Under certain conditions the rate of this reaction is zero order in dinitrogen monoxide with a rate constant of ·0.0056Ms−1:→2N2Og+2N2gO2gSuppose a 500.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 ·0.0056Ms−1:→2N2Og+2N2gO2gSuppose a 500.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 reaction is zero order in dinitrogen monoxide, which means the rate of the reaction is independent of the concentration of dinitrogen monoxide. The rate equation for a zero order reaction is:
Rate = k
where k is the rate constant. In this case, k = 0.0056 M/s.
We can rearrange this equation to find the time it takes for the reaction to occur:
t = (N2O_initial - N2O_final) / k
The initial amount of dinitrogen monoxide (N2O_initial) is 200 mmol in 500 mL, or 0.4 M. The final amount (N2O_final) is 100 mmol in 500 mL, or 0.2 M.
Substituting these values into the equation gives:
t = (0.4 M - 0.2 M) / 0.0056 M/s = 35.71 s
So, it will take approximately 36 seconds for the amount of dinitrogen monoxide to decrease from 200 mmol to 100 mmol.
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