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Consider the combustion of liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(I)\) $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(I)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H &=-726.5 \mathrm{~kJ} \end{aligned} $$ (a) What is the enthalpy change for the reverse reaction? (b) Balance the forward reaction with whole-number coefficients. What is \(\Delta H\) for the reaction represented by this equation? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If the reaction were written to produce \(\mathrm{H}_{2} \mathrm{O}(g)\) instead of \(\mathrm{H}_{2} \mathrm{O}(I),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

Short Answer

Expert verified
(a) +726.5 kJ; (b) 2CH₃OH + 3O₂ → 2CO₂ + 4H₂O, ΔH = -1453.0 kJ; (c) Forward reaction; (d) The magnitude of ΔH would increase.

Step by step solution

01

Determine Enthalpy Change for Reverse Reaction

The enthalpy change for a reaction,  ext{H}, is opposite in sign for the reverse reaction. Since the enthalpy change for the forward reaction,  ext{H}_{ ext{forward}}, is -726.5 kJ, the enthalpy change for the reverse reaction will be +726.5 kJ. Therefore,  ext{H}_{ ext{reverse}} = +726.5 kJ.
02

Balance the Forward Reaction

To balance the equation with whole-number coefficients, multiply everything by 2: 2  ext{CH}_{3} ext{OH}(l) + 3  ext{O}_{2}(g)  2  ext{CO}_{2}(g) + 4  ext{H}_{2} ext{O}(l). The enthalpy change for this balanced reaction, now occurring with 2 mol of methanol, will be 2 imes (-726.5) = -1453.0  kJ.
03

Determine Thermodynamically Favored Direction

A reaction is thermodynamically favored if it releases energy (exothermic). Since the forward reaction has a negative  ext{H} value (-726.5 kJ), it is exothermic, making it more likely to be thermodynamically favored over the endothermic reverse reaction (positive  ext{H}).
04

Effect of Producing Water Vapor Instead of Liquid Water

Producing  ext{H}_{2} ext{O}(g) instead of  ext{H}_{2} ext{O}(l) would require additional energy to convert liquid water to gaseous water, which involves overcoming the latent heat of vaporization. This would increase the magnitude of  ext{H}, making it less negative (or more positive), as additional energy is consumed in the conversion.

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Key Concepts

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

Combustion Reaction
A combustion reaction is a chemical process where a fuel reacts with an oxidant, commonly oxygen, releasing energy in the form of heat and often light. In the combustion of methanol, \( \text{CH}_3\text{OH}(l) \), it reacts with oxygen (\( \text{O}_2(g) \)) to form carbon dioxide (\( \text{CO}_2(g) \)) and water (\( \text{H}_2\text{O}(l) \)). The balanced equation for this combustion is:
  • 2 \( \text{CH}_3\text{OH}(l) + 3 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 4 \text{H}_2\text{O}(l) \)
A key aspect of combustion reactions is their exothermic nature, meaning they release energy. This energy release characterizes a combustion reaction, making these reactions essential for processes like heating, powering engines, and generating electricity.
This feature is what we often harness in real-world applications, emphasizing the importance of understanding the underlying chemical process.
Thermodynamic Favorability
Thermodynamic favorability refers to the tendency of a reaction to occur spontaneously under certain conditions. For a chemical reaction, this is largely determined by its enthalpy change (\( \Delta H \)).
For a reaction to be considered thermodynamically favored, it should generally release energy to its surroundings, meaning it is exothermic.
In the case of methanol combustion, the forward reaction has an enthalpy change of \( \Delta H = -726.5 \text{ kJ} \). The negative sign indicates that the reaction releases energy, thus it is exothermic and more likely to be thermodynamically favored over the reverse reaction.
  • Exothermic Reaction: Releases heat, more energetically stable products.
  • Endothermic Reaction: Absorbs heat, less energetically stable products.
The favorability indicates how nature leans towards reactions that increase disorder (entropy) and reduces free energy. It's important in determining which reaction pathway is more probable.
Energy Conversion
Energy conversion in chemical reactions involves transforming chemical energy into other forms, often heat or electricity. In the context of the methanol combustion reaction, the chemical energy stored in the bonds of methanol is converted mainly into heat energy.
The concept of energy conversion is crucial in various applications from powering vehicles to energy production in power plants. Efficient energy conversion ensures that maximum energy is harnessed from fuel sources.
During the combustion of methanol:
  • Chemical bonds are broken and formed.
  • Breaking bonds in reactants requires energy, while forming new bonds in products releases energy.
The net result of these processes is the conversion of stored chemical energy into heat, which we can harness for various purposes.
This concept underpins the practical use of fuels and the drive towards understanding and improving energy efficiency in chemical processes.

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Most popular questions from this chapter

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: $$ 2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2 (g) $$ Calculate the \(\Delta H^{\circ}\) for this reaction using the following thermochemical data: $$ \begin{aligned} \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I) & & \Delta H^{0}=-890.3 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H^{0} &=-571.6 \mathrm{~kJ} \\ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(I) & \Delta H^{0}=&-3120.8 \mathrm{~kJ} \end{aligned} $$

How much work (in J) is involved in a chemical reaction if the volume decreases from \(33.6 \mathrm{~L}\) to \(11.2 \mathrm{~L}\) against a constant pressure of \(90.5 \mathrm{kPa} ?\)

The specific heat of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(I),\) is \(2.22 \mathrm{~J} / \mathrm{g}-\mathrm{K} .(\mathrm{a}) \mathrm{How}\) many J of heat are needed to raise the temperature of \(80.0 \mathrm{~g}\) of octane from 10.0 to \(25.0^{\circ} \mathrm{C} ?\) (b) Which will require more heat, increasing the temperature of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}(I)\) by a certain amount or increasing the temperature of \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(I)\) by the same amount?

Consider two solutions, the first being \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{MCuSO}_{4}\) and the second \(50.0 \mathrm{~mL}\) of \(2.00 \mathrm{M} \mathrm{KOH}\). When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to \(27.7^{\circ} \mathrm{C}\). (a) Before mixing, how many grams of Cu are present in the solution of \(\mathrm{CuSO}_{4} ?\) (b) Predict the identity of the precipitate in the reaction. (c) Write complete and net ionic equations for the reaction that occurs when the two solutions are mixed. \((\mathbf{d})\) From the calorimetric data, calculate \(\Delta H\) for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is \(100.0 \mathrm{~mL},\) and that the specific heat and density of the solution after mixing are the same as those of pure water.

The standard enthalpies of formation of gaseous propyne \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)\), propylene \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)\), and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) are \(+185.4,+20.4,\) and \(-103.8 \mathrm{~kJ} / \mathrm{mol}\), respectively. (a) Calculate the heat evolved per mole on combustion of each substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) (b) Calculate the heat evolved on combustion of \(1 \mathrm{~kg}\) of each substance. \((\mathbf{c})\) Which is the most efficient fuel in terms of heat evolved per unit mass?

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