A chemical engineer is studying the rate of this reaction. 2Cl_2O_5(g) rightarro

Question

A chemical engineer is studying the rate of this reaction. 2Cl_2O_5(g) rightarrow 2Cl_2(g) + 5O_2(g) He fills a reaction vessel with Cl_2O_5 and measures its concentration as the reaction proceeds. Here's a graph of his data: Use this graph to answer the following questions: What is the half life of the reaction? Round your answer to 2 significant digits. t_1/2 = s Suppose the rate of the reaction is known to be first order in Cl_2O_5. Calculate the value of the rate constant k. Round your answer to 2 significant digits. Also be sure you include the correct unit symbol. k = Predict the concentration of Cl_2O_5 in the engineer's reaction vessel after 0.180 s seconds have passed. Assume no other reaction is important, and continue to assume the rate is first order in Cl_2O_5. Round your answer to 2 significant digits. [Cl_2O_5] = M

Explanation / Answer

To find t1/2 the concentration of [Cl2O5] must be 50% of intial concentration,
i.e) on the graph at [Cl2O5] = 0.5 look for the corresponding time by extending the line
from 0.5 to the graph,
If the rate of the reaction is first order in [Cl2O5] then,
t1/2 = 0.02 seconds
t1/2 = 0.693 / K
K = 0.693 / 0.02 = 34.65 sec-1
Given that t = 0.180 sec ,
from the graph it is clear that initial concentration at t=0 sec is [Cl2O5] = 1M
ln [Cl2O5] = -Kt + ln[Cl2O5]o
ln [Cl2O5] = -34.65 * 0.180 + ln [1]
ln  [Cl2O5] = -6.237 + 0
[Cl2O5] = e-6.237 = 1.9557*10-3 M = 0.00195 M approx

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