Question

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of \(0.791 \mathrm{~g} / \mathrm{mL}\) (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per \(\mathrm{kJ}\) of heat emitted.

Short answer

The combustion of methanol in air has a balanced equation of: CH\(_3\)OH (l) + \(\dfrac{3}{2}\)O\(_2\) (g) \(\to\) CO\(_2\) (g) + 2H\(_2\)O (g). The standard enthalpy change for this reaction is -726 kJ/mol. The heat produced by the combustion of 1 liter of methanol is -17930 kJ. The mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted is approximately 0.0607 g/kJ.

Step-by-step solution

a) Write a balanced equation for the combustion of liquid methanol in air

The combustion of methanol (CH\(_3\)OH) in air involves the reaction of methanol with oxygen(O\(_2\)) to produce carbon dioxide (CO\(_2\)) and water (H\(_2\)O) as products: CH\(_3\)OH (l) + O\(_2\) (g) \(\to\) CO\(_2\) (g) + H\(_2\)O (g) Now, we will balance the equation. First, balance the carbon atoms: 1 × CH\(_3\)OH + O\(_2\) \(\to\) 1 × CO\(_2\) + H\(_2\)O Next, balance the hydrogen atoms: CH\(_3\)OH + O\(_2\) \(\to\) CO\(_2\) + 2 × H\(_2\)O Lastly, balance the oxygen atoms: CH\(_3\)OH + \(\dfrac{3}{2}\times \)O\(_2\) \(\to\) CO\(_2\) + 2 × H\(_2\)O So, the balanced equation for the combustion of liquid methanol in air is: CH\(_3\)OH (l) + \(\dfrac{3}{2}\)O\(_2\) (g) \(\to\) CO\(_2\) (g) + 2H\(_2\)O (g)

b) Calculate the standard enthalpy change for the reaction

Standard enthalpy of combustion for methanol \(\left( \Delta H^\circ_\text{comb}(\mathrm{CH}_3\mathrm{OH}) \right)\) is -726 kJ/mol. We can use this value to find the standard enthalpy change for the reaction, since \(\mathrm{H}_{2} \mathrm{O}(g)\) is given as a product. Standard enthalpy change for the reaction \(\left( \Delta H^\circ_\text{r} \right)\): \(\Delta H^\circ_\text{r} = \Delta H^\circ_\text{comb}(\mathrm{CH}_3\mathrm{OH})\) = -726 kJ/mol The standard enthalpy change for the reaction is -726 kJ/mol.

c) Calculate the heat produced by combustion per liter of methanol

Given the density of methanol, d = 0.791 g/mL, we can find the mass of 1 L (1000 mL) of methanol: mass of 1 L methanol = 1000 mL × 0.791 g/mL = 791 g Next, we'll convert the mass of methanol to moles using molar mass (MM) of methanol (32.04 g/mol): moles of methanol = 791 g / 32.04 g/mol ≈ 24.7 mol Now, we can find the heat produced per liter of methanol using enthalpy change: heat produced = 24.7 mol × (-726 kJ/mol) ≈ -17930 kJ Therefore, the heat produced by the combustion of 1 liter of methanol is -17930 kJ.

d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per \(\mathrm{kJ}\) of heat emitted

First, let's find the moles of \(\mathrm{CO}_{2}\) produced for every mole of methanol burned: From the balanced equation, 1 mole of CH\(_3\)OH produces 1 mole of CO\(_2\). So, 24.7 moles of CH\(_3\)OH will produce 24.7 moles of CO\(_2\). Now, we'll convert the moles of CO\(_2\) to mass using the molar mass (MM) of CO\(_2\) (44.01 g/mol): mass of \(\mathrm{CO}_{2}\) = 24.7 mol × 44.01 g/mol ≈ 1087 g Next, we'll find the mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted: mass of \(\mathrm{CO}_{2}\) per kJ = 1087 g / (-17930 kJ) ≈ 0.0607 g/kJ Thus, the mass of \(\mathrm{CO}_{2}\) produced per kJ of heat emitted is approximately 0.0607 g/kJ.

Key concepts

Chemical Reactions

In the world of chemistry, a chemical reaction is essentially a process that transforms one set of chemicals into another. The combustion of methanol is one such transformation, where methanol reacts with oxygen to produce carbon dioxide and water. This specific type of reaction is known as a combustion reaction, which is a high-energy process that releases heat and light.

Understanding the balancing of chemical equations is crucial here as it obeys the law of conservation of mass, ensuring that the number of atoms for each element is equal on both sides of the equation. In the case of methanol combustion, the balanced equation is CH₃OH (l) + \(\frac{3}{2}\)O₂ (g) \to CO₂ (g) + 2H₂O (g). This tells us that one molecule of methanol reacts with one and a half molecules of oxygen to produce one molecule of carbon dioxide and two molecules of water.

Enthalpy Change

At the heart of many chemical reactions, including combustion, is the concept of enthalpy change, denoted as \(\Delta H\). It quantifies the heat absorbed or released during a chemical reaction at constant pressure. Enthalpy change can be exothermic, where energy is released to the surroundings (negative \(\Delta H\)), or endothermic, where energy is absorbed from the surroundings (positive \(\Delta H\)).

The standard enthalpy change for the combustion of methanol, \(\Delta H^\circ_\text{comb}(\mathrm{CH}_3\mathrm{OH})\), is -726 kJ/mol. This is a specific example of an exothermic reaction, meaning methanol releases heat as it combusts. The negative sign indicates that energy is being emitted, and in this context, it tells us how much energy is released when one mole of methanol is burned completely in air.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a quantitative relationship between the amounts of substances involved in a reaction, based on the balanced chemical equation. Through stoichiometry, one can determine the amount of product formed from a given amount of reactant, or vice versa.

In our exercise regarding methanol combustion, once we have the balanced equation, we use stoichiometry to convert the mass of methanol to moles, then use the enthalpy change to find the total heat produced. The steps involved include converting grams to moles, using the molar mass of methanol (32.04 g/mol), and then applying the stoichiometric coefficients from the balanced equation to relate methanol to the energy released.

Heat of Combustion

The heat of combustion refers to the amount of heat that is released when a substance is burned in the presence of oxygen. It is a measure of the energy content of a fuel, and higher values indicate a more energy-dense fuel. This is a significant factor in many industries, especially in the design of engines and selection of fuel sources.

For race cars using methanol as fuel, calculating the heat of combustion per liter of methanol, as we did in the exercise, is essential in determining the energy available to power the vehicle. Furthermore, the resulting mass of CO₂ produced per kJ of heat emitted highlights the environmental implications of the fuel's use. The heat of combustion is a key piece of the puzzle in assessing both efficiency and environmental impact.