Under certain conditions the rate of this reaction is zero order in ammonia with a rate constant of ·0.0065Ms−1:→2NH3g+N2g3H2gSuppose a 350.mL flask is charged under these conditions with 500.mmol of ammonia. How much is left 50.s later? 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 ammonia with a rate constant of ·0.0065Ms−1:→2NH3g+N2g3H2gSuppose a 350.mL flask is charged under these conditions with 500.mmol of ammonia. How much is left 50.s later? 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 given reaction is zero order in ammonia, which means the rate of reaction is independent of the concentration of ammonia. The rate equation for a zero order reaction is:
Rate = k
where k is the rate constant. But in this case, we are interested in the concentration of ammonia left after a certain time. For a zero order reaction, the concentration of the reactant (in this case, ammonia) decreases linearly with time. This can be expressed as:
[Ammonia] = -kt + [Ammonia]0
where [Ammonia] is the concentration of ammonia at time t, k is the rate constant, t is the time, and [Ammonia]0 is the initial concentration of ammonia.
First, we need to convert the amount of ammonia from mmol to mol (since the rate constant is given in M/s, we need the concentration in M):
500 mmol = 0.500 mol
Then, we calculate the initial concentration of ammonia ([Ammonia]0) in the flask:
[Ammonia]0 = n/V = 0.500 mol / 0.350 L = 1.43 M
Now we can calculate the concentration of ammonia left after 50 s:
[Ammonia] = -kt + [Ammonia]0 = -0.0065 M/s * 50 s + 1.43 M = 1.43 M - 0.325 M = 1.10 M
So, the concentration of ammonia left after 50 s is 1.10 M. However, the question asks for the amount of ammonia left, not the concentration. To find this, we multiply the concentration by the volume of the flask:
Amount of ammonia = [Ammonia] * V = 1.10 M * 0.350 L = 0.385 mol
Converting this to mmol gives:
0.385 mol * 1000 mmol/mol = 385 mmol
So, after 50 s, there are approximately 385 mmol of ammonia left in the flask.
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