Gases

Gases

• Gases do not have a definite volume or shape.
• The attractive forces between gas particles are insignificant.
• Gases have low density.
• Gases can be compressed.
• Gases form homogeneous mixtures.
• Gases can diffuse and effuse.
• Gases exert pressure.

Elements Existing as Gases at 25°C and 1 Atmosphere

• Lists elements that exist as gases under standard conditions (25°C and 1 atm).
• Includes elements like Hydrogen (H), Helium (He), Nitrogen (N), Oxygen (O), Fluorine (F), Chlorine (Cl), and noble gases.

Substances Found as Gases at 1 atm and 25°C

• Elements:
  • Molecular hydrogen ($H_2$).
  • Molecular nitrogen ($N_2$).
  • Molecular oxygen ($O_2$).
  • Ozone ($O_3$).
  • Molecular fluorine ($F_2$).
  • Molecular chlorine ($Cl_2$).
  • Helium (He).
  • Neon (Ne).
  • Argon (Ar).
  • Krypton (Kr).
  • Xenon (Xe).
  • Radon (Rn).
• Compounds:
  • Hydrogen fluoride (HF).
  • Hydrogen chloride (HCl).
  • Hydrogen bromide (HBr).
  • Hydrogen iodide (HI).
  • Carbon monoxide (CO).
  • Carbon dioxide ($CO_2$).
  • Ammonia ($NH_3$).
  • Nitric oxide (NO).
  • Nitrogen dioxide ($NO_2$).
  • Nitrous oxide ($N_2O$).
  • Sulfur dioxide ($SO_2$).
  • Hydrogen sulfide ($H_2S$).
  • Hydrogen cyanide (HCN) - boiling point is close to qualify as a gas at ordinary atmospheric conditions.

Air Pressure

• Air pressure decreases with altitude.
• Examples of air pressure at different altitudes:
  • Sea level: 1 atm
  • 6 km: 0.5 atm
  • 16 km: 0.2 atm

Definition of Pressure

• Pressure is defined as force per unit area: $Pressure = \frac{Force}{Area}$.
• Units of pressure:
  • 1 pascal (Pa) = 1 N/$m^2$
  • 1 atm = 760 mm Hg = 760 torr = 101,325 Pa = 14.7 psi = 29.92 in. Hg

Pressure Units

• Gas pressure can be measured in:
  • Torr
  • mmHg
  • Pascal (Pa)
  • Kilopascal (kPa)
  • Atmosphere (atm)
  • Bar
  • Pounds per square inch (PSI)

Temperature

• Always use absolute temperature (Kelvin) when working with gases.
• $K = °C + 273$

Standard Temperature and Pressure (STP)

• STP is a standard condition for comparing amounts of gases.
• STP conditions:
  • Temperature: 273 K (0°C)
  • Pressure: 1 atm or 101.325 kPa or 760 mm Hg

Kinetic Molecular Theory

• Gas particles do not attract or repel each other.
• Gas particles are much smaller than the space between them; most of the volume of a gas is empty space.
• Gas particles are in constant, random motion.
• No kinetic energy is lost when gas particles collide (elastic collisions).
• All gases have the same average kinetic energy at a given temperature.

Assumptions in the Kinetic Theory of Gases

• The gas is ideal (molecules do not interact with each other).
• Collisions of molecules with the walls of the vessel are elastic (no energy is lost).
• Gas molecules move constantly in random directions with a distribution of speeds, having an average velocity.
• The average kinetic energy of gas particles is proportional to temperature.

Scientists and Gas Laws

• Evangelista Torricelli (1608-1647):
  • Published the first scientific explanation of a vacuum.
  • Invented the mercury barometer.
• Robert Boyle (1627-1691):
  • Volume is inversely related to pressure (at constant temperature).
• Jacques Charles (1746-1823):
  • Volume is directly related to temperature (at constant pressure).
• Joseph Gay-Lussac (1778-1850):
  • Pressure is directly related to temperature (at constant volume).

Boyle’s Law

• Pressure is inversely proportional to Volume if moles and temperature are constant ($P \propto \frac{1}{V}$).
• $P<em>1V</em>1 = P<em>2V</em>2$

Charles’s Law

• Volume and Temperature are directly proportional if n and P are constant ($V \propto T$).
• $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$

Gay-Lussac’s Law

• Pressure and Temperature are directly proportional if n and V are constant ($P \propto T$).
• $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$

Combined Gas Law

• Combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation.
• $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$

Ideal Gas Law

• Ideal gases follow all assumptions of the kinetic molecular theory.
• Ideal gases conform to all gas laws.

