Problem 47 - Chemistry The Central Science In Si Units

Question

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.

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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}).

Step 4: 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.

Key Concepts

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.