Question

The heat of combustion of 1 mole of liquid decane to give carbon dioxide and liquid water is \(1620.1\) kcal The heat of vaporization of decane at \(25^{\circ}\) is \(11.7\) kcal \(\mathrm{mol}^{-1}\). Calculate the heat of combustion that would be observed for all the participants in the vapor phase.

Short answer

The heat of combustion for gaseous decane is 1631.8 kcal.

Step-by-step solution

Understand the Problem

We need to find the heat of combustion for decane when all participants are in the vapor phase. We know the combustion reaction for liquid decane and the heat of vaporization. Our job is to adjust the heat of combustion to account for the phase change from liquid to vapor.

Define Given Data

The heat of combustion for 1 mole of liquid decane is given as \(1620.1\) kcal. The heat of vaporization for decane at \(25^{\circ}\) C is \(11.7\) kcal/mol. These values will be used to calculate the combustion heat for gaseous decane.

Calculate Heat for Phase Change

Since we need to convert liquid decane to gaseous decane, add the heat of vaporization to the heat of combustion. This is because extra energy is required to convert the liquid decane to vapor before combustion takes place.

Adjust Heat of Combustion

Add the heat of vaporization to the given heat of combustion: \(1620.1\) kcal + \(11.7\) kcal = \(1631.8\) kcal. This is the heat of combustion for gaseous decane where all participants are vapor.

Conclusion

The calculated heat of combustion considers the phase transition from liquid to gas for decane before undergoing combustion. This adjusted value represents the energy released when decane is in vapor form during combustion.

Key concepts

Heat of combustion

In thermochemistry, the heat of combustion refers to the energy released as heat when a substance undergoes complete combustion with oxygen. It is usually measured in units of kilocalories (kcal) or kilojoules (kJ) per mole of substance. When combusting decane, a hydrocarbon, the process involves breaking multiple carbon-hydrogen bonds to form carbon dioxide and water. This process releases a significant amount of energy.
One key point here is that the heat of combustion is typically calculated under standard conditions, which assume the products like carbon dioxide and water are in specified states – usually gaseous at certain temperatures. The given example talks about the combustion of liquid decane resulting in liquid water and gaseous carbon dioxide.
This process releases a lot of energy, and for liquid decane, it was specifically measured as 1620.1 kcal per mole. This indicates the energy obtained when decane burns fully, but it doesn't consider if decane were initially in the vapor phase, which requires additional energy adjustments.

Heat of vaporization

The heat of vaporization is the amount of energy required to transform a substance from a liquid into a gas or vapor. This transformation is a type of phase change, which is crucial in thermochemistry when considering energy calculations for reactions involving phase changes.

• For decane, the provided heat of vaporization is 11.7 kcal per mole.
• This means that it takes an additional 11.7 kcal for each mole of decane to transition from liquid to vapor before participating in a chemical reaction such as combustion.

Understanding this concept is essential because when substances like decane need to undergo a phase change before engaging in a reaction, this extra energy requirement must be added to the overall energy calculations. Hence, in exercises like our current example, heat of vaporization becomes a critical component in determining the complete energetic profile of the combustion process.

Phase change

A phase change refers to the transition of a substance from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. In thermochemistry, phase changes are significant because they involve energy absorption or release without changing the chemical identity of a substance.
In the example with decane, the phase change involves its transition from liquid to vapor prior to combustion. This transition requires energy, termed the heat of vaporization, as discussed earlier. When calculating energies in thermochemical reactions, accounting for phase changes is necessary to accurately reflect the conditions under which a reaction takes place.

• Phase changes can either absorb energy (endothermic) or release energy (exothermic).
• In the case of decane, moving from liquid to vapor requires an endothermic input of energy.

Thus, when considering the energy changes in a complete thermochemical process, including phase changes, ensures more accurate and realistic results, providing a better understanding of the nature and extent of the reactions involved.