Avogadro's Law

• Volume is proportional to the number of moles (n).
• $V \propto n$
• $V = constant \times n$
• $\frac{V<em>1}{n</em>1} = \frac{V<em>2}{n</em>2}$

Ideal Gas Equation

• Combines Charles's, Avogadro's, and Boyle's laws.
• $V \propto \frac{nT}{P}$
• $PV = nRT$ where R is the gas constant.

Ideal Gas Law Constant

• At STP (0°C and 1 atm), 1 mole of an ideal gas occupies 22.414 L.
• $R = 0.082057 \frac{L \cdot atm}{mol \cdot K}$

Ideal Gas Law Equation and Constant

• $PV = nRT$
• P = pressure (atm)
• V = volume (L)
• n = moles (mol)
• R = 0.0821 L·atm/mol·K (Ideal Gas Constant)
• T = temperature (K)

Ideal Gas Law Constant Values

• Different values of R with different units:
  • $0.0821 \frac{L \cdot atm}{mole \cdot K}$
  • $62.4 \frac{L \cdot mmHg}{mole \cdot K}$
  • $8.314 \frac{L \cdot kPa}{mole \cdot K}$

Ideal Gas Law Example 1

• Problem: At what pressure would 0.212 mol of a gas occupy 6.84 L at 89°C?
• Solution:
  • Given:
    • n = 0.212 mol
    • V = 6.84 L
    • T = 89°C = 362 K
    • R = 0.0821 L·atm/mol·K
  • Using $PV = nRT$, $P = \frac{nRT}{V} = \frac{(0.212 \, mol)(0.0821 \, L \cdot atm/mol \cdot K)(362 \, K)}{6.84 \, L} = 0.92 \, atm$

Ideal Gas Law Example 2

• Problem: At what temperature would 52.3g of methane ($CH_4$) gas occupy 65.7 L at 184 kPa?
• Solution:
  • Given:
    • P = 184 kPa = 1.82 atm
    • V = 65.7 L
    • n = 52.3 g CH4 = 3.26 mol CH4
    • R = 0.0821 L·atm/mol·K
  • Using $PV = nRT$, $T = \frac{PV}{nR} = \frac{(1.82 \, atm)(65.7 \, L)}{(3.26 \, mol)(0.0821 \, L \cdot atm/mol \cdot K)} = 447 \, K$

Molar Mass Calculation Example

• A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.00C. What is the molar mass of the gas?
• Use $PV = nRT$ to find n, then molar mass = mass/moles.

Real vs. Ideal Gases

• Ideal gases have no molecular volume and no attractive forces.
• Real gases approximate ideal gas behavior under most conditions.
• Deviations from ideal gas behavior occur under:
  1. High pressure
  2. Low Temperature
  3. High molar mass
  4. Polar molecules

Dalton's Law of Partial Pressures

• The total pressure of a mixture of gases is equal to the sum of the individual (partial) pressures.

Dalton’s Law

• $P<em>{total} = P</em>1 + P<em>2 + P</em>3 + …$
• Units of pressure must match.

Example: Dalton’s Law

• What is the total pressure for a mixture of O2 and CO2 if $P<em>{O</em>2}$= 0.719 atm and $P<em>{CO</em>2}$= 423 mmHg.
• Solution:
  • $P<em>{O</em>2} = 0.719 \, atm = 546 \, mmHg$
  • $P_{total} = 546 \, mmHg + 423 \, mmHg = 969 \, mmHg$

Dalton's Law of Partial Pressures (cont.)

• $P<em>{total} = P</em>1 + P_2$

Collecting Gas Over Water

• $2KClO<em>3(s) \rightarrow 2KCl(s) + 3O</em>2(g)$
• When collecting gas over water: $P<em>T = P</em>{O<em>2} + P</em>{H_2O}$

Pressure of Water Vapor at Various Temperatures

• Table provides the pressure of water vapor at different temperatures.

Summary of Kinetic Molecular Theory of Gases

1. Gas molecules are separated by distances far greater than their own dimensions and can be considered as points with mass but negligible volume.
2. Gas molecules are in constant motion in random directions, and collisions among molecules are perfectly elastic.
3. Gas molecules exert neither attractive nor repulsive forces on one another.
4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins, and any two gases at the same temperature will have the same average kinetic energy.