters)

To make our calculations consistent, it's essential to convert the initial volume from cubic centimeters to cubic meters. 1 cubic meter = \(10^6\) cubic centimeters. So, the initial volume in cubic meters is: V_initial = \(\frac{40}{10^6}\) m³ = \(4 \times 10^{-5}\) m³
03

Calculate the work done by the gas

Since all the energy (950 J) is converted into work to push back the piston, the work done by the gas (W) is equal to the energy released during combustion: W = 950 J
04

Use the work formula to find the final volume

Now, we can use the formula W = P(V_final - V_initial) to determine the final volume of the gases. Rearrange the formula to solve for V_final: V_final = V_initial + \(\frac{W}{P}\) Substitute the values: V_final = \(4 \times 10^{-5}\) m³ + \(\frac{950 J}{86609.3 Pa}\)
05

Calculate the final volume

Now, perform the operations to find the final volume: V_final = \(4 \times 10^{-5}\) m³ + \(\frac{950}{86609.3}\) m³ ≈ \(4.01097 \times 10^{-5}\) m³
06

Convert the final volume to cubic centimeters

To convert the final volume from cubic meters to cubic centimeters, multiply the volume by \(10^6\): V_final = \(4.01097 \times 10^{-5}\) m³ × \(10^6\) cm³/m³ = 40.1097 cm³ Thus, the gases expand to a volume of approximately 40.11 cm³ when all the energy from the combustion is converted into work to push back the piston.

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

A sample of an ideal gas at 15.0 atm and 10.0 \(\mathrm{L}\) is allowed to expand against a constant external pressure of 2.00 atm at a constant temperature. Calculate the work in units of kJ for the gas expansion. (Hint: Boyle's law applies.)

The enthalpy change for the reaction $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ is \(-891 \mathrm{kJ}\) for the reaction as written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

Which of the following substances have an enthalpy of formation equal to zero? a. \(C l_{2}(g)\) b. \(\mathrm{H}_{2}(g)\) c. \(\mathrm{N}_{2}(l)\) d. \(\mathrm{Cl}(g)\)

Given the following data $$ \begin{array}{ll}{\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=-23 \mathrm{kJ}} \\ {3 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=-39 \mathrm{kJ}} \\ {\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \longrightarrow 3 \mathrm{FeO}(s)+\mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=18 \mathrm{kJ}}\end{array} $$ calculate \(\Delta H^{\circ}\) for the reaction $$ \mathrm{FeO}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) $$

A sample of nickel is heated to \(99.8^{\circ} \mathrm{C}\) and placed in a coffeecup calorimeter containing 150.0 \(\mathrm{g}\) water at $23.5^{\circ} \mathrm{C}$ . After the metal cools, the final temperature of metal and water mixture is \(25.0^{\circ} \mathrm{C}\) . If the specific heat capacity of nickel is 0.444 \(\mathrm{J} /^{\prime} \mathrm{C} \cdot \mathrm{g}\) what mass of nickel was originally heated? Assume no heat loss to the surroundings.
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

Nuclear 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.

Sign-up for free