Under certain conditions the rate of this reaction is zero order in dinitrogen monoxide with a rate constant of ·0.0096Ms−1:→2N2Og+2N2gO2gSuppose a 250.mL flask is charged under these conditions with 200.mmol of dinitrogen monoxide. After how much time is there only 100.mmol left? You may assume no other reaction is important.Be sure your answer has a unit symbol, if necessary, and round it to 2 significant digits.
Question
Under certain conditions the rate of this reaction is zero order in dinitrogen monoxide with a rate constant of ·0.0096Ms−1:→2N2Og+2N2gO2gSuppose a 250.mL flask is charged under these conditions with 200.mmol of dinitrogen monoxide. After how much time is there only 100.mmol left? You may assume no other reaction is important.Be sure your answer has a unit symbol, if necessary, and round it to 2 significant digits.
Solution
The rate of a zero order reaction is given by the equation:
[At] = -kt + [A0]
where: [At] is the concentration at time t, k is the rate constant, [A0] is the initial concentration.
We are given that the rate constant k = 0.0096 M/s, the initial concentration [A0] = 200 mmol in 250 mL = 0.8 M, and we want to find the time t when the concentration [At] = 100 mmol in 250 mL = 0.4 M.
Substituting these values into the equation gives:
0.4 M = -0.0096 M/s * t + 0.8 M
Rearranging for t gives:
t = (0.8 M - 0.4 M) / 0.0096 M/s = 41.67 s
So, it will take approximately 42 seconds for the concentration of dinitrogen monoxide to decrease from 200 mmol to 100 mmol.
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