At a certain temperature the rate of this reaction is second order in NH3 with a rate constant of ·0.759M−1s−1:→2NH3g+N2g3H2gSuppose a vessel contains NH3 at a concentration of 0.700M. Calculate the concentration of NH3 in the vessel 6.30 seconds later. You may assume no other reaction is important.Round your answer to 2 significant digits.
Question
At a certain temperature the rate of this reaction is second order in NH3 with a rate constant of ·0.759M−1s−1:→2NH3g+N2g3H2gSuppose a vessel contains NH3 at a concentration of 0.700M. Calculate the concentration of NH3 in the vessel 6.30 seconds later. You may assume no other reaction is important.Round your answer to 2 significant digits.
Solution
The reaction is second order with respect to NH3, so the rate law for the reaction is:
Rate = k[NH3]^2
where k is the rate constant, and [NH3] is the concentration of NH3.
Since the reaction is second order, we can use the second order integrated rate law to find the concentration of NH3 at a later time:
1/[A]t = kt + 1/[A]0
where [A]t is the concentration of NH3 at time t, k is the rate constant, t is the time, and [A]0 is the initial concentration of NH3.
We can plug in the given values into this equation:
1/[A]t = (0.759 M^-1 s^-1)(6.30 s) + 1/(0.700 M)
Solving for [A]t gives:
1/[A]t = 4.78 M^-1 + 1.43 M^-1
1/[A]t = 6.21 M^-1
Taking the reciprocal to solve for [A]t gives:
[A]t = 0.16 M
So, the concentration of NH3 in the vessel 6.30 seconds later is 0.16 M.
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