Question

Calculate the fuel values of gaseous benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right) .\) Does one mole of benzene have a higher or lower fuel value than three moles of ethylene?

Short answer

Answer: No, one mole of benzene has a lower fuel value than three moles of ethylene. The fuel value of one mole of benzene is 3268 kJ/mol, while the fuel value of three moles of ethylene is 4233 kJ.

Step-by-step solution

Determine the standard enthalpies of combustion

The standard enthalpy of combustion, \(\Delta H_c^\circ\), is the energy released when one mole of a compound is burned in excess oxygen under standard conditions. These values can usually be found in a textbook or a chemistry reference table. For this exercise, let's assume the following standard enthalpies of combustion: Benzene: \(\Delta H_c^\circ (C_6H_6) = -3268 \ \text{kj/mol}\) Ethylene: \(\Delta H_c^\circ (C_2H_4) = -1411 \ \text{kj/mol}\)

Calculate the fuel values of benzene and ethylene

To calculate the fuel values, we simply use the standard enthalpies of combustion. The fuel values for one mole of each compound are: Fuel value of benzene: \(-(-3268 \ \text{kj/mol}) = 3268 \ \text{kj/mol}\) Fuel value of ethylene: \(-(-1411 \ \text{kj/mol}) = 1411 \ \text{kj/mol}\)

Compare the fuel values of benzene and ethylene

Now, we can compare the fuel values of one mole of benzene to three moles of ethylene: One mole of benzene: \(3268 \ \text{kj/mol}\) Three moles of ethylene: \(3 \times 1411 \ \text{kj/mol} = 4233 \ \text{kj}\)

Conclude

One mole of benzene has a fuel value of \(3268 \ \text{kj/mol}\), which is lower than the fuel value of three moles of ethylene, which is \(4233 \ \text{kj}\). Therefore, one mole of benzene has a lower fuel value than three moles of ethylene.

Key concepts

Fuel Value

Fuel value refers to the amount of energy that can be obtained from the combustion of a specific quantity of a fuel. Essentially, it reflects how much heat is produced during complete combustion. When we talk about the fuel value of certain compounds, like benzene and ethylene gas, we are considering the heat released when these substances are burnt with excess oxygen. This measurement is usually expressed in kilojoules per mole (kJ/mol).

Calculating the fuel value involves using the standard enthalpies of combustion. This refers to the energy change that occurs when one mole of a compound is burned under standard conditions. For our compounds, the fuel value is derived from the standard enthalpy of combustion, which has a negative sign when expressed normally because combustion is an exothermic process. However, when stating the fuel value, we take the absolute value (positive) to reflect the energy released. Hence, the fuel value becomes a useful benchmark when comparing how energy-efficient different fuels can be.

Benzene

Benzene ( C_6H_6 ) is a simple aromatic hydrocarbon that's well-known in both industrial chemistry and fuel calculations. It's an essential component in the petrochemical industry and is commonly referred to as a high-energy compound due to the amount of energy it releases upon combustion.

The standard enthalpy of combustion for benzene is notably high at -3268 ext{ kJ/mol} . This means when one mole of benzene undergoes combustion, it releases 3268 kJ of energy. In fuel calculations, this energy release is significant, especially when comparing benzene to other fuels. Yet, despite its high individual fuel value, when comparing the efficiency of benzene to ethylene in larger quantities, it might not provide as much total energy. This aspect is crucial when considering fuel efficiency and economic energy sources for broader industrial applications.

Ethylene Gas

Ethylene gas ( C_2H_4 ) is another integral compound in the realm of industrial chemistry and fuel comparisons. It's a simple, double-bonded hydrocarbon, which makes it an incredibly versatile chemical not only as a fuel but also as a precursor in the production of polymers like polyethylene.

The standard enthalpy of combustion for ethylene stands at -1411 ext{ kJ/mol} , indicating the energy released when burning one mole of ethylene. While this value is lower than benzene's, ethylene's practicality as a fuel source comes into play with scalability. For instance, when measuring three moles of ethylene burning, the total energy release amounts to 4233 kJ. This fact underlines that ethylene, even with a lower initial energy release per mole, can attain a higher total energy output than benzene when considered in bulk. This property positions ethylene as a favorable candidate in large-scale energy computations.