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Phosphine is a poisonous gas responsible in part for the odor of decaying fish.

ID: 987664 • Letter: P

Question

Phosphine is a poisonous gas responsible in part for the odor of decaying fish. Concentrations below 8 parts per million (ppm) arc detectable by the human olfactory system. Higher concentrations cause weakness, vertigo, convulsions, coma, or even death. At 680^degreeC, pure phosphine decomposes into phosphorus and hydrogen gas with a half-life that is independent of the initial phosphine pressure. This half-life at 680^degreeC is 35.0 s. How long would it take for 96.88% of the phosphine to decompose at 680^degreeC?

Explanation / Answer

for first order reaction, half life is independent of inititlal concentration and relation between half life and rate constant (k) is given by half life= 0.693/k

k= 0.693/ half life= 0.693/35=0.0198sec-1

for first order reaction CA/CO =e(-kt)

CA= concentration at any time t, CAO = initial concentration

ln(CA/CAO)= -kt

since 96.88% of Phosphine is decomposed CA= {(100-96.88)/100 }CAO =0.0312CAO

ln (0.0312)= -0.0198t

t= 175 seconds