Question
Consider an example of reaction in series, benzene is chlorinated in a semi batch process where chlorine is bubbled through a well-agitated solution of benzene at 55 degrees C. Assume that chlorine is added sufficiently slowing that (i) Cl2 and HCl concentrations in the liquid phase are small (ii) all the Cl2 reacts and (iii) the liquid has a constant density. Under these reaction conditions, the significant reactions are the three substitution ones leading to mono-, di-, and tri- chlorobenzene
C6H6 + Cl2 --> C6H5Cl + HCl
C6H5Cl + Cl2 --> C6H4Cl2 + HCl
C6H4Cl2 + Cl2 --> C6H3Cl3 + HCl
The selectivity of benzene to mono-chlorobenzene is 0.25 and the conversion of benzene is 50%. If the process produces 30 moles of tri-chlorobenzene per 100 moles of benzene feed, how many moles of chlorine are required?
Explanation / Answer
Chemical reactions that take place during metamorphism produce mineral assemblages stable under the new conditions of temperature and pressure. Thus, in order to understand the mineral assemblages and what they mean in terms of the pressure and temperature of metamorphism, we must first explore the various types of metamorphic reactions. A metamorphic reaction is an expression of how the minerals got to their final state, but a reaction does not necessarily tell us the path that was actually taken to arrive at this state. Sometimes it is possible to deduce the path by means of a reaction mechanism. Thus, we will also explore reaction mechanisms. If we are considering a rock of fixed chemical composition, then a metamorphic reaction states the principles of equilibrium. In other words, if we can write a reaction expressing equilibrium between the minerals we see in the rock, we expect that the reaction must have been taking place during metamorphism. We will first look at various types of metamorphic reactions. Univariant Reactions For a given rock composition, a univariant reaction is one that plots as a line or curve on a pressure-temperature diagram. If all phases in the reaction are present in the rock, then we know that the rock must have been metamorphosed at some pressure and temperature along the reaction boundary Consider for example the simple Al2SiO5 system with excess SiO2 and H2O. In low grade metamorphic in this system, the reaction: Al2Si4O10(OH)2 Al2SiO5 + 3SiO2 + H2O Pyrophyllite Ky or Andal Qtz fluid defines a reaction boundary on a P-T diagram. This boundary can be determined experimentally or can be calculated using thermodynamic properties of the phases involved. If we find a rock that contains pyrophyllite, quartz, and an Al2SiO5 mineral, then we know that metamorphism took place somewhere along the trajectory of the reaction boundary. Furthermore, combining this with the knowledge of the stability fields of the Al2SiO5 minerals, we could place boundaries on the conditions of metamorphism. For example, if the mineral is andalusite, then we know the rock was metamorphosed at a pressure less than about 2.5 kilobars. If the mineral is kyanite, then we know that the pressure was greater than about 2.5 kilobars. Combinations of other such reactions could further constrain the pressure and temperature conditions of metamorphism. The example above, however, is probably too simple for a real rock. Although simple, we can use the diagram to illustrate another point. Imagine that a group of rocks are buried along the geothermal gradient shown in the diagram to the right. Rocks buried to a pressure less than about 4 kb and a temperature less than about 420 oC should have pyrophyllite so long as they have the right composition. Rocks buried to pressures between about 4 and 5 kb and temperatures between 420 and about 600 oC should have kyanite + quartz, and rocks buried to pressures along the geothermal gradient greater than about 5 kb and temperatures greater than about 600 oC should have Sillimanite + Quartz.