Question

Methanol (CH \(_{3} \mathrm{OH}\) ) 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 kJ of heat emitted.

Short answer

The balanced equation for the combustion of methanol in air is: \(CH_3OH (l) + \frac{3}{2} O_2 (g) \rightarrow CO_2 (g) + 2 H_2O (g)\). The standard enthalpy change for the reaction is \(-725.6\,kJ/mol\). The heat produced by combustion per liter of methanol is \(-17912\,kJ\). The mass of \(CO_2\) produced per kJ of heat emitted is \(-0.0606\,g/kJ\).

Step-by-step solution

Write the balanced equation for the combustion of methanol

The balanced equation for the combustion of methanol in air is given by: CH3OH (l) + 3/2 O2 (g) -> CO2 (g) + 2 H2O (g)

Calculate the standard enthalpy change for the reaction

Standard enthalpy change can be calculated using the enthalpies of formation of the reactants and products in the balanced reaction: ΔH° = Σ ΔfH°(products) - Σ ΔfH°(reactants) Using the standard enthalpies of formation, we have: ΔH° = [ 1 × ΔfH°(CO2) + 2 × ΔfH°(H2O) ] - [ ΔfH°(CH3OH) + 3/2 × ΔfH°(O2)] Now, we need to substitute the values of the enthalpies of formation from the given data. The enthalpies of formation are (in kJ/mol): ΔfH° (CH3OH) = -239 ΔfH° (O2) = 0 (since O2 is an element in its standard state) ΔfH°(CO2) = -393.5 ΔfH°(H2O) = -241.8 Plugging these values into the equation, we get: ΔH° = [ 1 × (-393.5) + 2 × (-241.8) ] - [ (-239) + 3/2 × 0 ] ΔH° = -725.6 kJ/mol

Calculate the heat produced by combustion per liter of methanol

To find the heat produced per liter of methanol, we first need to find the number of moles present in one liter of methanol. The given density of methanol is 0.791 g/mL, so for one liter (1000 mL), the mass of methanol is: mass of methanol = density × volume = 0.791 g/mL × 1000 mL = 791 g The molar mass of methanol (CH3OH) = 12 + 3 × 1 + 1 × 16 + 1 = 32 g/mol The number of moles of methanol in 1 liter = mass / molar mass = 791 g / 32 g/mol = 24.7 mol We have already found the standard enthalpy change for the balanced equation as -725.6 kJ/mol. Therefore, the heat produced by combustion per liter of methanol is: Heat produced = number of moles × ΔH° = 24.7 mol × -725.6 kJ/mol = -17912 kJ

Calculate the mass of CO2 produced per kJ of heat emitted

From the balanced equation of combustion, we know that 1 mole of CH3OH produces 1 mole of CO2. Therefore, the stoichiometric ratio of CH3OH to CO2 is 1:1. The molar mass of CO2 = 12 + 2 × 16 = 44 g/mol The mass of CO2 produced per mole of CH3OH = 1 × 44 g/mol = 44 g The heat emitted per mole of CH3OH, ΔH° = -725.6 kJ/mol To find the mass of CO2 produced per kJ of heat emitted, we can use the following formula: Mass of CO2 per kJ = (Mass of CO2 produced per mole of CH3OH) / (Heat emitted per mole of CH3OH) Mass of CO2 per kJ = 44 g / -725.6 kJ = -0.0606 g/kJ.

Key concepts

Chemical Reactions

Understanding chemical reactions is pivotal when analyzing the combustion of methanol, which serves as a fuel in race cars. In simple terms, a chemical reaction is a process that transforms one set of chemical substances into another. In the context of combustion, this entails a reactant (methanol) reacting with oxygen to produce carbon dioxide and water as products.

For methanol (CH₃OH), the balanced chemical equation reflects the exact stoichiometry of the reaction, ensuring that the number of atoms for each element is conserved. Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction, and it dictates the proportions needed to react completely without any excess of any reactant. In the balanced equation for the combustion of methanol, every one molecule of CH₃OH reacts with three halves of an O₂ molecule to produce one molecule of CO₂ and two molecules of H₂O.

Stoichiometry

Stoichiometry is a segment of chemistry that involves calculating the quantities of reactants and products involved in chemical reactions. When examining the combustion of methanol, it is crucial to use stoichiometry to predict how much heat is produced and how much CO₂ is generated per unit of energy released.

The stoichiometric calculation often begins with a balanced chemical equation, proceeding to relate the amounts of reactants to the amounts of products using molar ratios. These calculations are fundamental in various applications including optimizing fuel consumption in race cars, as well as in industrial processes. Besides, stoichiometry allows us to calculate the theoretical yield of a reaction, which can be compared with the actual yield to determine efficiency.

Enthalpy Change

The enthalpy change, represented as \( \Delta H^\circ \), is a measure of the total heat content of a system and is a crucial concept in thermochemistry. It reflects the amount of energy released or absorbed during a chemical reaction under constant pressure. For combustion processes, such as the burning of methanol, the enthalpy change is negative, indicating that energy is released as heat.

The calculation of the standard enthalpy change involves subtracting the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products. In the combustion of methanol, the equation simplifies by eliminating the enthalpy of diatomic oxygen, as elements in their standard state have a standard enthalpy of formation of zero. This calculated enthalpy change helps us understand the amount of energy a certain amount of fuel can release, thus determining its efficacy as an energy source.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is a fundamental concept for converting between mass and amount of substance (measured in moles), which is critical in stoichiometry. The molar mass of any compound, such as methanol (CH₃OH), is calculated by summing the atomic masses of all atoms present in one molecule of the compound.

When calculating the amount of heat produced upon the complete combustion of one liter of methanol, the molar mass is used to convert the mass of methanol to moles. This conversion is essential to determine the heat produced for a given amount of fuel. Additionally, understanding the molar mass allows us to calculate the mass of carbon dioxide produced per kilojoule of heat emitted, showing the direct relationship between the quantity of fuel burned and its environmental impact.