Ch 5 Gases Lecture Notes

Gases

Definition of Pressure:
- Pressure is defined as the force exerted per unit of surface area. The formula is given by:
- \text{Pressure (P)} = \frac{\text{Force (F)}}{\text{Area (A)}}
Units of Measurement:
- The unit of force is Newtons (N).
- The unit of area is square meters (m²).
- Hence, the unit for pressure becomes N/m² or equivalently, kg·m/s².
- 1 Pascal (Pa) is defined as 1 N/m².
- 1 kilopascal (kPa) = 1000 Pa.
- Pascal honors Blaise Pascal (1623 – 1662), who studied pressure and its transmission through fluids.
Characteristics of Gas Pressure:
- Gas pressure is exerted in all directions.
Reading Material:
- Review Section 5-2, pages 150 – 153.

Dependence on Height and Density:
- The pressure of a liquid depends on the height of the liquid column and the density of the liquid. The pressure can be expressed through the formula:
- P_{liquid} = \frac{F}{A} = \frac{weight}{Area} = \frac{gravity \times mass}{Area}
- Can also be expressed as:
  - P = g \cdot h \cdot \rho, where
  - g = gravitational acceleration,
  - h = height of the liquid,
  - ρ = density of the liquid.

Definition and Functionality:
- Evangelista Torricelli developed the barometer to measure atmospheric pressure.
- Barometers use liquid mercury, which has a density approximately 13.6 times that of water.
Importance of Barometer:
- The barometer measures the pressure exerted by the atmosphere.

Standard Atmosphere (atm):
- 1 atm is defined as the pressure exerted by a mercury column of exactly 760 mm in height when the density of mercury equals 13.5951 g/cm³ at 0°C with g = 9.80665 m/s².
Equivalency of Units:
- 1 atm = 760 mm Hg = 101.325 kPa = 1.01325 × 10⁵ Pa.
- The unit "Torr" (named after Evangelista Torricelli) is defined as 1/760 of a standard atmosphere. Thus:
- 1 atm = 760 Torr = 760 mm Hg.
Measuring Gas Pressure:
- To measure gas pressure using a barometer, it needs to be placed in a chamber filled with gas. This can be technically challenging.

Barometer Calculation with Diethylene Glycol:
- Given: density of diethylene glycol (d = 1.118 g/cm³) and height (9.25 m).
- Calculate atmospheric pressure in mm Hg.
- P{atm} = \frac{g \cdot h{diethylene} \cdot d{diethylene}}{g \cdot h{mercury} \cdot d_{mercury}}
- The answer is calculated as: \frac{1.118 \cdot 9.25 \cdot 1000}{13.6} = 760 mm Hg
Example with Triethylene Glycol:
- When a barometer is filled with triethylene glycol (density unspecified in general), it measures a height of 9.14 m. Calculating the density requires knowledge of the pressure exerted by this gas (757 mm Hg).
- Using similar relationships, find density:
- Set up the pressure equations similar to the previous example.

Definition of Manometer:
- Manometers are devices used to measure gas pressure in experiments. They compare gas pressure against atmospheric (barometric) pressure.
Types of Manometers:
- Closed-end and open-end types are prevalent.
- Closed-end Manometer: Measures pressure in a basic chamber.
- Open-end Manometer: Measures pressure relative to atmospheric pressure, taking into account the height difference in liquid columns.

Various Units of Measurement:
- Pascal (Pa): SI unit; physics, chemistry
- Kilopascal (kPa): 1 kPa = 1.01325 × 10⁵ Pa
- Atmosphere (atm): 1 atm = 760 mm Hg
- Millimeters of Mercury (mm Hg): 760 mm Hg
- Torr: 760 Torr
- Pounds per square inch (psi): 14.69 lb/in², engineering
- Bar and Millibar (mb): Common in meteorology, chemistry; 1 bar = 1.01325 atm, 1013.25 mb = 1 atm.

Example 1: Open-end manometer with mercury level difference of 7.8 mm and barometric pressure of 748.2 mmHg.
- P{gas} = P{barometric} + \Delta P = 748.2 + 7.8 = 756.0 mm Hg
Example 2: Gas pressure is given as 739.6 mm Hg. What is the height difference in a manometer filled with glycerol (density = 1.26 g/cm³)?
- ΔP = P{barometric} - P{gas} = 748.2 - 739.6 = 8.6 mm Hg
- Convert units via comparison of densities.

Boyle's Law:
- States that for a fixed amount of gas at constant temperature, the volume is inversely proportional to the pressure.
- Mathematically given by:
- P{1}V{1} = P{2}V{2}
- At constant temperature refers to an isothermal process.
- Represents a straight line on a graph of V against 1/P.

Definition:
- Relationship between the volume and temperature; when pressure is constant, the volume of a fixed amount of gas is directly proportional to its absolute temperature (in Kelvin).
- V\propto T
- Formulated as:
- \frac{V{1}}{T{1}} = \frac{V{2}}{T{2}}

Definition:
- At constant temperature and pressure, the volume is directly proportional to the number of moles of gas present.
- Mathematically summarized as:
- V\propto n

Definition and Relationship:
- The combination of the various gas laws presented leads to the ideal gas law:
- PV = nRT

Standard Conditions:
- Standard Temperature and Pressure (STP) is 0°C or 273.15 K and 1 atm (101.325 kPa).
- Under STP, one mole of an ideal gas occupies 22.7 L.

Density of Gas:
- Density (d) of a gas can be derived from the ideal gas equation:
- d = \frac{PM}{RT}
- Where M is molar mass.

Mole Fraction (χ):
- Defines the fraction of all molecules contributed by a particular gas in a mixture.
- \chi{A} = \frac{n{A}}{n_{total}}
Dalton's Law of Partial Pressure:
- Total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases:
- PT = P{1} + P_{2} + \ldots

Assumptions of KMT:
1. Gas particles have negligible volume compared to the container volume.
2. Gas particles are in constant, random motion, colliding elastically with container walls.
3. Collisions do not cause a loss of energy, and the average kinetic energy depends on the absolute temperature.
Mean Free Path:
- The mean free path refers to the average distance a molecule travels between collisions with other molecules.

Definition:
- The rate of effusion is inversely proportional to the square root of the molar mass of the gas, given by:
- \frac{rate{A}}{rate{B}} = \sqrt{\frac{M{B}}{M{A}}}

Differences from Ideal Behavior:
- Real gases exhibit ideal behavior at high temperatures and low pressures but deviates significantly at low temperatures and high pressures due to molecular volume and intermolecular forces.
Van der Waals Equation:
- Corrects the ideal gas law:
- \left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT
- Where a and b are constants associated with attraction and molecular volume.

Understand key definitions and measurements for pressure, gas laws, ideal gas law applications, and real gas behaviors.
Solve various types of gas law problems and understand the implications of kinetic molecular theory on gas behavior and characteristics.