Diamond and graphite are two forms of elemental carbon. Under the appropriate conditions they will be in equilibrium with each other: \(C_{\text {diamond }} \rightleftarrows C_{\text {graphite }}\) If graphite is subjected to very high pressure and temperature, it will convert into the diamond form. (a) Is the above equilibrium reaction exothermic or endothermic? Explain how you know. (b) Which form, graphite or diamond, has the higher density? (Hint: Think about what increasing the pressure of a gas does to its density. It works the same for the solid and liquid phases as well.)

To determine if the reaction is exothermic or endothermic, we need to analyze the conditions under which the phase transition occurs. The problem states that at very high pressure and temperature, graphite turns into diamond. Recall that an exothermic reaction is one where heat is released and an endothermic reaction is where heat is absorbed. According to Le Châtelier's principle, a system in equilibrium will shift in such a way as to counteract a change in conditions applied to the system. In this case, the equilibrium undergoes an increase in both pressure and temperature. If the reaction were exothermic, then increasing the temperature would shift the equilibrium towards the reactant, graphite, as the system tries to absorb the extra heat. However, we are given that graphite converts to diamond under these conditions, which implies that the reaction is endothermic. Thus, at high temperature and pressure, the equilibrium shifts towards the product, diamond, as the system absorbs the extra heat.

To determine which form of carbon has the higher density, we can use the hint provided. We are told to think about what increasing the pressure of a gas does to its density and apply the same principle to solid and liquid phases. Recall that when the pressure of a gas increases, its volume generally decreases, leading to an increase in density. We are given that at high pressure, graphite converts to diamond. This means that increasing the pressure of graphite makes it denser, resulting in the diamond form. Therefore, diamond has a higher density than graphite.