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.
![**Practice Exercise 1**
Given the reaction:
\[ 2 \text{SO}_2(g) + \text{O}_2(g) \rightarrow 2 \text{SO}_3(g) \]
Which of the following equations is correct?
(a) \(\Delta H_f^\circ[\text{SO}_3] = \Delta H_{rxn}^\circ - \Delta H_f^\circ[\text{SO}_2]\)
(b) \(\Delta H_f^\circ[\text{SO}_3] = \Delta H_{rxn}^\circ + \Delta H_f^\circ[\text{SO}_2]\)
(c) \(2\Delta H_f^\circ[\text{SO}_3] = \Delta H_{rxn}^\circ + 2\Delta H_f^\circ[\text{SO}_2]\)
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This exercise involves determining the correct enthalpy relation for the formation of sulfur trioxide (\(\text{SO}_3\)) from sulfur dioxide (\(\text{SO}_2\)) and oxygen (\(\text{O}_2\)). Enthalpy changes (\(\Delta H\)) for the reaction (\(\Delta H_{rxn}^\circ\)) and the formation (\(\Delta H_f^\circ\)) are key to solving this.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b2ad7e-71be-4993-92e0-fe2030354ee3%2Fdccc6a1b-133a-4906-9165-0339086d6e78%2Fzzx2xpo_processed.png&w=3840&q=75)
![### Thermochemical Equations
The image contains two thermochemical equations related to the formation of sulfur trioxide (\(\text{SO}_3\)) and sulfur dioxide (\(\text{SO}_2\)). These equations involve enthalpy (\(\Delta H\)), a measure of heat change at constant pressure.
#### (d)
\[ 2 \Delta H_f^\circ [\text{SO}_3] = \Delta H^\circ_{\text{rxn}} - 2 \Delta H_f^\circ [\text{SO}_2] \]
- **\(2 \Delta H_f^\circ [\text{SO}_3]\)**: Represents the standard enthalpy of formation for two moles of SO\(_3\).
- **\(\Delta H^\circ_{\text{rxn}}\)**: Represents the standard enthalpy change for the reaction.
- **\(2 \Delta H_f^\circ [\text{SO}_2]\)**: Represents the standard enthalpy of formation for two moles of SO\(_2\).
#### (e)
\[ 2 \Delta H_f^\circ [\text{SO}_3] = 2 \Delta H_f^\circ [\text{SO}_2] - \Delta H^\circ_{\text{rxn}} \]
- This equation also expresses the formation enthalpy of sulfur trioxide in relation to sulfur dioxide and the reaction enthalpy, but in a different arrangement compared to equation (d).
#### Explanation
These equations are typically used in the study of chemical thermodynamics to calculate unknown enthalpy values, using known data from tables of standard enthalpies of formation and reaction. The enthalpy of formation (\( \Delta H_f^\circ \)) refers to the change in enthalpy when one mole of a compound is formed from its elements under standard conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b2ad7e-71be-4993-92e0-fe2030354ee3%2Fdccc6a1b-133a-4906-9165-0339086d6e78%2Ffmsk8ir_processed.png&w=3840&q=75)
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