SL S1.5 Ideal Gas PDF

SL S1.5 Ideal gas Xuesi Liu Learning outcomes  Structure 1.5.1—An ideal gas consists of moving particles with negligible volume and no intermolecular forces. All collisions between particles are considered elastic.  Recognize the key assumptions in the ideal gas mod...

SL S1.5 Ideal gas Xuesi Liu Learning outcomes  Structure 1.5.1—An ideal gas consists of moving particles with negligible volume and no intermolecular forces. All collisions between particles are considered elastic.  Recognize the key assumptions in the ideal gas model.  Structure 1.5.2—Real gases deviate from the ideal gas model, particularly at low temperature and high pressure.  Explain the limitations of the ideal gas model.  Structure 1.5.3—The molar volume of an ideal gas is a constant at a specific temperature and pressure.  Investigate the relationship between temperature, pressure and volume for a fixed mass of an ideal gas and analyse graphs relating these variables.  Structure 1.5.4—The relationship between the pressure, volume, temperature and amount of an ideal gas is shown in the ideal gas equation PV = nRT and the combined gas law  Solve problems relating to the ideal gas equation. Overview  Assumptions of the idea gas model  Real gases vs ideal gases  The molar volume of an ideal gas  Pressure, volume temperature and amount of an ideal gas Assumptions of the ideal gas model  1. Molecules of a gas are in constant random motion  Gas molecules are not stationary. They move in straight lines until they collide with another molecule or the side of a container.  2. Collisions between molecules are perfectly elastic  In inelastic collisions of larger objects, energy can be transferred as heat or sound. However, the collisions between molecules in an ideal gas are perfectly elastic and no energy is lost from the system.  3. There are no intermolecular forces between gas particles  For an ideal gas, the intermolecular forces are negligible compared to the kinetic energy of the molecules. As such, an ideal gas will not condense into a liquid. Assumptions of the ideal gas model  4. The kinetic energy of the molecules is directly proportional to Kelvin temperature.  5. The volume occupied by gas molecules is negligible compared to the volume of the container they occupy.  Vaporized water occupies 1600 times the volume of liquid water at 273.15 K and 100 kPa pressure (standard temperature and pressure, STP). So the volume of the gas is >99.9% empty space. This is the space in which the gas molecules are free to move. Pressure-volume relationships  Boyle’s law—at constant temperature, the pressure of a given amount of gas is inversely proportional to its volume  In a container, gas molecules are constantly striking and bouncing off the walls of the container, creating a measurable pressure  What happens if the volume is halved? Pressure-volume relationships Pressure-volume relationships  The SI unit of pressure is Pascal (Pa), where 1 Pa = 1 N m-2 = 1 J m-3  Other commonly used units of pressure—atmosphere (atm), millimeters of mercury (mm Hg), bar, and pounds per square inch (psi)  Standard temperature and pressure (STP) for gases is 273.15 K and 100 kPa Real gases vs ideal gases  When the volume of a real gas decreases significantly, the molecules begin to occupy a large proportion of the container  With so little space to move, intermolecular forces become significant  This decreases the number of collisions, reducing the pressure  So the inverse relationship between pressure and volume no longer applies  For the real gas, doubling the pressure no longer halves the volume Real gases vs ideal gases  For a gas to deviate from ideal gas behaviour, there must be detectable intermolecular forces and/or a significant volume of the gas must be occupied by the molecules themselves  This commonly occurs at a low temperature and high pressure  Low temperature: the kinetic energy of the gas molecules is reduced. As they collide with one another, intermolecular forces of attraction form and molecules may not necessarily rebound elastically  High pressure: the volume of the molecules becomes a significant part of the volume of the gas. As molecules themselves cannot be compressed, only the space between them, the relationship between pressure and volume is no longer inverse, so the gas is not considered to be an ideal gas Real gases vs ideal gases  Ideal gas conditions: low pressure and high temperature  At low pressure, there are very few molecules per unit of volume in the container, so the space occupied by molecules themselves is negligible  At high temperature, the molecules are moving too fast to allow for intermolecular forces of attraction to form The molar volume of an ideal gas  Equal volumes of any two gases at the same temperature and pressure contain equal number of particles  The molar volume of an ideal gas, Vm, at STP, is equal to 22.7 dm3 mol-1 Combined gas law Ideal gas equation  pV = nRT  R is the universal gas constant, which equals 8.31 J K-1 mol-1  p in Pa, V in m3, T in K and n in mol