Question

Consider the combustion of liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l) :\) $$\begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H &=-726.5 \mathrm{kJ} \end{aligned}$$ (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 \(\mathrm{H}_{2} \mathrm{O}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

Short answer

(a) The enthalpy change for the reverse reaction is \(+\)726.5 kJ. (b) The reaction is already balanced with whole-number coefficients: \( \mathrm {CH_3OH(l) + \dfrac{3}{2}\thinspace O_2(g) \rightarrow CO_2(g) + 2 \thinspace H_2O(l)} \), and its enthalpy change is \(-\)726.5 kJ. (c) The forward reaction is more likely to be thermodynamically favored because it is exothermic (\(\Delta H\) is negative). (d) If the reaction produced \( \mathrm{H_2O}(g)\) instead of \( \mathrm {H_2O}(l)\), the magnitude of \(\Delta H\) would be expected to increase (become less negative) as additional energy is needed to convert water from the liquid to the gaseous phase.

Step-by-step solution

Determining Enthalpy Change for Reverse Reaction

The reverse reaction of a chemical process is always opposite to the forward reaction. Therefore to find the enthalpy change for the reverse reaction, reverse the sign of the given enthalpy change. In this case, since the enthalpy change for the forward reaction is -726.5 kJ, the enthalpy change for the reverse reaction will be: ΔH_reverse = +726.5 kJ #b) Balance the reaction and find its enthalpy change#

Balancing the Equation

The given equation is already balanced with the lowest whole-number coefficients: CH3OH(l) + 3/2 O2(g) → CO2(g) + 2 H2O(l)

Finding Enthalpy Change

Since the equation is already balanced, the enthalpy change for the balanced forward reaction using whole-number coefficients is the same as what was given: ΔH = -726.5 kJ #c) Thermodynamically favored reaction#

Comparing Forward and Reverse Reactions

A forward reaction with a negative enthalpy change indicates that the reaction is exothermic and releases energy. In general, exothermic reactions are more thermodynamically favored in comparison to endothermic reactions (which have positive enthalpy changes). In this case, the forward reaction is exothermic with a negative value for ΔH, thus making it more likely to be thermodynamically favored over the reverse reaction. #d) Predicting change in enthalpy value if H2O was in its gaseous state#

Comparing Liquid and Gaseous H2O

If the reaction was written as: CH3OH(l) + 3/2 O2(g) → CO2(g) + 2 H2O(g) We would need to figure out how the change in the phase of water will affect the enthalpy of the reaction. In general, when going from a liquid phase to a gaseous phase, the substance gains energy. As a result, the enthalpy change for the forward reaction should increase in magnitude (become less negative) to account for the additional energy needed to convert the water from the liquid to the gaseous phase. So, the magnitude of ΔH would be expected to increase.

Key concepts

Thermodynamics

Thermodynamics is the study of energy, work, and heat and their transformations in chemical processes. It helps us understand how energy is exchanged and conserved, which is crucial for analyzing chemical reactions.
The first law of thermodynamics, which is often the focus, states that energy cannot be created or destroyed, only transformed. This means that the total energy in a closed system remains constant. In chemical reactions, this concept is particularly important when discussing enthalpy change (\( \Delta H \)), which is the heat change at constant pressure.
When considering the combustion of liquid methanol, \( \Delta H \) indicates whether the reaction is endothermic or exothermic. Thermodynamics helps us determine whether the reaction releases or absorbs energy by analyzing the sign and magnitude of \( \Delta H \). Knowing these details allows chemists to predict the energy flow in chemical processes, which is fundamental for efficient energy use and safety concerns.

Exothermic Reaction

Exothermic reactions are chemical reactions that release energy, usually in the form of heat, to their surroundings. These reactions have a negative enthalpy change (\( \Delta H \)).
The combustion of methanol is an exothermic reaction, as indicated by \( \Delta H = -726.5 \, \mathrm{kJ} \). This negative value shows that the energy of the products is lower than the energy of the reactants, meaning energy is released during the reaction.
A common example of exothermic reactions is the burning of fuels, which are vital in everyday applications like heating and powering engines. They are essential in thermodynamic studies, as they demonstrate the flow of energy from the system to the surroundings. The favorability of exothermic reactions is often due to their ability to release energy and increase the surrounding temperature, making them spontaneous under many conditions.

Balancing Chemical Equations

Balancing chemical equations involves making sure that the number of each type of atom on the reactants side is equal to the number on the products side. It is necessary for obeying the law of conservation of mass.
In the given example of methanol combustion, the equation is balanced as \( \text{CH}_3\text{OH}(l) + \frac{3}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(l) \). While this form uses fractional coefficients, whole-number coefficients can be used by multiplying through to simplify the stoichiometry without changing the relative proportions.
Balancing equations not only obeys the principles of stoichiometry but is also crucial for calculating subsequent energy changes, such as enthalpy. Proper balancing ensures accurate thermodynamic calculations and predicts reactants' and products' quantities in a chemical reaction.

Phase Change in Reactions

Phase changes involve the transformation of a substance from one state of matter to another, such as from liquid to gas. This involves changes in energy as well.
In the combustion reaction given, water is produced as a liquid. If water instead transitions from liquid to gas, it would require additional energy input, reflecting an increase in the enthalpy change of the reaction. This is because vaporizing water consumes energy to overcome intermolecular forces, making \( \Delta H \) less negative.
Understanding phase changes is critical in thermodynamics as it affects calculations of energy changes in reactions. Considering phase transitions ensures accurate predictions of how a reaction's enthalpy varies with different physical states of reactants and products. For example, when considering energy efficiency and environmental impact, changing the phase of one component in an industrial reaction could significantly affect the overall energy balance.