Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![### Thermochemistry and Spontaneity of Reactions
Consider the following chemical reaction:
\[ 2 \text{C}_5\text{H}_{10} (\text{l}) + 15 \text{O}_2 (\text{g}) \rightarrow 10 \text{CO}_2 (\text{g}) + 10 \text{H}_2\text{O} (\text{l}) \]
**a. Calculate \( \Delta H^\circ \) of the reaction.**
**b. Calculate \( \Delta S^\circ \) of the reaction.**
**c. Show by calculation whether or not the reaction is spontaneous at 298.15 K.**
**d. At what temperature is this reaction in equilibrium? In one brief sentence, explain the temperature dependence of the spontaneity of this reaction.**
### Explanation of Components:
1. **Enthalpy Change (\( \Delta H^\circ \)) Calculation**:
- To find \( \Delta H^\circ \), use standard enthalpies of formation (\( \Delta H_f^\circ \)) for each compound involved.
- The equation is:
\[
\Delta H^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})
\]
2. **Entropy Change (\( \Delta S^\circ \)) Calculation**:
- Similar to enthalpy, calculate \( \Delta S^\circ \) using standard entropy values (\( S^\circ \)).
- The equation is:
\[
\Delta S^\circ = \sum S^\circ (\text{products}) - \sum S^\circ (\text{reactants})
\]
3. **Spontaneity at a Given Temperature**:
- Determine spontaneity using Gibbs free energy change (\( \Delta G^\circ \)).
- The equation is:
\[
\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ
\]
- If \( \Delta G^\circ < 0 \), the reaction is spontaneous.
4. **Equilibrium Temperature**:
- At equilibrium, \( \Delta G^\circ = 0 \).
- The rearranged equation is:
\[
T = \frac{\Delta H^\circ}{\Delta S^\circ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbca33481-84f0-4d0e-9458-2fdcb949c0ec%2Fa5a92b60-4587-4bda-8205-57edcac622de%2F0v980e_processed.jpeg&w=3840&q=75)
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