VII. Gases

Key focus of this chapter: ideal gas law

This chapter focuses on the ideal gas law and gives concise summaries of the important things about speed of gases, Dalton’s law of partial pressures, and gas stoichiometry in more detail.

A. Temperature

1. Fahrenheit and Celsius

2. Kelvin and Celsius

B. Gases theory

1. Kinetic molecular theory (ideal gases)

  • No attraction or repulsion between gas molecules
  • Random and straight movement of gas molecules
  • Gas molecules are of negligible size
  • No change of energy from collision of gas molecules (elastic collisions)
  • Average translational kinetic energy is directly proportional to absolute temperature (kelvin).

2. Real gases

  • Do not always behave as predicted by kinetic molecular theory.
  • Deviations from ideal behavior are greatest at high pressure and low temperature because intermolecular attractions and finite molecular volume become important.
  • Van der Waals equation (interaction of molecules) is a good predictor of behavior of real gases.

C. Gas Laws

1. Symbols of gas laws

     P: Pressure (Pi = initial pressure, Pf = final pressure)

     V: Volume  (Vi = initial volume, Vf = final volume)

     n: Number of moles (ni = initial mole, nf = final mole)

     R: Gas constant

     T: Temperature (Kelvin, K) (Ti = initial temp, Tf = final temp)

2. STP (Standard Temperature and Pressure for gas)

     T = 273.15 K (0°C)

     P = 1 atm (760 mmHg), the traditional STP convention used here. Modern standard pressure is 1 bar.

     R = 0.08206 L·atm/(mol·K)

3. Ideal gas laws

Boyle’s law holds at constant temperature and amount; Charles’s law at constant pressure and amount; Gay-Lussac’s law at constant volume and amount; Avogadro’s law at constant temperature and pressure. Temperature must be in kelvin. For connected flasks, apply the ideal gas law to each gas using its final total accessible volume.

Classification

Features and equations

4. Relationships described by ideal gas law

Relationships described by ideal gas law

D. Speed of gases

E. Dalton’s law of partial pressures

1. Dalton’s Law

: For a mixture of nonreacting ideal gases at the same temperature and volume, the total pressure equals the sum of the component partial pressures. Each partial pressure is the pressure that component would exert alone in the mixture volume.

Ptotal  = PA + PB

2. Partial pressure and volume

: For nonreacting ideal gases initially in separate connected flasks at the same temperature, opening the valve lets both gases fill the total volume. Each final partial pressure is P(initial) times V(initial) divided by V(total); their sum gives the final total pressure. After mixing, both gases are distributed throughout both flasks.

3. Mole fraction, X

  • Concentration of an individual gas in a mixture of gases
  • Expression of the mole of the individual gas divided by the total mole of the gas mixture

4. Partial pressure and mole

: partial pressure A in a gas mixture is expressed by mole fraction (XA) multiplied by the total pressure of the gas mixture.

F. Gas stoichiometry

: ideal gas law (PV = nRT) is applied to stoichiometry.

  • Qs/ When 5 mole of A is reacted with an excess of B, the volume of 6L of D is produced at 27 oC. Calculate the pressure of D.

     2A(g) + B(g)  →   3C(g) + 4D(g) 

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