Question

Tutored Practice Problem 15.4.6 CESTO Determine half-life, order and k from concentration-time data The following data were collected for the gas phase decomposition of sulfuryl chloride at 600 K. SO,C12()— SO2(g) + Cl2() [SO,C1), M 2.50x103 time, min 1.25103 174.00 6.25*10+ 348.00 3.13*10+ 522.00 (a) What is the half-life for the reaction when [SO,Ch] -2.5010' M? (b) What is the half-life for the reaction when [SO_C12] -1.25 10 M? (c) Is the reaction first order? If so, what is the rate constant for the reaction? (If not first order leave blank) Check & Submit Answer Show Approach

Answer 1

Half life of a reaction is the time required for the reactant to become half of its initial concentration.

Here

When initial concentration of SO₂Cl₂ = 2.50 x10^-3 M

Half of this concentration [so, Cl2] _ 2.50x10M = 1.25x10² m. 2 this to the time required for 30. Cl₂ to become half of its concentration .., 2 25x15²m from 2.50 x 10²m is 174.80 min t = 174.00 min Hence half time half-life for the reaction when [so, C2] = 2.50x103 M is 174.00 min Again half of concentration 4.25x103 is 0.625x153 = 6.25 X 10AM Time required for the concentration 1.25x153 m to become 6.25x109 m is (348.00- 174.00) = 174.00 min min Hence, Half life for Half-life for the reaction when [5o. C/2] = 1.25110 is 174.00 min

From the given data it can be seen that half life for the reaction remains constant throughout i.e., half life is independent of initial concentration of SO₂Cl2 (satisfying first order condition) . So the reaction is an example of first order reaction.

For & first order reaction we know if t = half-life of reaction A ndredion rate constant K = then , 0.693 * 0.693 Here - t = 174 min 0.693 rate constant, k = 174 min = 3.98 x 10 min