Chemistry - Chemical Kinetics Question with Solution | TestHub
Pure X(g) decomposes irreversibly as X(g) → 2Y(g) in a rigid vessel. The disappearance law is a single power law -d[X]/dt = k[X]ⁿ with fixed k and n. The measured times from the start satisfy = 2, establishing first-order kinetics for this model. Final total pressure after complete decomposition is 720 kPa; at 20.0 min the total pressure is 540 kPa. Express the Y-formation rate law as d[Y]/dt = [X]. Find in min⁻¹, rounded to two decimals. Use ln 2 = 0.693.
Answer:
Solution:
The first-order disappearance constant has units min⁻¹. Initially = 720/2 = 360 kPa. At 20.0 min, the remaining X partial pressure is = 720 - 540 = 180 kPa. Thus one half-life takes 20.0 min and k = 0.693/20.0 = 0.03465 min⁻¹. Stoichiometry gives d[Y]/dt = 2(-d[X]/dt) = 2k[X], so = 2k = 0.06930 min⁻¹, which rounds to 0.07. This coefficient is not the same as the disappearance constant of X; the concentration variable in the requested formation law is explicitly [X], not [Y].
