Chapter 6 Notes

Properties of Gases: Gas Pressure

• Pressure is defined by force per unit area.
  • The unit for pressure is a Pascal, or a Newton/meter^2
  • That's very small so a kilopascal (kPa) is more common
• Pressure = F/A = W/A = gm/A = gVd/A = ghAd/A = ghd
  • Pressure is directly proportional to the liquid desnity and the height of the liquid column.
• Standard atmosphere is defined as the pressure exerted by a mercury column of exactly 760 mm in height when the density equals 13.5951 and gravity is normal. 
• 1 atm = 760mmHg
• 1 atm = 760 Torr, or a unit that means 1/760 of an atmosphere of pressure.
• The unit bar equals 100 * a kiloPascal

Simple Gas Laws

• Boyle's Law

  •  Volume is inversely proportional to pressure

  • V = bT (where b is a constant)

• Charles's Law

  • The volume of a fixed amount of gas is directly proportional to the temperature.
  • Example: If you have a balloon pumped at room temperature, and you take it outside during the winter, it would deflate.

• Avogadro's Law

  • The volume of a gas is proportional to the amount of gas.
  • At STP, 1 mol gas = 22.4 L gas
  • Example: 1 liter of gas has less gas than 2 liters of gas

Combining the Gas Laws: The Ideal Gas Equation and the General Gas Equation

• Ideal Gas Equation

  • PV = nRT
    • Volume of a gas is proportional to amount of gas, the temperature, and inversely proportional to the pressure

• General Gas Equation

  • PiVi/(niTi) = PfVf/(nfTf)
    • So, at the initial condition PiVi = niRTi, R being a constant, and all other variables being the values at their initial states.
    • At the initial and final states, they remain equal, and this is especially useful when some of the variables stay constant, so you can cross them out, and get an even simpler formula. 

Applications of the Ideal Gas Equation

• Molar Mass Determination

  • Because n, the number of moles of a gas equals the mass of the gas (m) divided by the molar mass (M), we can solve the expression n = m/M, for the molar mass, M.
  • PV = mRT/M

• Gas Densities

  • he equation of density is d = m/v, and rearranging the equation before, m = nM.
  • Now, we substitute it in: d = n/V * M
  • Another way to express density is we can replace n/V with P/RT, so d = MP/RT

Mixtures of Gases

• Dalton's Law of Partial Pressures

  • Total pressure of a mixture of gases is the sum of the partial pressures of the components of a mixtures of gases.
  • Partial pressure means the hypothetical pressure a gas would have if it alone occupied the same volume as the mixture
  • Ptot = Pa + Pb + Pc  + ...
  • Vtot = Va + Vb + Vc + ...
  • Na/Ntot = Pa/Ptot = Va/Vtot = Xa
  • The moles of a specific gas divided by the total moles (Na/Ntot) is called the mole fraction.  
  • The mole fraction of a component in a mixture is the fraction of all the molecules in the mixture contributed by that component.