Chemistry Notes: Chapter 8 - Gases and Properties of Gases

Introduction to Respiratory Therapy and Gas Properties

• Role of Respiratory Therapists: These professionals assess and treat a variety of patients and perform diagnostic tests. Key measurements include:     * Breathing capacity.     * Concentrations of oxygen ($O_2$) and carbon dioxide ($CO_2$) in the patient's blood.     * Blood pH levels.

• General Properties of Gases:     * Molecules with fewer than five atoms from the first two periods of the periodic table are typically gases at room temperature.     * Specific Elemental Gases: Hydrogen ($H_2$), Nitrogen ($N_2$), Oxygen ($O_2$), Fluorine ($F_2$), and Chlorine ($Cl_2$).     * Nonmetal Oxides: Found in the upper right corner of the periodic table, including Carbon Monoxide ($CO$), Carbon Dioxide ($CO_2$), Nitrogen Monoxide ($NO$), Nitrogen Dioxide ($NO_2$), Sulfur Dioxide ($SO_2$), and Sulfur Trioxide ($SO_3$).     * Noble Gases: All elements in Group 18 of the periodic table.

Kinetic Molecular Theory (KMT)

• Assumptions of KMT: A gas consists of small particles that:     * Move rapidly in straight lines.     * Have essentially no attractive or repulsive forces between particles.     * Are situated very far apart from one another.     * Occupying very small volumes compared to the total volume of the container.     * Possess kinetic energies that increase proportionally with an increase in temperature.

Fundamental Properties Describing a Gas

• Gases are characterized by four physical properties:     * Pressure ($P$): A measurement of gas particle collisions with the sides of a container.     * Volume ($V$): The space occupied by the gas, equivalent to the container's volume. It is usually measured in liters ($L$) or milliliters ($mL$). Volume increases with temperature if pressure remains constant.     * Temperature ($T$): Relates to the average kinetic energy of the molecules. It must be measured in the Kelvin ($K$) scale for all gas law calculations. Lowering temperature leads to fewer collisions; raising temperature leads to more collisions.     * Amount ($n$): Usually measured in moles.

Pressure and Its Measurement

• Units of Pressure:     * Millimeters of mercury ($mmHg$) or torr.     * Atmospheres ($atm$).     * Pascals ($Pa$) or kilopascals ($kPa$).     * Pounds per square inch ($psi$).

• Atmospheric Pressure: The pressure exerted on us by gas particles in the air. It is the pressure exerted by a column of air stretching from the top of the atmosphere to the Earth's surface.     * Altitude Correlation: Atmospheric pressure decreases as altitude increases.     * Sea Level Standard: Atmospheric pressure is exactly $1.00000000…\,atm$ at sea level.

• Barometers: Instruments used to measure the pressure exerted by gases in the atmosphere.     * Invented by Evangelista Torricelli.     * The height of the mercury column indicates pressure. At exactly $1\,atm$, the column is exactly $760\,mm$ high.     * Standard Conversions: $760\,mmHg = 1\,atm = 760\,torr$.

• Weather and Altitude Effects:     * On hot, sunny days, the mercury column rises, indicating higher atmospheric pressure.     * On rainy days, the atmosphere exerts less pressure, causing the mercury column to fall.     * In the mountains, atmospheric pressure is lower than at sea level. This causes water to boil at a lower temperature because the vapor pressure reaches atmospheric pressure more easily.

Boyle’s Law: Pressure and Volume

• Definition: There is an inverse relationship between the pressure and volume of a gas when temperature ($T$) and amount ($n$) are held constant.

• Mathematical Expression:     * $P imes V = ext{constant}$     * $P_1V_1 = P_2V_2$

• Relationship: If volume increases, pressure decreases. If volume decreases, pressure increases.

• Chemistry Link to Health: Breathing:     * Inhalation: The lungs expand ($V$ increases), causing pressure in the lungs to decrease ($P$ decreases). Air flows from the higher outside pressure into the lower pressure of the lungs.     * Exhalation: Lung volume decreases ($V$ decreases), causing pressure within the lungs to increase ($P$ increases). Air flows from the higher pressure in the lungs to the outside.

Charles’s Law: Volume and Temperature

• Definition: The Kelvin temperature of a gas is directly related to its volume, provided pressure ($P$) and amount ($n$) are constant.

• Mathematical Expression:     * $\frac{V_1}{T_1} = \frac{V_2}{T_2}$     * To solve for $T_2$: $T_2 = \frac{V_2 \times T_1}{V_1}$.

• Key Requirement: Temperature must always be converted to Kelvin: $T_K = T_{^{\circ}C} + 273$.

• Behavior: When temperature increases, the kinetic energy of particles increases, causing the volume of the container to increase to maintain constant pressure.

Gay-Lussac’s Law: Temperature and Pressure

• Definition: The pressure exerted by a gas is directly related to its Kelvin temperature when volume ($V$) and amount ($n$) are held constant.

• Mathematical Expression:     * $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• Concept: If the Kelvin temperature doubles, the pressure also doubles.

