MATS 201B / MAE 271B / ECE 238BWinter 2017Midterm ExamClosed book, open notesEach question worth 25 points1.The decomposition of ammonia on Pt is given as2NH3→N2+3H2The rate is first order in [NH3] and inversely proportional to [H2]. Write thedifferential rate equation for the rate of formation of H2, d[H2]/dt in terms ofthe initial concentration of NH3([NH3]o) and [H2].NH3→12N2+32H2d NH3⎡⎣⎤⎦dt=−kNH3⎡⎣⎤⎦H2⎡⎣⎤⎦NH3⎡⎣⎤⎦=NH3⎡⎣⎤⎦o−ξH2⎡⎣⎤⎦=32ξd NH3⎡⎣⎤⎦dt=−dξdt=−kNH3⎡⎣⎤⎦o−ξ32ξ⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥d H2⎡⎣⎤⎦dt=32dξdt=32kNH3⎡⎣⎤⎦o−ξ32ξ⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥d H2⎡⎣⎤⎦dt=32kNH3⎡⎣⎤⎦o−23H2⎡⎣⎤⎦H2⎡⎣⎤⎦⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥=k32NH3⎡⎣⎤⎦o−H2⎡⎣⎤⎦H2⎡⎣⎤⎦⎡⎣⎢⎢⎢⎤⎦⎥⎥⎥2.Isotopes of A, B and C are part of a radioactive decay sequence.A→B→CThe half-life of A (relative to the decay to B) is one year. The half-life of B(relative to the decay to C) is one hour.(a)What fraction of the original A is left after one month?
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