At a certain temperature the rate of this reaction is first order in N2O5 with a rate constant of 4.96s−1:→2N2O5g+2N2O4gO2gSuppose a vessel contains N2O5 at a concentration of 0.530M. Calculate the concentration of N2O5 in the vessel 0.150 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 first order in N2O5 with a rate constant of 4.96s−1:→2N2O5g+2N2O4gO2gSuppose a vessel contains N2O5 at a concentration of 0.530M. Calculate the concentration of N2O5 in the vessel 0.150 seconds later. You may assume no other reaction is important.Round your answer to 2 significant digits.
Solution
The rate law for a first order reaction is given by the equation:
[At] = [A0] * e^(-kt)
where: [At] is the concentration of N2O5 at time t, [A0] is the initial concentration of N2O5, k is the rate constant, and t is the time.
Given: [A0] = 0.530 M, k = 4.96 s^-1, and t = 0.150 s,
we can substitute these values into the rate law equation to find [At]:
[At] = 0.530 M * e^(-4.96 s^-1 * 0.150 s)
Calculating the above expression gives:
[At] = 0.530 M * e^(-0.744) = 0.530 M * 0.475
Therefore, the concentration of N2O5 in the vessel 0.150 seconds later is approximately 0.25 M, rounded to two significant digits.
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