Chapter 6: Gases – General Chemistry Study Notes

Chapter 6: Gases

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Unlike solids and liquids, gases have neither fixed shape nor fixed volume, and their particles are in constant, rapid motion. Understanding the properties and behavior of gases is essential in general chemistry, as it underpins many physical and chemical processes.

Pressure and Its Units

Definition of Pressure

Pressure is defined as the force exerted per unit area by gas particles as they collide with the walls of their container. It is a key measurable property of gases.

• Formula: $P = \frac{F}{A}$, where P is pressure, F is force, and A is area.

• Common Units: Atmospheres (atm), Pascals (Pa), millimeters of mercury (mmHg), torr, pounds per square inch (psi).

Table: Common Units of Pressure

Unit	Abbreviation	Average Air Pressure at Sea Level
Pascals	Pa	101,325 Pa
Pounds per square inch	psi	14.7 psi
Torr (mmHg)	torr	760 torr (exact)
Inches of mercury	in Hg	29.92 in Hg
Atmosphere	atm	1 atm

Converting Between Pressure Units

Pressure can be expressed in various units, and conversion between these units is often necessary in chemical calculations.

• Key Conversion Factors:

  • 1 atm = 760 mmHg = 14.7 psi = 101,325 Pa

• Example: To convert 132 psi to mmHg:

  • First, convert psi to atm: $132~\text{psi} \times \frac{1~\text{atm}}{14.7~\text{psi}}$

  • Then, convert atm to mmHg: $\text{result} \times \frac{760~\text{mmHg}}{1~\text{atm}}$

  • Final answer: $132~\text{psi} \times \frac{1~\text{atm}}{14.7~\text{psi}} \times \frac{760~\text{mmHg}}{1~\text{atm}} = 6.82 \times 10^3~\text{mmHg}$

Gas Laws

Boyle's Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas at constant temperature and amount.

• Formula: $P_1V_1 = P_2V_2$

• Application: If the volume of a gas increases, its pressure decreases, provided temperature and amount of gas remain constant.

• Example: A woman has an initial lung volume of 2.75 L at 1.02 atm. If her lung volume increases to 3.25 L, the new pressure is:

  • $P_2 = \frac{V_1}{V_2} P_1 = \frac{2.75~\text{L}}{3.25~\text{L}} \times 1.02~\text{atm} = 0.863~\text{atm}$

Additional info:

• Other gas laws (Charles's Law, Avogadro's Law, Ideal Gas Law, etc.) are typically covered in this chapter and relate volume, temperature, pressure, and amount of gas.

Summary Table: Key Gas Laws

Law	Relationship	Equation
Boyle's Law	$P \propto \frac{1}{V}$ (at constant T, n)	$P_1V_1 = P_2V_2$
Charles's Law	$V \propto T$ (at constant P, n)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Avogadro's Law	$V \propto n$ (at constant P, T)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$
Ideal Gas Law	Relates P, V, n, T	$PV = nRT$

Practice Problems

• Convert a barometric pressure of 30.44 in Hg to psi.

• Given a pressure of 23.8 in Hg, convert to mmHg or atm.

• Apply Boyle's Law to determine the pressure at a new volume.

Conclusion

Understanding the properties of gases and the relationships between pressure, volume, temperature, and amount is essential for solving problems in general chemistry. Mastery of unit conversions and gas laws enables students to analyze real-world scenarios involving gases, from laboratory experiments to atmospheric phenomena.