Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 92

The standard enthalpy of combustion of ethene gas, $\mathrm{C}_{2} \mathrm{H}_{4}(g),$ is \(-1411.1 \mathrm{kJ} / \mathrm{mol}\) at 298 \(\mathrm{K}\) . Given the following enthalpies of formation, calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for $\mathrm{C}_{2} \mathrm{H}_{4}(g) .$ $$ \begin{array}{ll}{\mathrm{CO}_{2}(g)} & {-393.5 \mathrm{kJ} / \mathrm{mol}} \\\ {\mathrm{H}_{2} \mathrm{O}(l)} & {-285.8 \mathrm{kJ} / \mathrm{mol}}\end{array} $$

Short Answer

Expert verified
The standard enthalpy of formation for ethene gas, \(C_2H_4(g)\), is \(52.5 \text{ kJ/mol}\).

Step by step solution

01

Write the balanced combustion equation for ethene

The combustion of ethene gas can be represented as: \(C_2H_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(l)\) Since there are 2 carbon atoms in ethene, the reaction will produce 2 moles of CO2. Also, 4 hydrogen atoms in ethene will produce 2 moles of H2O. To balance the equation, we need to add appropriate coefficients. Therefore, the balanced equation is: \(C_2H_4(g) + 3O_2(g) \rightarrow 2CO_2(g) + 2H_2O(l)\)
02

Write down the enthalpy change relationship

The standard enthalpy change of the reaction can be calculated using the enthalpies of formation of the products and reactants. The relationship can be written as: \(\Delta H_{rxn}^\circ = \sum \Delta H_{f, products}^\circ - \sum \Delta H_{f, reactants}^\circ\) For our reaction: \(\Delta H_{comb}^\circ = [2 \times \Delta H_{f, CO_2}^\circ + 2 \times \Delta H_{f, H_2O}^\circ] - [\Delta H_{f, C_2H_4}^\circ + 3 \times \Delta H_{f, O_2}^\circ]\) Since the enthalpy of formation of elemental oxygen gas is zero (\(\Delta H_{f, O_2}^\circ = 0\)), the equation simplifies to: \(-1411.1 \text{ kJ/mol} = [2 \times (-393.5 \text{ kJ/mol}) + 2 \times (-285.8 \text{ kJ/mol})] - [\Delta H_{f, C_2H_4}^\circ]\)
03

Solve for the enthalpy of formation of ethene

Now, we can solve for the enthalpy of formation of ethene gas \(\Delta H_{f, C_2H_4}^\circ\). We first calculate the term inside the brackets: = \(2 \times (-393.5 \text{ kJ/mol}) + 2 \times (-285.8 \text{ kJ/mol})\) = \(-787 \text{ kJ/mol} - 571.6 \text{ kJ/mol}\) = \(-1358.6 \text{ kJ/mol}\) Now, plug this value into the equation: \(-1411.1 \text{ kJ/mol} = -1358.6 \text{ kJ/mol} - \Delta H_{f, C_2H_4}^\circ\) Rearrange the equation and solve for \(\Delta H_{f, C_2H_4}^\circ\): \(\Delta H_{f, C_2H_4}^\circ = -1358.6 \text{ kJ/mol} + 1411.1 \text{ kJ/mol}\) \(\Delta H_{f, C_2H_4}^\circ = 52.5 \text{ kJ/mol}\) The standard enthalpy of formation for ethene gas is \(52.5 \text{kJ/mol}\).

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

Some automobiles and buses have been equipped to burn propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) .\) Compare the amounts of energy that can be obtained per gram of \(\mathrm{C}_{3} \mathrm{H}_{8}(g)\) and per gram of gasoline, assuming that gasoline is pure octane, $\mathrm{C}_{8} \mathrm{H}_{18}(l) .\( See Example \)6.11 .$ ) Look up the boiling point of propane. What disadvantages are there to using propane instead of gasoline as a fuel?

The complete combustion of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g),\) produces 1300 . kJ of energy per mole of acetylene consumed. How many grams of acetylene must be burned to produce enough heat to raise the temperature of 1.00 gal water by \(10.0^{\circ} \mathrm{C}\) if the process is 80.0\(\%\) efficient? Assume the density of water is 1.00 \(\mathrm{g} / \mathrm{cm}^{3}\)

Photosynthetic plants use the following reaction to produce glucose, cellulose, and so forth: $$6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \frac{\text { Sunlight }}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)$$ How might extensive destruction of forests exacerbate the greenhouse effect?

Which has the greater kinetic energy, an object with a mass of 2.0 \(\mathrm{kg}\) and a velocity of 1.0 \(\mathrm{m} / \mathrm{s}\) or an object with a mass of 1.0 \(\mathrm{kg}\) and a velocity of 2.0 $\mathrm{m} / \mathrm{s}$ ?

Consider the following statements: “Heat is a form of energy, and energy is conserved. The heat lost by a system must be equal to the amount of heat gained by the surroundings. Therefore, heat is conserved.” Indicate everything you think is correct in these statements. Indicate everything you think is incorrect. Correct the incorrect statements and explain
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

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.

Sign-up for free