Stoichiometry w/Gases

1. Stoichiometry w/Gases Many chemical reactions involve gases. Assuming the gases are ideal, then we can convert quantities to moles using the ideal gas equation and work the problems as stoichiometry problems.

2. Steps for Stoichiometry • Write and Balance the equation; • Change given quantities to moles; • Use mole ratio to convert to moles of sought for; • Change to unit required;

3. Example • Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume of CO2. Calculate the volume of CO2 at STP produced from the decomposition of the CaCO3.

4. Volume–volume Stoich • Some stoichiometry problems are ridiculously simple. • Avogadro’s hypothesis tell us that equal volumes of ideal gases contain equal number of molecules (another way of saying the moles are equal). • This should make sense – one mole of an ideal gas occupies 22.4 L; so the same volume should have the same number of moles.

5. Volume–Volume Stoich • So, we can simply use the mole ratio as our volume ratio. • This only works is the conditions of both of the gases are the same. Otherwise, you must use the ideal gas equation and change things to moles.

6. Example • Water is produced by the reaction of hydogen and oxygen. If 10 L of hydrogen reacts with a sufficient quantity of oxygen, how much oxygen is required?

7. Kinetic Theory of Matter • So for we’ve only looked at the behavior of gases from an experimental point of view. In other words, we’ve discussed the gas Laws. • But we would really like to know Why the gases behave as they do. • For this we need to develop a model of the physical world.

8. Models • Models are speculations about what is actually happening at a level beyond what we can actually observe. • In this case we’re going to talk about what the molecules (or atoms) are doing.

9. Models • A model is considered successful (not correct) if it can explain a variety of past experiments and predict the results of future ones. • Models are always approximations and will fail at some point.

10. Kinetic Molecular Theory (KMT) • The KMT makes several assumptions that are only true for ideal gases. • These assumptions are reasonably good for real gases, but they will fail at some point.

11. KMT Assumptions • The particles are infinitely small. • Obviously, this is only strickly true for ideal gases. But real gases are so spread out that at low pressures this assumption is very nearly true.

12. Gas molecules are spread very far apart.

13. KMT Assumptions • The particles are in constant motion. The collisions of the particles with the sides of the container are the cause of gas pressure.

14. Why Boyle’s Law works • The effect of making the volume smaller means more collisions with the walls of the container.

15. KMT Assumptions • Particles are assumed to exert no forces on each other. • This is only true for ideal gases, but is close enough when temperature is high • because…

16. KMT Assumptions • The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the absolute temperature of the gas.

17. The meaning of Temperature • Temperature, then, is a measure of the speed of the molecules of a gas. • Turns out it is also true for solids and liquids.

18. The meaning of Temperature • But, all the molecules can’t be moving at the same speed. • If they were, there would be no meaning to vapor pressure of a liquid. Either the liquid would evaporate instantly or not at all.

19. The Meaning of Temperature • The distribution of the speeds of the molecules at a given temperature.

20. The Meaning of Temperature • Applying a little physics, we can show that PV/n = RT = 2/3(KE)average • So, (KE)average = 3/2RT

21. The Meaning of Temperature • What happens to the distribution of the velocities as the temperature increases? • According to the plot at right, the distribution spreads out as temperature increases.

22. Effusion and Diffusion • Diffusion is a term used to describe the mixing of gases. • Effusion is the term used to describe the passage of a gas through a tiny opening.