At high temperatures, phosphine (PH3) dissociates into phosphorus and hydrogen by the following reaction: 4PH3 → P4 + 6H2. At 800 degrees Celsius, the rate at which phosphine dissociates is dC_PH3/dt = -3.715 × 10^-6 C_PH3 for t in seconds. The reaction occurs in a constant-volume, 2-L vessel, and the initial concentration of phosphine is 5 kmol/m^3.
a. If 3 mol of phosphine reacts, how much phosphorus and hydrogen are produced?
b. Develop expressions for the number of moles of phosphine, phosphorus, and hydrogen present at any time, and determine how long it would take for 3 mol of phosphine to have reacted.