The Combined Gas Law

• Definition: This law merges the relationships of Boyle’s, Charles’s, and Gay-Lussac’s laws into one equation where the amount of gas ($n$) is the only constant.

• Mathematical Expression:     * $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Application: Useful for calculating changes when pressure, volume, and temperature vary simultaneously.

Avogadro’s Law and Molar Volume

• Avogadro’s Law: The volume of a gas is directly related to the number of moles ($n$) of gas when temperature ($T$) and pressure ($P$) are constant.     * $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Standard Temperature and Pressure (STP):     * Standard Temperature: $0\,^{\circ}C$ ($273\,K$).     * Standard Pressure: $1\,atm$ ($760\,mmHg$).

• Molar Volume: At STP, $1\,mole$ of any gas occupies a volume of $22.4\,L$.     * Analogy: The molar volume at STP ($22.4\,L$) is approximately the same as the volume of three basketballs.     * Conversion Factor: $\frac{22.4\,L}{1\,mole}$.

Dalton’s Law of Partial Pressures

• Partial Pressure: The pressure that each individual gas in a mixture would exert if it were alone in the container.

• Dalton’s Law Statement: Pressure depends on the total number of gas particles, not the specific types. The total pressure ($P_T$) is the sum of the partial pressures of all gases in the mixture.     * $P_T = P_1 + P_2 + P_3 + …$

• Atmospheric Air: Air is a mixture, primarily Nitrogen ($N_2$) and Oxygen ($O_2$). Atmospheric pressure is the sum of these partial pressures.

• Total Pressure at STP: $1.0\,mole$ of a gas mixture in $22.4\,L$ at STP will exert $1.0\,atm$ of pressure regardless of the mixture's composition (e.g., $0.4\,mol\,O_2 + 0.6\,mol\,He$ exerts same total pressure as $0.5\,mol\,O_2 + 0.3\,mol\,He + 0.2\,mol\,Ar$).

Blood Gases and Respiration

• Gas exchange in the body:     * In the Lungs: $O_2$ enters the blood and $CO_2$ is released from the blood through the membranes of the alveoli (tiny air sacs at the ends of airways).     * In the Tissues: $O_2$ enters the cells and $CO_2$ is released into the blood.

• Partial Pressure Gradients:     * $O_2$ flows into tissues because partial pressure is higher in the blood and lower in the tissues.     * $CO_2$ flows out of tissues because partial pressure is higher in the tissues and lower in the blood.

• Typical Partial Pressures ($mmHg$):     * Alveolar Air: $P_{O_2} = 100$, $P_{CO_2} = 40$.     * Oxygenated Blood: $P_{O_2} = 100$, $P_{CO_2} = 40$.     * Deoxygenated Blood: $P_{O_2} = 40$, $P_{CO_2} = 46$.     * Tissues: $P_{O_2} = 40$ or less, $P_{CO_2} = 46$ or greater.

Questions & Discussion

• Q1: What is 475 mmHg expressed in atmospheres?     * Calculation: $475\,mmHg \times \frac{1\,atm}{760\,mmHg} = 0.625\,atm$.     * Answer: B, 0.625 atm.

• Q2: The pressure in a tire is 2.00 atm. What is this pressure in millimeters of mercury?     * Calculation: $2.00\,atm \times 760\,mmHg/atm = 1520\,mmHg$.     * Answer: B, 1520 mmHg.

• Q3: The downward pressure on the Hg in a barometer is _____ the pressure of the atmosphere.     * Answer: C, the same as.

• Q4: A water barometer is 13.6 times taller than a Hg barometer ($d_{Hg} = 13.6\,g/mL$) because…     * Answer: A, $H_2O$ is less dense than mercury.

• Q5: Solve for the new volume of an 8.0-L sample of Freon gas initially at 550 mmHg after pressure changes to 2200 mmHg (constant T and n).     * Data: $P_1 = 550\,mmHg$, $V_1 = 8.0\,L$, $P_2 = 2200\,mmHg$.     * Calculation: $V_2 = V_1 \times \frac{P_1}{P_2} = 8.0\,L \times \frac{550\,mmHg}{2200\,mmHg} = 2.0\,L$.

• Q6: A sample of oxygen gas has a volume of 420 mL at 18 °C. At what temperature (in °C) will the volume be 640 mL?     * Data: $V_1 = 420\,mL$, $T_1 = 18\,^{\circ}C = 291\,K$, $V_2 = 640\,mL$.     * Calculation: $T_2 = T_1 \times \frac{V_2}{V_1} = 291\,K \times \frac{640\,mL}{420\,mL} = 443\,K$.     * Convert to Celsius: $443 - 273 = 170\,^{\circ}C$.     * Answer: B, 170 °C.

• Q7: A scuba tank contains $O_2$ at 0.450 atm and He at 855 mmHg. What is total pressure in mmHg?     * Convert $P_{O_2}$: $0.450\,atm \times 760\,mmHg/atm = 342\,mmHg$.     * Sum: $P_T = 342\,mmHg + 855\,mmHg = 1197\,mmHg$ (expressed as $1.20 \times 10^3\,mmHg$).