Any help stepping through a solution here would be much appreciated. Three part

Question

Any help stepping through a solution here would be much appreciated. Three part question...

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Consider the following reaction,

SO2Cl2(g) -----> SO2(g) + Cl2(g)

The concentration of SO2Cl2 was monitored at a fixed temperature as a function of time during the decomposition reaction and some data was collected. I am presenting the data grouped in parenthesis, the number on the right is the molar concentration of SO2Cl2 and the number in the left is time in units of seconds.

(0, 0.100), (100, 0.0971), (200, 0.0944), (300, 0.0917), (400, 0.0890), (500, 0.0865), (600, 0.0840), (700, 0.0816), (800, 0.0793), (900, 0.0770), (1000, 0.0748), (1100, 0.0727), (1200, 0.0706), (1300, 0.0686), (1400, 0.0666), (1500, 0.0647)


1) Determine the order of the reaction and
2) Write a narrative of your approach to determine its order.
3) What is the rate constant for the reaction?

Explanation / Answer

Use integrated first order rate law, which give you the concentration of reactant sulfuryl chloride as function of time t: ln[SO2Cl2] = ln[SO2Cl2]0 - k·t ([SO2Cl2]0 i the initial concentration and k is the rate constant) => [SO2Cl2] = e^(ln[SO2Cl2]0 - k·t) = e^(ln[SO2Cl2]0) · e^( - k·t) = [SO2Cl2]0 ·e^( - k·t) The decomposition of SO2Cl2 follows the reaction equation SO2Cl2 ? SO2 + Cl2 So per mole of sulfuryl chloride disappeared one mole of sulfur dioxide is formed. Hence the changes in concentrations of these compounds are related as: -?[SO2Cl2] = ?{SO2] [SO2Cl2]0 - [SO2Cl2] = [SO2] - [SO2]0 Assuming there was initially no sulfur dioxide you get for its concentration: [SO2] = [SO2Cl2]0 - [SO2Cl2] = [SO2Cl2]0 - [SO2Cl2]0 ·e^( - k·t) = [SO2Cl2]0 ·(1 - e^( - k·t)) after 210s starting with 0.175M of [SO2Cl2] [SO2]= 0.175M ·(1 - e^( - 1.48×10?4s?¹k · 240s) = 6.11×10?³ M

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