Question

Determine the adiabatic, stoichiometric flame temperature at constant pressure for n-butanol, an alternative biofuel, give \((25 \mathrm{C}, 1 \mathrm{~atm})\) the enthalpy of combustion is \(-26\)

Short answer

Answer: To find the adiabatic stoichiometric flame temperature for n-butanol, you must follow these steps: 1. Calculate the initial moles of each species involved in the combustion (1 mole n-butanol, 6 moles O2, 0 moles CO2, and 0 moles H2O). 2. Determine the initial enthalpy of the reactants using the provided specific heat values and initial temperature. 3. Calculate the final enthalpy of the products using the given enthalpy of combustion and initial enthalpy of reactants. 4. Determine the final moles of each species involved in the combustion (0 moles n-butanol, 0 moles O2, 4 moles CO2, and 5 moles H2O). 5. Use an energy balance equation and final enthalpy of products to calculate the final temperature. 6. The adiabatic stoichiometric flame temperature is the final temperature calculated in step 5.

Step-by-step solution

Calculate initial moles of each species involved in the combustion

From the stoichiometric equation, 1 mole of n-butanol reacts with 6 moles of O2 to produce 4 moles of CO2 and 5 moles of H2O. So, initially, we have: - 𝑛𝑏𝑢𝑡𝑎𝑛𝑜𝑙,0 = 1 mole - 𝑛𝑂2,0 = 6 moles - 𝑛𝐶𝑂2,0 = 0 moles - 𝑛𝐻2𝑂,0 = 0 moles

Determine the initial enthalpy of the reactants

The initial enthalpy of the reactants can be calculated using the given specific heat values and initial temperature (25°C or 298.15 K): \(H_{reactants, initial} = (1.1\times 1 \times (298.15))+ (1.0\times 6 \times (298.15))\)

Calculate the final enthalpy of the products

The enthalpy of combustion is equal to the difference in enthalpy between products and reactants. Rearranging and using the given enthalpy of combustion (-26 kJ/g): \( H_{products, final} = H_{reactants, initial} + \Delta H_{combustion}\)

Determine the final moles of each species involved in the combustion

After the reaction, we have: - 𝑛𝑏𝑢𝑡𝑎𝑛𝑜𝑙,final = 0 moles - 𝑛𝑂2,final = 6 - 6 = 0 moles - 𝑛𝐶𝑂2,final = 4 moles - 𝑛𝐻2𝑂,final = 5 moles

Calculate final temperature

Use energy balance (with Q = 0) and final enthalpy of products to determine the final temperature: \(H_{products,final} = H_{CO2,final} + H_{H2O,final} = (1.0 \times 4 \times (T_{final}))+ (1.0 \times 5 \times (T_{final}))\) Solve for \(T_{final}\).

Obtain adiabatic stoichiometric flame temperature

The adiabatic stoichiometric flame temperature is the final temperature calculated in Step 5. This value represents the flame temperature under adiabatic conditions, presuming the reaction goes to completion, and considering only the major species involved in the combustion process.

Key concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It ensures that the proportions used in chemical equations are balanced, meaning that the number of atoms in the reactants equals the number in the products.
In the context of combustion, like with n-butanol, stoichiometry helps us determine the exact amount of oxygen needed and the yields of carbon dioxide and water in a reaction. According to the stoichiometric equation for n-butanol combustion, 1 mole of n-butanol requires 6 moles of oxygen and produces 4 moles of carbon dioxide and 5 moles of water.
This precise calculation is crucial as it helps us predict the behavior of a chemical reaction accurately, aiding in efficient energy use and minimizing byproducts.

Biofuel Combustion

Biofuel combustion refers to the burning of biofuels, which are derived from biological materials like plants and animal waste. n-butanol is one such biofuel that has garnered attention due to its cleaner burning properties in comparison to fossil fuels.
When biofuels like n-butanol undergo combustion, they react with oxygen to produce carbon dioxide, water, and energy. Understanding these reactions is important for promoting sustainable energy solutions because it helps in harnessing energy more efficiently while reducing carbon emissions.

• Biofuel combustion contributes to lower emissions due to the cleaner nature of the fuel.
• It represents a renewable energy source which can be replanted and managed sustainably.

In this context, studying the combustion process also involves examining factors like adiabatic stoichiometric flame temperature, which helps in optimizing energy output.

Enthalpy Calculations

Enthalpy calculations play a vital role in thermodynamics, particularly in understanding the energy exchanges during chemical reactions. Enthalpy, represented by the symbol \(H\), signifies the total heat content of a system.
In combustion reactions, enthalpy calculations help determine the energy difference between reactants and products. For instance, the enthalpy of combustion for a substance like n-butanol is known, which means we know how much energy is released as heat when the fuel combusts completely. This release is usually negative, indicating an exothermic reaction, where energy is released into the surroundings.

• The initial enthalpy of reactants is calculated using specific heat capacities and initial temperatures.
• The final enthalpy of products is measured combining the initial enthalpy and the enthalpy change due to combustion.

These calculations are crucial for designing processes and systems that make efficient use of biofuels.

Chemical Thermodynamics

Chemical thermodynamics is the branch of science that deals with the relationship between heat, work, and chemical reactions. It allows us to predict whether a reaction will occur spontaneously, its equilibrium position, and how energy is distributed within a system.
One of its applications in combustion includes determining the adiabatic flame temperature, which is the temperature a burning substance reaches without heat loss to its surroundings. This is particularly vital in the analysis of biofuel combustion because it allows for the optimization of engine and reactor designs.
By examining reactions under adiabatic conditions, chemical thermodynamics provides insights into:

• The maximum achievable temperature of a reaction.
• How different variables can influence energy outputs and efficiencies.

Being able to predict these factors helps in understanding how to leverage biofuels like n-butanol for better energy sustainability.