/*! 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 55 "Gasohol," a mixture of gasoline... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 55

"Gasohol," a mixture of gasoline and ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is used as automobile fuel. The alcohol releases energy in a combustion reaction with \(\mathrm{O}_{2}\). $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ If \(0.115 \mathrm{~g}\) ethanol evolves \(3.62 \mathrm{~kJ}\) when burned at constant pressure, calculate the combustion enthalpy for ethanol.

Short Answer

Expert verified
The combustion enthalpy for ethanol is \(-1448\) kJ/mol.

Step by step solution

01

Calculate the moles of ethanol

First, we need to find the number of moles in 0.115 g of ethanol. The molar mass of ethanol, \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \), is calculated as follows: \(2\times 12.01 + 6\times 1.01 + 16.00 = 46.08\) g/mol. Thus, the number of moles \( n \) of ethanol is given by the formula:\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{0.115 \text{ g}}{46.08 \text{ g/mol}} = 0.00249 \text{ mol} \approx 0.0025 \text{ mol}\]
02

Determine the enthalpy change per mole

The problem states that when 0.115 g of ethanol is burned, it evolves 3.62 kJ of energy. Therefore, we can calculate the energy released per mole of ethanol:\[ \Delta H = \frac{3.62 \text{ kJ}}{0.0025 \text{ mol}} = 1448 \text{ kJ/mol} \]
03

Assign the sign for combustion enthalpy

Combustion reactions are exothermic, meaning they release heat. Therefore, the combustion enthalpy should be negative, indicating the release of energy:\[ \Delta H_{combustion} = -1448 \text{ kJ/mol} \]

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Key Concepts

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

Ethanol Combustion
Ethanol, a type of alcohol, serves as an alternative fuel source due to its ability to combust with oxygen. When ethanol burns, it reacts with oxygen (O_{2}) to form carbon dioxide (CO_{2}) and water (H_{2}O). This reaction is significant because it converts chemical energy within the ethanol into heat energy. The balanced chemical equation for ethanol combustion is:\[\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g})\longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}\mathrm{O}(\ell)\]This reaction is important in various applications, such as powering engines. Ethanol combustion releases energy, making it a useful fuel. The energy evolved from ethanol when it combusts can be measured in terms of enthalpy, a concept we will explore further.
Exothermic Reaction
Combustion reactions, like ethanol burning, fall into the category of exothermic reactions. These reactions are characterized by the release of heat or energy into the surroundings.
  • In the case of ethanol combustion, energy is released in the form of heat, which can be felt as warmth.
  • This characteristic of releasing energy is what makes exothermic reactions crucial for various practical applications like heating and energy generation.
The enthalpy change (\Delta H) for exothermic reactions is negative, which indicates energy is released. For ethanol combustion in our example, the enthalpy is \(-1448 \text{ kJ/mol}\), indicating a release of 1448 kJ of energy per mole of ethanol combusted. Understanding that the process is exothermic helps explain why ethanol is such an appealing fuel source.
Molar Mass Calculation
To accurately determine the enthalpy of combustion, knowing the molar mass of ethanol is essential. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (\text{g/mol}). It helps in converting grams of a substance to moles, a vital step in many chemical calculations.
  • For ethanol, \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH},\) calculate its molar mass by adding up the atomic masses:
  • 2 carbon atoms: 2 \times 12.01 = 24.02 \,\text{g/mol}
  • 6 hydrogen atoms: 6 \times 1.01 = 6.06 \,\text{g/mol}
  • 1 oxygen atom: 16.00 \,\text{g/mol}
  • Sum: 24.02 + 6.06 + 16.00 = 46.08 \,\text{g/mol}This value is used to convert the given mass of ethanol to moles, which in turn helps determine how much energy is released per mole when ethanol is combusted. Keeping the concept of molar mass in mind aids in effective chemical calculations and understanding stoichiometry.

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Most popular questions from this chapter

Calculate the standard reaction enthalpy, \(\Delta_{\mathrm{t}} H^{\circ}\), for formation of \(1 \mathrm{~mol}\) strontium carbonate (the material that gives the red color in fireworks) from its elements. $$ \mathrm{Sr}(\mathrm{s})+\mathrm{C}(\text { graphite })+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{Sr} \mathrm{CO}_{3}(\mathrm{~s}) $$ The information available is $$ \begin{array}{ll} \mathrm{Sr}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SrO}(\mathrm{s}) & \Delta_{\mathrm{r}} H^{\circ}=-592 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{SrO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SrCO}_{3}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-234 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g}) & \Delta_{\mathrm{r}} H^{\circ}=-394 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

In their home laboratory, two students do an experiment (a rather dangerous one-don't try it without proper safety precautions!) with drain cleaner (Drano, a solid) and toilet bowl cleaner (The Works, a liquid solution). The students measure 1 teaspoon (tsp) of Drano into each of four Styrofoam coffee cups and dissolve the solid in half a cup of water. Then they wash their hands and go have lunch. When they return, they measure the temperature of the solution in each of the four cups and find it to be \(22.3^{\circ} \mathrm{C}\). Next they measure into separate small empty cups \(1,2,3,\) and 4 tablespoons (Tbsp) of The Works. In each cup they add enough water to make the total volume 4 Tbsp. After a few minutes they measure the temperature of each cup and find it to be \(22.3^{\circ} \mathrm{C}\). Finally the two students take each cup of The Works, pour it into a cup of Drano solution, and measure the temperature over a period of a few minutes. Their results are reported in the table. $$ \begin{array}{ccc} \hline & \text { Volume of } & \text { Highest } \\ \text { Experiment } & \text { The Works (Tbsp) } & \text { Temperature ( } \left.{ }^{\circ} \mathrm{C}\right) \\ \hline 1 & 1 & 28.0 \\ 2 & 2 & 33.6 \\ 3 & 3 & 39.3 \\ 4 & 4 & 39.4 \\ \hline \end{array} $$ Discuss these results and interpret them in terms of the thermochemistry and stoichiometry of the reaction. Is the reaction exothermic or endothermic? Why is more energy transferred in some cases than others? For each experiment, which reactant, Drano or The Works, is limiting? Why are the final temperatures nearly the same in experiments 3 and \(4 ?\) What can you conclude about the stoichiometric ratio between the two reactants?

What is the value of the standard formation enthalpy for any element under standard conditions?

For each situation, define a system and its surroundings, and give the direction of heat transfer: (a) Propane is burning in a Bunsen burner in the laboratory. (b) After you have a swim, water droplets on your skin evaporate. (c) Water, originally at \(25^{\circ} \mathrm{C}\), is placed in the freezing compartment of a refrigerator. (d) Two chemicals are mixed in a flask on a laboratory bench. A reaction occurs and heat is evolved.

You wish to know the standard formation enthalpy of liquid \(\mathrm{PCl}_{3}\) $$ \mathrm{P}_{4}(\mathrm{~s})+6 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PCl}_{3}(\ell) $$ These reaction enthalpies have been determined experimentally: $$ \begin{array}{ll} \mathrm{P}_{4}(\mathrm{~s})+10 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PCl}_{5}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-1774.0 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{PCl}_{3}(\ell)+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-123.8 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate the formation enthalpy for \(\mathrm{PCl}_{3}(\ell)\).
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